














                           NYQUIST REFERENCE MANUAL

                                 Version 3.01


                     Copyright 2008 by Roger B. Dannenberg
                                24 January 2008











                          Carnegie Mellon University

                          School of Computer Science

                         Pittsburgh, PA 15213, U.S.A.
  .
Preface
  This  manual  is a guide for users of Nyquist, a language for composition and
sound synthesis.  Nyquist grew out of a series of  research  projects,  notably
the  languages Arctic and Canon.  Along with Nyquist, these languages promote a
functional  style  of  programming  and  incorporate  time  into  the  language
semantics.

  Please  help  by  noting  any errors, omissions, or suggestions you may have.
You can send your suggestions to Dannenberg@CS.CMU.EDU (internet) via  computer
mail,  or by campus mail to Roger B. Dannenberg, School of Computer Science, or
by ordinary mail to Roger B. Dannenberg, School of Computer  Science,  Carnegie
Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213-3890, USA.

  Nyquist  is  a successor to Fugue, a language originally implemented by Chris
Fraley, and extended by George Polly and Roger Dannenberg.  Peter Velikonja and
Dean  Rubine  were early users, and they proved the value as well as discovered
some early problems of the system.  This led to Nyquist, a reimplementation  of
Fugue by Roger Dannenberg with help from Joe Newcomer and Cliff Mercer. Ning Hu
ported Zheng (Geoffrey) Hua and Jim Beauchamp's piano  synthesizer  to  Nyquist
and  also  built  NyqIDE,  the  Nyquist Interactive Development Environment for
Windows.  Dave  Mowatt  contributed  the  original  version  of  jNyqIDE,   the
cross-platform  interactive  development  environment.   Dominic Mazzoni made a
special version of Nyquist that runs within the Audacity audio  editor,  giving
Nyquist a new interface and introducing Nyquist to many new users.

  Many  others have since contributed to Nyquist.  Chris Tchou and Morgan Green
worked on the Windows port. Eli Brandt contributed  a  number  of  filters  and
other  synthesis  functions. Pedro J. Morales, Eduardo Reck Miranda, Ann Lewis,
and Erich Neuwirth have all contributed nyquist examples  found  in  the  demos
folder of the Nyquist distribution.  Philip Yam ported some synthesis functions
from Perry Cook and Gary Scavone's STK to Nyquist.  Pedro Morales  ported  many
more STK instruments to Nyquist.  Dave Borel wrote the Dolby Pro-Logic encoding
library and Adam Hartman  wrote  stereo  and  spatialization  effects.  Stephen
Mangiat  wrote  the MiniMoog emulator. Phil Light recorded the drum samples and
wrote drum machine software.  The  Xmusic  library,  particularly  the  pattern
specification,  was  inspired  by  Rick Taube's Common Music. The functions for
generating probability distributions were implemented by Andreas Pfenning.

  Starting with Version 3, Nyquist supports a  version  of  SAL,  providing  an
alternative  to  Lisp  syntax.  SAL  was  designed  by  Rick Taube, and the SAL
implementation in Nyquist is based on Taube's original implementation  as  part
of his Common Music system.

  The  current  jNyqIDE includes contributions from many. Chris Yealy and Derek
D'Souza implemented early versions of the envelope  editor.  Daren  Makuck  and
Michael  Rivera  wrote  the  original  equalizer  editor.    Priyanka  Raghavan
implemented the sound browser.

  Many others have made contributions, offered suggestions, and found bugs.  If
you  were  expecting  to find your name here, I apologize for the omission, and
please let me know.

  I also wish to acknowledge support from CMU, Yamaha, and IBM for this work.






























.
1. Introduction and Overview
  Nyquist is a language for sound synthesis  and  music  composition.    Unlike
score  languages  that  tend  to  deal  only  with events, or signal processing
languages that tend to deal only with signals and  synthesis,  Nyquist  handles
both  in  a single integrated system.  Nyquist is also flexible and easy to use
because it is based on an interactive Lisp interpreter.

  With Nyquist, you can design instruments by combining functions (much as  you
would  using  the  orchestra languages of Music V, cmusic, or Csound).  You can
call upon these instruments and generate  a  sound  just  by  typing  a  simple
expression.    You can combine simple expressions into complex ones to create a
whole composition.

  Nyquist runs under Linux, Apple Mac OS X, Microsoft Windows NT, 2000, XP, and
Vista,  and  it  produces  sound  files  or  directly  generates audio.  Recent
versions have also run on AIX, NeXT, SGI, DEC pmax,  and  Sun  Sparc  machines.
(Makefiles  for  many  of these are included, but out-of-date).  Let me know if
you have problems with any of these machines.

  To use Nyquist, you should have a basic knowledge of Lisp.  An excellent text
by  Touretzky  is  recommended [Touretzky  84].    Appendix IV is the reference
manual for XLISP, of which Nyquist is a  superset.  Starting  with  Version  3,
Nyquist  supports  a  variant  of SAL, which is also available in Common Music.
Since there are some differences, one should generally call this implementation
``Nyquist  SAL;''  however,  in  this  manual, I will just call it ``SAL.'' SAL
offers most of the capabilities of Lisp, but it uses an Algol-like syntax  that
may be more familiar to programmers with experience in Java, C, Basic, etc.

1.1. Installation
  Nyquist  is  a  C  program  intended  to  run under various operating systems
including Unix, MacOS, and Windows.



1.1.1. Unix Installation
  For Unix systems, Nyquist is distributed  as  a  compressed  tar  file  named
nyqsrc2nn.zip,   where   nn   is   the   version  number  (e.g.  v2.36  was  in
nyqsrc236.zip).  To install Nyquist, copy nyqsrc2nn.zip  to  the  directory  on
your machine where you would like to install Nyquist, and type:

    gunzip nyqsrc2nn.zip
    cd nyquist
    ln -s sys/unix/linux/Makefile Makefile
    setenv XLISPPATH `pwd`/runtime:`pwd`/lib
    make

The  first line creates a nyquist directory and some subdirectories. The second
line (cd) changes directories to the new  nyquist  directory.  The  third  line
makes  a  link from the top-level directory to the Makefile for your system. In
place of linux in sys/unix/linux/Makefile, you should  substitute  your  system
type.  Current systems are next, pmax, rs6k, sgi, linux, and sparc.  The setenv
command tells Nyquist where to search for lisp files to be loaded when  a  file
is  not  found in the current directory. The runtime directory should always be
on your XLISPPATH when you run Nyquist, so you may want  to  set  XLISPPATH  in
your   shell  startup  file,  e.g.    .cshrc.    Assuming  the  make  completes
successfully, you can run Nyquist as follows:

    ./ny

When you get the prompt, you may begin typing expressions such as the  ones  in
the following ``Examples'' section.

  One  you  establish  that  Nyquist (ny) is working from the command line, you
should try using  jNyqIDE,  the  Java-based  Nyquist  development  environment.
First, make jny executable (do this only once when you install Nyquist):

    chmod +x jny

Then try running jNyqIDE by typing:

    ./jny

If  the  jNyqIDE  window does not appear, make sure you have Java installed (if
not, you probably already encountered errors when you ran make). You  can  also
try recompiling the Java files:

    cd jnyqide
    javac *.java
    cd ..

  Note:  With  Linux  and  the  Macintosh OS X, jNyqIDE defines the environment
passed to Nyquist. If you set XLISPPATH as shown above, it will be passed along
to  Nyquist  under  jNyqIDE.  If not, a default XLISPPATH will have the lib and
runtime directories only.  This does not apply to Windows because  even  though
the  environment  is  there, the Windows version of Nyquist reads the XLISPPATH
from the Registry.

  You can also specify the search path by creating the file  nyquist/xlisppath,
which  should  have  colon-separated  paths on a single line of text. This file
will override the environment variable XLISPPATH.

  It is good to have USER in the environment with your user ID. This string  is
used to construct some file names. jNyqIDE will look for it in the environment.
You can also specify your user ID using the file nyquist/user, but if you  have
a shared installation of Nyquist, this will not be very useful.

  Note:  Nyquist  looks for the file init.lsp in the current directory.  If you
look in the init.lsp in runtime, you will notice two things.   First,  init.lsp
loads  nyquist.lsp  from  the  Nyquist  directory,  and  second, init.lsp loads
system.lsp which in turn defines the macro  play.    You  may  have  to  modify
system.lsp to invoke the right programs on your machine.



1.1.2. Win32 Installation
  The  Win32  version  of  Nyquist  is  packaged  in three versions: the source
version and two runtime versions. The source  version  is  a  superset  of  the
runtime  version  intended  for  developers  who want to recompile Nyquist. The
source version exists as a .zip file, so you need  a  utility  like  WinZip  to
unpack  them.   The URL http://www.winzip.com/ has information on this product.
Typically, the contents of  the  zip  file  are  extracted  to  the  C:\nyquist
directory,  but  you  can  put  it  anywhere  you  like.  You can then open the
workspace file, nyquist.sln, using Microsoft Visual C++. You can build and  run
the command line and the NyqWin versions of Nyquist from within Visual C++.

  The  runtime  versions  contain everything you need to run Nyquist, including
the executable, examples, and documentation. Each runtime version  is  packaged
as an executable installer program.  I recommend setupnyqiderun2xx.exe (``2xx''
refers to the current version number), a graphical interface  written  in  Java
that  runs nyquist.exe as a separate process. This IDE has a simple lisp editor
built in. Alternatively, you can  install  setupnyqwinrun2xx.exe,  a  different
graphical  interface  written  in C++. Just copy the installer you want to your
system and run it. Then find Nyquist in your Start menu to run  it.    You  may
begin  typing  expressions  such  as  the  ones  in  the following ``Examples''
section.

  Optional: Nyquist needs to know where to find the standard runtime files. The
location  of  runtime  files  must  be  stored in the Registry.  The installers
create a registry entry, but  if  you  move  Nyquist  or  deal  with  different
versions, you can edit the Registry manually as follows:

   - Run     the     Registry    editor.    Under    Windows    NT,    run
     C:\WINNT\system32\regedt32.exe.      Under       Windows95,       run
     C:\WINDOWS\regedit.exe.

   - Find and highlight the SOFTWARE key under HKEY_LOCAL_MACHINE.

   - Choose  Add  key  ...  from the Edit menu, type CMU, and click the OK
     button.

   - Highlight the new CMU key.

   - Choose Add key ... from the Edit menu, type Nyquist, and click the OK
     button.  (Note that CMU and Nyquist are case sensitive.)

   - Highlight the new Nyquist key.

   - Choose  Add  value  ... from the Edit menu, type XLISPPATH, and click
     the OK button.  (Under WinXP the menu item is Edit:New:String  Value,
     after  which  you  need to select the new string name that appears in
     the right panel, select Edit:Rename, and type XLISPPATH.)

   - In the String Edit box (select the Edit:Modify menu item  in  WinXP),
     type  a  list of paths you want Nyquist to search for lisp files. For
     example, if you installed Nyquist as C:\nyquist, then type:

         C:\nyquist\runtime,C:\nyquist\lib

     The paths should be separated by a comma or semicolon and  no  space.
     The  runtime path is essential, and the lib path may become essential
     in a future release. You can also add paths to personal libraries  of
     Lisp and Nyquist code.

   - Click  the  OK  button  of  the string box and exit from the Registry
     Editor application.


1.1.2.1. What if Nyquist functions are undefined?
  If you do not have administrative privileges for your machine, the  installer
may  fail to set up the Registry entry that Nyquist uses to find initialization
files. In this case, Nyquist will run a  lisp  interpreter,  but  many  Nyquist
functions  will  not  be defined. If you can log in as administrator, do it and
reinstall Nyquist. If you do not have permission, you can still run Nyquist  as
follows:

  Create  a  file  named  init.lsp  in  the  same directory as Nyquist.exe (the
default location is C:\Program Files\Nyquist, but you may have installed it  in
some other location.) Put the following text in init.lsp:

    (setf *search-path* "C:/Program Files/Nyquist/runtime,C:/Program Files/
    (load "C:/Program Files/Nyquist/runtime/init.lsp")


Note:  in  the  three places where you see C:/Program Files/Nyquist, insert the
full path where Nyquist is actually installed. Use forward slashes  (/)  rather
than  back  slashes  (\)  to  separate  directories. For example, if Nyquist is
installed at D:\rbd\nyquist, then init.lsp should contain:

    (setf *search-path* "D:/rbd/nyquist/runtime,D:/rbd/nyquist/lib")
    (load "d:/rbd/nyquist/runtime/init.lsp")


The variable *search-path*, if defined, is used in place  of  the  registry  to
determine search paths for files.


1.1.2.2. SystemRoot
  (Ignore  this  paragraph  if  you  are not planning to use Open Sound Control
under Windows.)  If Nyquist prints an error message and quits when  you  enable
Open  Sound Control (using osc-enable), check to see if you have an environment
variable SystemRoot, e.g. type set to a command prompt and look for  the  value
of  SystemRoot. The normal value is C:\windows. If the value is something else,
you should put the environment entry, for example:

    SystemRoot="D:\windows"

into a file named systemroot (no extension). Put  this  file  in  your  nyquist
directory.  When  you  run  jNyqIDE,  it  will  look for this file and pass the
contents as an environment variable to Nyquist. The Nyquist process needs  this
to open a UDP socket, which is needed for Open Sound Control.



1.1.3. MacOS X Installation
  The  OS  X version of Nyquist is very similar to the Linux version, but it is
developed using Xcode, Apple's programming environment. With a little work, you
can use the Linux installation instructions to compile Nyquist, but it might be
simpler to just open the Xcode project that is included in the Nyquist sources.

  You can also download a pre-compiled version of Nyquist for the  Mac.    Just
download  nyqosx2xx.tgz  to  the  desktop  and  open  it  to extract the folder
<tt>nyqosx2xx</tt>. (Again, "2xx" refers to the current  version  number,  e.g.
v2.31  would  be  named  with "231".) Open the folder to find a Mac Application
named jNyqIDE and a directory named <tt>nyquist/doc</tt>. Documentation  is  in
the <tt>nyquist/doc</tt> directory.

  The  file <tt>jNyqIDE.app/Contents/Resources/Java/ny</tt> is the command line
executable (if you should need it). To run from the command line, you will need
to  set  the  XLISPPATH environment variable as with Linux. On the topic of the
XLISPPATH, note that this variable is set by jNyqIDE  when  running  with  that
application,  overriding  any  other  value.  You can extend the search path by
creating the file xlisppath in the same directory as the nyquist executable ny.
The xlisppath file should have colon-separated paths on a single line of text.

1.2. Using jNyqIDE
  The  program  named  jNyqIDE is an ``integrated development environment'' for
Nyquist. When you run jNyqIDE, it starts the Nyquist program and  displays  all
Nyquist  output  in  a  window.  jNyqIDE  helps you by providing a Lisp and SAL
editor, hints for command completion and function  parameters,  some  graphical
interfaces  for  editing  envelopes  and  graphical  equalizers, and a panel of
buttons for common operations. A more complete description  of  jNyqIDE  is  in
Chapter 2.

  For  now,  all you really need to know is that you can enter Nyquist commands
by typing into the upper left window. When you type return, the expression  you
typed  is  sent to Nyquist, and the results appear in the window below. You can
edit files by clicking on the New File or Open File buttons. After editing some
text,  you  can load the text into Nyquist by clicking the Load button. jNyqIDE
always saves the file first; then it tells Nyquist to load the file.  You  will
be prompted for a file name the first time you load a new file.

1.3. Using SAL
  SAL  mode  means  that  Nyquist  reads and evaluates SAL commands rather than
Lisp. The SAL mode prompt is "SAL> " while the Lisp mode prompt is "> ".   When
Nyquist  starts  it  normally enters SAL mode automatically, but certain errors
may exit SAL mode. You can reenter SAL  mode  by  typing  the  Lisp  expression
(sal).

  In SAL mode, you type commands in the SAL programming language. Nyquist reads
the commands, compiles them into Lisp, and evaluates the commands. Commands can
be entered manually by typing into the upper left text box in jNyqIDE.

1.4. Helpful Hints
  Under  Win95  and  Win98,  the console sometimes locks up. Activating another
window and then reactivating the Nyquist window should unlock the output.   (We
suggest  you use JNyqIDE, the interactive development environment rather than a
console window.)

  You can cut and paste text into Nyquist, but for serious work, you will  want
to  use the Lisp load command. To save even more time, write a function to load
your working file, e.g. (defun l () (load "myfile.lsp")). Then you can type (l)
to (re)load your file.

  Using SAL, you can type

    define function l () load "myfile.lsp"

and then

    exec l()

to (re)load the file.

  The  Emacs  editor is free GNU software and will help you balance parentheses
if you use Lisp mode. In fact, you can run  nyquist  (without  the  IDE)  as  a
subprocess   to   Emacs.  A  helful  discussion  is  at  //http://www.audacity-
forum.de/download/edgar/nyquist/nyquist-doc/examples/emacs/main.html.

  The jNyqIDE also runs Nyquist as a subprocess and has built-in Lisp  and  SAL
editors.  If  your  editor  does not help you balance parentheses, you may find
yourself counting parens and searching for unbalanced expressions. If  you  are
confused  or desperate, try the :print t option o fthe load command. By looking
at the expressions  printed,  you  should  be  able  to  tell  where  the  last
unbalanced  expression  starts.  Alternatively, type (file-sexprs) and type the
lisp file name at the prompt. This function will  read  and  print  expressions
from the file, reporting an error when an extra paren or end-of-file is reached
unexpectedly.

1.5. Using Lisp
  Lsip mode means that Nyquist reads and evaluates Nyquist expressions in  Lisp
syntax. Since Nyquist is build on a Lisp interpreter, this is the ``native'' or
machine language of Nyquist, and certain errors and functions may break out  of
the  SAL  interpreter,  leaving  you  with  a  prompt  for  a  Lisp expression.
Alternatively, you can exit SAL simply by typing exit to get a Lisp  prompt  (>
).  Commands  can be entered manually by typing into the upper left text box in
jNyqIDE.

1.6. Examples
  We will begin with some simple Nyquist programs. Throughout  the  manual,  we
will assume SAL mode and give examples in SAL, but it should be emphasized that
all of these examples can be performed using Lisp syntax. See  Section  6.2  on
the relationship between SAL and Lisp.

  Detailed  explanations  of  the  functions  used  in  these  examples will be
presented in later chapters, so at this  point,  you  should  just  read  these
examples to get a sense of how Nyquist is used and what it can do.  The details
will  come  later.    Most  of  these  examples  can  be  found  in  the   file
nyquist/demos/examples.sal.  Corresponding Lisp syntax examples are in the file
nyquist/demos/examples.lsp.

  Our first example makes and plays a sound:

    ;; Making a sound.
    play osc(60) ; generate a loud sine wave

This example is about the simplest way to create a sound with Nyquist.  The osc
function generates a sound using a table-lookup oscillator.  There are a number
of optional parameters, but the default  is  to  compute  a  sinusoid  with  an
amplitude  of  1.0.    The  parameter 60 designates a pitch of middle C. (Pitch
specification will be described in greater detail later.)  The  result  of  the
osc function is a sound.  To hear a sound, you must use the play command, which
plays the file through  the  machine's  D/A  converters.    It  also  writes  a
soundfile  in  case the computation cannot keep up with real time. You can then
(re)play the file by typing:

    exec r()

This (r) function is a general way to ``replay''  the  last  thing  written  by
play.
                                                                   15
  Note:  when  Nyquist  plays  a  sound,  it scales the signal by 2  -1 and (by
default) converts to a 16-bit integer format. A signal  like  (osc  60),  which
ranges from +1 to -1, will play as a full-scale 16-bit audio signal.



1.6.1. Waveforms
  Our next example will be presented in several steps.  The goal is to create a
sound using a wavetable consisting of several harmonics as opposed to a  simple
sinusoid.    In  order to build a table, we will use a function that computes a
single harmonic and add harmonics to form a wavetable.  An oscillator  will  be
used to compute the harmonics.

  The  function  mkwave  calls  upon build-harmonic to generate a total of four
harmonics with amplitudes 0.5, 0.25, 0.125, and 0.0625.  These are  scaled  and
added (using +) to create a waveform which is bound temporarily to *table*.

  A  complete Nyquist waveform is a list consisting of a sound, a pitch, and T,
indicating a periodic waveform.  The pitch  gives  the  nominal  pitch  of  the
sound.  (This is implicit in a single cycle wave table, but a sampled sound may
have many periods of the fundamental.)  Pitch is expressed in half-steps, where
middle  C is 60 steps, as in MIDI pitch numbers.  The list of sound, pitch, and
T is formed in the last line of mkwave: since build-harmonic  computes  signals
with  a  duration  of  one  second, the fundamental is 1 Hz, and the hz-to-step
function converts to pitch (in units of steps) as required.

    define mkwave()
      set *table* = 0.5 * build-harmonic(1.0, 2048) +
                    0.25 * build-harmonic(2.0, 2048) +
                    0.125 * build-harmonic(3.0, 2048) +
                    0.0625 * build-harmonic(4.0, 2048)
      set *table* = list(*table*, hz-to-step(1.0), #t)

  Now that we have defined a function, the last step  of  this  example  is  to
build  the  wave.    The following code calls mkwave the first time the code is
executed (loaded from a file).  The second time, the variable *mkwave* will  be
true, so mkwave will not be invoked:

    if not boundp(quote(*mkwave*)) then
      exec mkwave()
      set *mkwave* = #t



1.6.2. Wavetables
  When  Nyquist  starts,  several  waveforms  are  created and stored in global
variables  for  convenience.   They   are:   *sine-table*,   *saw-table*,   and
*tri-table*, implementing sinusoid, sawtooth, and triangle waves, respectively.
The variable *table* is initialized to *sine-table*, and  it  is  *table*  that
forms the default wave table for many Nyquist oscillator behaviors. If you want
a proper, band-limited waveform, you should construct it yourself, but  if  you
do  not understand this sentence and/or you do not mind a bit of aliasing, give
*saw-table* and *tri-table* a try.

  Note that in Lisp  and  SAL,  global  variables  often  start  and  end  with
asterisks  (*).  These  are  not  special  syntax, they just happen to be legal
characters for names, and their use is purely a convention.
1.6.3. Sequences
  Finally, we define note to use the waveform, and  play  several  notes  in  a
simple score:

    define function note(pitch, dur)
      return osc(pitch, dur, *table*)

    play seq(note(c4 i), note(d4 i), note(f4 i),
             note(g4 i), note(d4 q))


Here, note is defined to take pitch and duration as parameters; it calls osc to
do the work of generating a waveform, using *table* as a wave table.

  The seq function is used to invoke a sequence of behaviors.    Each  note  is
started  at  the  time  the previous note finishes.  The parameters to note are
predefined in Nyquist: c4 is middle C, i (for eIghth note) is 0.5, and  q  (for
Quarter  note) is 1.0.  See Section 1.7 for a complete description.  The result
is the sum of all the computed sounds.

  Sequences can also be constructed using the at transformation to specify time
offsets.   See   sequence_example.htmdemos,  sequence  for  more  examples  and
explanation.



1.6.4. Envelopes
  The next example will illustrate the use of envelopes.  In Nyquist, envelopes
are  just  ordinary sounds (although they normally have a low sample rate).  An
envelope is applied to another sound by multiplication using the mult function.
The  code  shows  the  definition  of  env-note,  defined  in terms of the note
function in the previous example.  In env-note, a 4-phase envelope is generated
using the env function, which is illustrated in Figure 1.















     Figure 1:  An envelope generated by the env function.


    ; env-note produces an enveloped note.  The duration
    ;   defaults to 1.0, but stretch can be used to change
    ;   the duration.
    ;
    define function env-note(p)
      return note(p, 1.0) *
             env(0.05, 0.1, 0.5, 1.0, 0.5, 0.4)

    ; try it out:
    ;
    play env-note(c4)

While  this  example shows a smooth envelope multiplied by an audio signal, you
can  also  multiply  audio  signals  to  achieve  what  is  often  called  ring
modulation.  See  the code and description in demos/scratch_tutorial.htm for an
interesting use of ring modulation to create ``scratch'' sounds.

  In the next example, The stretch operator (~)is used to modify durations:

    ; now use stretch to play different durations
    ;
    play seq(seq(env-note(c4), env-note(d4)) ~ 0.25,
             seq(env-note(f4), env-note(g4)) ~ 0.5,
             env-note(c4))

  In addition to stretch, there are a number of  transformations  supported  by
Nyquist,  and  transformations of abstract behaviors is perhaps the fundamental
idea behind Nyquist.  Chapter 3 is devoted  to  explaining  this  concept,  and
further elaboration can be found elsewhere [Dannenberg 89].



1.6.5. Piece-wise Linear Functions
  It is often convenient to construct signals in Nyquist using a list of (time,
value) breakpoints which are linearly interpolated to  form  a  smooth  signal.
Envelopes  created  by  env  are  a special case of the more general piece-wise
linear functions created by pwl.  Since pwl is used in some examples later  on,
we  will  take  a look at pwl now.  The pwl function takes a list of parameters
which denote (time, value) pairs.  There is an implicit initial  (time,  value)
pair  of  (0,  0), and an implicit final value of 0.  There should always be an
odd number of parameters, since the final value (but not  the  final  time)  is
implicit.  Here are some examples:

    ; symetric rise to 10 (at time 1) and fall back to 0 (at time 2):
    ;
    pwl(1, 10, 2)

    ; a square pulse of height 10 and duration 5.
    ; Note that the first pair (0, 10) overrides the default initial
    ; point of (0, 0).  Also, there are two points specified at time 5:
    ; (5, 10) and (5, 0).  (The last 0 is implicit).  The conflict is
    ; automatically resolved by pushing the (5, 10) breakpoint back to
    ; the previous sample, so the actual time will be 5 - 1/sr, where
    ; sr is the sample rate.
    ;
    pwl(0, 10, 5, 10, 5)

    ; a constant function with the value zero over the time interval
    ; 0 to 3.5.  This is a very degenerate form of pwl.  Recall that there
    ; is an implicit initial point at (0, 0) and a final implicit value of
    ; 0, so this is really specifying two breakpoints: (0, 0) and (3.5, 0):
    ;
    pwl(3.5)

    ; a linear ramp from 0 to 10 and duration 1.
    ; Note the ramp returns to zero at time 1.  As with the square pulse
    ; above, the breakpoint (1, 10) is pushed back to the previous sample.
    ;
    pwl(1, 10, 1)

    ; If you really want a linear ramp to reach its final value at the
    ; specified time, you need to make a signal that is one sample longer.
    ; The RAMP function does this:
    ;
    ramp(10) ; ramp from 0 to 10 with duration 1 + one sample period
    ;
    ; RAMP is based on PWL; it is defined in nyquist.lsp.
    ;

1.7. Predefined Constants
  For  convenience  and readability, Nyquist pre-defines some constants, mostly
based on the notation of the Adagio score language, as follows:

   - Dynamics Note: these dynamics values are subject to change.

         lppp = -12.0 (dB)
         lpp = -9.0
         lp = -6.0
         lmp = -3.0
         lmf = 3.0
         lf = 6.0
         lff = 9.0
         lfff = 12.0
         dB0 = 1.00
         dB1 = 1.122
         dB10 = 3.1623

   - Durations

         s = Sixteenth = 0.25
         i = eIghth = 0.5
         q = Quarter = 1.0
         h = Half = 2.0
         w = Whole = 4.0
         sd, id, qd, hd, wd = dotted durations.
         st, it, qt, ht, wt = triplet durations.

   - PitchesPitches are based on an A4 of 440Hz.  To achieve  a  different
     tuning,  set  *A4-Hertz*  to  the  desired frequency for A4, and call
     (set-pitch-names).  This will recompute the names listed below with a
     different  tuning.    In  all cases, the pitch value 69.0 corresponds
     exactly to 440Hz, but fractional values are allowed, so for  example,
     if  you  set *A4-Hertz* to 444 (Hz), then the symbol A4 will be bound
     to 69.1567, and C4 (middle  C),  which  is  normally  60.0,  will  be
     60.1567.

         c0 = 12.0
         cs0, df0 = 13.0
         d0 = 14.0
         ds0, ef0 = 15.0
         e0 = 16.0
         f0 = 17.0
         fs0, gf0 = 18.0
         g0 = 19.0
         gs0, af0 = 20.0
         a0 = 21.0
         as0, bf0 = 22.0
         b0 = 23.0
         c1 ... b1 = 24.0 ... 35.0
         c2 ... b2 = 36.0 ... 47.0
         c3 ... b3 = 48.0 ... 59.0
         c4 ... b4 = 60.0 ... 71.0
         c5 ... b5 = 72.0 ... 83.0
         c6 ... b6 = 84.0 ... 95.0
         c7 ... b7 = 96.0 ... 107.0
         c8 ... b8 = 108.0 ... 119.0

   - Miscellaneous

         ny:all = ``all the samples'' (i.e. a big number) = 1000000000

1.8. More Examples
  More  examples  can  be  found  in  the directory demos, part of the standard
Nyquist release. In this directory, you will find the following and more:

   - Gong   sounds   by   additive   synthesis(demos/pmorales/b1.lsp   and
     demos/mateos/gong.lsp

   - Risset's spectral analysis of a chord (demos/pmorales/b2.lsp)

   - Bell     sounds     (demos/pmorales/b3.lsp,    demos/pmorales/e2.lsp,
     demos/pmorales/partial.lsp, and demos/mateos/bell.lsp)

   - Drum sounds by Risset (demos/pmorales/b8.lsp

   - Shepard tones (demos/shepard.lsp and demos/pmorales/b9.lsp)

   - Random signals (demos/pmorales/c1.lsp)

   - Buzz with formant filters (demos/pmorales/buzz.lsp

   - Computing samples directly in Lisp (using Karplus-Strong and physical
     modelling as examples) (demos/pmorales/d1.lsp

   - FM  Synthesis examples, including bell, wood drum, brass sounds, tuba
     sound          (demos/mateos/tuba.lsp     and     clarinet     sounds
     (demos/pmorales/e2.lsp

   - Rhythmic patterns (demos/rhythm_tutorial.htm

   - Drum Samples and Drum Machine (demos/plight/drum.lsp.
2. The jNyqIDE Program
  The  jNyqIDE  program  combines many helpful functions and interfaces to help
you get the most out of Nyquist. jNyqIDE is implemented in Java, and  you  will
need  the  Java runtime system or development system installed on your computer
to use jNyqIDE. The best way to learn about jNyqIDE is to  just  use  it.  This
chapter  introduces  some  of the less obvious features. If you are confused by
something and you do not find the information you need here, please contact the
author.

2.1. jNyqIDE Overview
  The  jNyqIDE  runs  the  command-line  version  of  Nyquist  as a subtask, so
everything that works in  Nyquist  should  work  when  using  the  jNyqIDE  and
vice-versa.  Input  to Nyquist is usually entered in the top left window of the
jNyqIDE. When you type return, if the expression or  statement  appears  to  be
complete,  the  expression  you  typed  is sent to Nyquist. Output from Nyquist
appears in a window below. You cannot type into or edit the output window text.

  The normal way to use the jNyqIDE is to create or open one or more files. You
edit  these files and then click the Load button. To load a file, jNyqIDE saves
the file, sets the current directory of Nyquist  to  that  of  the  file,  then
issues  a  load  command  to  Nyquist. In this case and several others, you may
notice that jNyqIDE sends expressions to Nyquist automatically for  evaluation.
You can always see the commands and their results in the output window.

  Notice  that  when  you  load  a selected file window, jNyqIDE uses setdir to
change Nyquist's current directory. This helps to  keep  the  two  programs  in
sync.  Normally,  you  should  keep  all  the  files  of  a project in the same
directory and avoid manually changing Nyquist's current directory  (i.e.  avoid
calling setdir in your code).

  Arranging  windows in the jNyqIDE can be time-consuming, and depending on the
operating system, it is possible for a window to get into a position where  you
cannot  drag  it to a new position. The Window:Tile menu command can be used to
automatically lay out windows in a rational way. There is a preference  setting
to  determine  the  height of the completion list relative to the height of the
output window.

2.2. Command Completion
  To help with programming, jNyqIDE maintains a command-completion window.   As
you  type the first letters of function names, jNyqIDE lists matching functions
and their parameters in the Completion List window. If you click on an entry in
this  window,  the  displayed  expression  will  replace the incompletely typed
function name. A  preference  allows  you  to  match  initial  letters  or  any
substring  of  the complete function name. This is controlled by the ``Use full
search for code completion'' preference.

  In addition, if you right click (or under Mac OS X, hold down the  Alt/Option
key  and  click)  on  an  entry,  jNyqIDE  will  display  documentation for the
function.  Documentation can come from a local copy or  from  the  online  copy
(determined  by  the  ``Use  online manual instead of local copy'' preference).
Documentation can be displayed within the jNyqIDE  window  or  in  an  external
browser  (determined  by  the  ``Use  window  in  jNyqIDE  for  help  browser''
preference.) Currently, the external browser option does  not  seem  to  locate
documentation properly, but this should be fixed in the future.

2.3. Browser
  If  you  click  on  the  Browse button or use the Window:Browse menu command,
jNyqIDE will display a browser window that  is  pre-loaded  with  a  number  of
Nyquist  commands  to  create  sounds.  You can adjust parameters, audition the
sounds, and capture the expression that creates the sound. In many  cases,  the
expression  checks  to see if necessary functions are defined, loading files if
necessary before playing the sound. If you want to use  a  sound  in  your  own
program,  you can often simplify things by explicitly loading the required file
just once at the beginning of your file.

  Since Nyquist now supports a mix of Lisp and SAL, you may  find  yourself  in
the  position  of  having  code  from the browser in one language while you are
working in the other. The best way to handle this is to put the  code  for  the
sound  you  want  into  a function defined in a Lisp (.lsp) or SAL (.sal) file.
Load the file (from Lisp, use the sal-load command to load  a  SAL  file),  and
call the function from the language of your choice.

2.4. Envelope Editor
  The  envelope  editor  allows  you  graphically to design and edit piece-wise
linear and exponential envelopes. The editor maintains a list of envelopes  and
you  select  the  one  to  edit or delete using the drop down list in the Saved
Envelopes List area. The current envelope appears  in  the  Graphical  Envelope
Editor  area.  You  can click to add or drag points. Alternatively, you can use
the Envelope Points  window  to  select  and  edit  any  breakpoint  by  typing
coordinates.  The  duration  of the envelope is controlled by the Stop field in
the Range area, and the vertical axis is controlled by the Min and Max fields.

  When you click the Save button, all envelopes are written to  Nyquist.    You
can  then  use  the  envelope by treating the envelope name as a function.  For
example, if you define an envelope named ``fast-attack,'' then you  can  create
the   envelope   within  a  Nyquist  SAL  program  by  writing  the  expression
fast-attack().

  These edited envelopes are saved to a file named workspace.lsp in the current
directory.  The  workspace  is Nyquist's mechanism for saving data of all kinds
(see Section 13.4.5). The normal way to work with workspaces is to (1) load the
workspace, i.e.  load "workspace", as soon as you start Nyquist; (2) invoke the
envelope editor to change values in the workspace; and (3) save  the  workspace
at  any  time,  especially  before you exit jNyqIDE. If you follow these steps,
envelopes will be preserved from session to session, and the entire  collection
of  envelopes  will  appear  in  the  editor.  Be  sure to make backups of your
workspace.lsp file along with your other project files.

  The envelope editor can create linear and exponential envelopes. Use the Type
pull-down  menu  to  select  the  type you want. Envelopes can be created using
default starting and ending values using pwl or pwe, or  you  can  specify  the
initial  values  using pwlv or pwev.  The envelope editor uses pwl or pwe if no
point is explicitly entered as the initial or final point. To create a pwlv  or
pwev  function, create a point and drag it to the leftmost or rightmost edge of
the graphical editing window. You will see the automatically generated  default
starting or ending point disappear from the graph.

  Exponential  envelopes  should  never  decay  to  zero.  If  you enter a zero
amplitude, you will  see  that  the  envelope  remains  at  zero  to  the  next
breakpoint.  To get an exponential decay to ``silence,'' try using an amplitude
of about 0.001 (about -60dB). To enter small values like  this,  you  can  type
them into the Amplitude box and click ``Update Point.''

  The  Load button refreshes the editor from data saved in the Nyquist process.
Normally, there is no need to use this because the editor  automatically  loads
data when you open it.

2.5. Equalizer Editor
  The  Equalizer  Editor  provides  a  graphical  EQ interface for creating and
adjusting equalizers. Unlike the  envelope  editor,  where  you  can  type  any
envelope  name,  equalizers  are  named  eq-0,  eq-1,  etc., and you select the
equalizer to edit using a pull-down menu. The  Set  button  should  be  use  to
record changes.
3. Behavioral Abstraction
  In  Nyquist,  all functions are subject to transformations.  You can think of
transformations as additional parameters to every function, and  functions  are
free  to use these additional parameters in any way.  The set of transformation
parameters  is  captured  in  what  is  referred  to  as   the   transformation
environment.  (Note that the term environment is heavily overloaded in computer
science.  This is yet another usage of the term.)

  Behavioral abstraction is the ability of functions to adapt their behavior to
the  transformation environment.  This environment may contain certain abstract
notions, such as loudness, stretching a sound in time, etc.  These notions will
mean  different  things  to  different  functions.   For example, an oscillator
should produce more periods of oscillation in order to stretch its output.   An
envelope,  on  the  other  hand,  might only change the duration of the sustain
portion of the envelope in order to stretch.  Stretching a  sample  could  mean
resampling it to change its duration by the appropriate amount.

  Thus,  transformations  in Nyquist are not simply operations on signals.  For
example, if I want to stretch a note, it does not make  sense  to  compute  the
note  first  and  then  stretch the signal.  Doing so would cause a drop in the
pitch.  Instead, a transformation modifies the  transformation  environment  in
which  the  note  is  computed.  Think of transformations as making requests to
functions.  It is up to the function to carry  out  the  request.    Since  the
function   is   always   in   complete  control,  it  is  possible  to  perform
transformations with ``intelligence;'' that is, the  function  can  perform  an
appropriate   transformation,   such  as  maintaining  the  desired  pitch  and
stretching only the ''sustain'' portion of an envelope to obtain a longer note.

3.1. The Environment
  The transformation environment consists of a set of special variables.  These
variables  should  not be read directly and should never be set directly by the
programmer.    Instead,  there  are  functions  to  read  them,  and  they  are
automatically  set  and  restored  by  transformation  operators, which will be
described below.

  The transformation environment consists of the following elements.   Although
each  element  has a ``standard interpretation,'' the designer of an instrument
or the composer of a complex behavior is free to interpret the  environment  in
any  way.    For  example,  a  change  in  *loud*  may  change timbre more than
amplitude, and *transpose* may be ignored by percussion instruments:

*warp*          Time transformation, including time shift,  time  stretch,  and
                continuous  time warp.  The value of *warp* is interpreted as a
                function from logical (local score) time  to  physical  (global
                real)  time.    Do  not  access  *warp* directly.  Instead, use
                local-to-global(t) to convert from a logical  (local)  time  to
                real  (global)  time.    Most  often,  you  will call local-to-
                global(0).  Several transformation operators operate on *warp*,
                including at (@), stretch (~), and warp.

*loud*          Loudness,   expressed  in  decibels.    The  default  (nominal)
                loudness is 0.0 dB (no change).  Do not access *loud* directly.
                Instead,  use get-loud() to get the current value of *loud* and
                either loud or loud-abs to modify it.

*transpose*     Pitch transposition, expressed in semitones.   (Default:  0.0).
                Do   not   access   *transpose*   directly.      Instead,   use
                get-transpose() to get the current  value  of  *transpose*  and
                either transpose or transpose-abs to modify it.

*sustain*       The  ``sustain,''  ``articulation,'' ``duty factor,'' or amount
                by which to separate or overlap sequential notes.  For example,
                staccato might be expressed with a *sustain* of 0.5, while very
                legato playing might be expressed  with  a  *sustain*  of  1.2.
                Specifically,   *sustain*   stretches  the  duration  of  notes
                (sustain) without affecting the inter-onset time (the  rhythm).
                Do  not  access *sustain* directly.  Instead, use get-sustain()
                to get the current value of *sustain*  and  either  sustain  or
                sustain-abs to modify it.

*start*         Start  time  of  a clipping region.  Note:  unlike the previous
                elements  of   the   environment,   *start*   has   a   precise
                interpretation:  no  sound  should be generated before *start*.
                This is implemented in all the low-level sound functions, so it
                can  generally  be ignored.  You can read *start* directly, but
                use extract or extract-abs to modify it.  Note 2: Due  to  some
                internal  confusion between the specified starting time and the
                actual starting time of a signal after clipping, *start* is not
                fully implemented.

*stop*          Stop  time of clipping region.  By analogy to *start*, no sound
                should be generated after this time.  *start* and *stop*  allow
                a  composer  to  preview  a  small  section  of  a work without
                computing it from beginning  to  end.    You  can  read  *stop*
                directly,  but  use extract or extract-abs to modify it.  Note:
                Due to some internal confusion between the  specified  starting
                time  and  the actual starting time of a signal after clipping,
                *stop* is not fully implemented.

*control-srate* Sample rate of  control  signals.    This  environment  element
                provides the default sample rate for control signals.  There is
                no formal distinction between a control  signal  and  an  audio
                signal.    You  can  read  *control-srate*  directly,  but  use
                control-srate or control-srate-abs to modify it.

*sound-srate*   Sample rate  of  musical  sounds.    This  environment  element
                provides  the  default sample rate for musical sounds.  You can
                read   *sound-srate*   directly,   but   use   sound-srate   or
                sound-srate-abs to modify it.

3.2. Sequential Behavior
  Previous  examples  have  shown  the  use  of  seq,  the  sequential behavior
operator.  We can now explain seq in terms of transformations.    Consider  the
simple expression:

    play seq(note(c4, q), note(d4, i))

The idea is to create the first note at time 0, and to start the next note when
the first  one  finishes.    This  is  all  accomplished  by  manipulating  the
environment.   In particular, *warp* is modified so that what is locally time 0
for the second note is transformed, or warped, to the logical stop time of  the
first note.

  One  way to understand this in detail is to imagine how it might be executed:
first, *warp* is set to an initial value  that  has  no  effect  on  time,  and
note(c4,  q)  is  evaluated.   A sound is returned and saved.  The sound has an
ending time, which in this case will be 1.0 because  the  duration  q  is  1.0.
This ending time, 1.0, is used to construct a new *warp* that has the effect of
shifting time by 1.0.  The second note is evaluated, and will start at time  1.
The  sound that is returned is now added to the first sound to form a composite
sound, whose duration will be 2.0.  *warp* is restored to its initial value.

  Notice  that  the  semantics  of  seq  can   be   expressed   in   terms   of
transformations.  To generalize, the operational rule for seq is:  evaluate the
first behavior according to the  current  *warp*.    Evaluate  each  successive
behavior  with  *warp*  modified  to  shift the new note's starting time to the
ending time of the previous behavior.  Restore *warp* to its original value and
return a sound which is the sum of the results.

  In  the Nyquist implementation, audio samples are only computed when they are
needed, and the second part of the seq is not evaluated until the  ending  time
(called  the  logical  stop time) of the first part.  It is still the case that
when the second part is evaluated, it will see *warp* bound to the ending  time
of the first part.

  A  language  detail: Even though Nyquist defers evaluation of the second part
of the seq, the  expression  can  reference  variables  according  to  ordinary
Lisp/SAL  scope  rules.    This is because the seq captures the expression in a
closure, which retains all of the variable bindings.

3.3. Simultaneous Behavior
  Another operator is sim, which invokes multiple behaviors at the  same  time.
For example,

    play 0.5 * sim(note(c4, q), note(d4, i))

will play both notes starting at the same time.

  The operational rule for sim is: evaluate each behavior at the current *warp*
and return the sum of the results. (In SAL, the sim function applied to  sounds
is  equivalent  to adding them with the infix + operator. The following section
illustrates two concepts: first, a sound is not a behavior, and second, the sim
operator and and the at transformation can be used to place sounds in time.

3.4. Sounds vs. Behaviors
  The  following example loads a sound from a file in the current directory and
stores it in a-snd:

    ; load a sound
    ;
    set a-snd = s-read(strcat(current-path(), "demo-snd.aiff"))

    ; play it
    ;
    play a-snd

  One might then be tempted to write the following:

    play seq(a-snd, a-snd)  ;WRONG!

Why is this wrong? Recall that seq works by modifying *warp*, not by  operating
on  sounds.   So, seq will proceed by evaluating a-snd with different values of
*warp*.  However, the result of evaluating a-snd (a  variable)  is  always  the
same  sound,  regardless  of  the  environment;  in this case, the second a-snd
should start at time 0.0, just like the first. In this case,  after  the  first
sound  ends,  Nyquist  is  unable to ``back up'' to time zero, so in fact, this
will play two sounds in sequence, but that is a  result  of  an  implementation
detail  rather  than  correct  program  execution. In fact, a future version of
Nyquist might (correctly) stop and report an error when  it  detects  that  the
second sound in the sequence has a real start time that is before the requested
one.

  How then do we obtain a sequence of two sounds properly?  What we really need
here  is  a  behavior  that  transforms  a given sound according to the current
transformation environment.  That job is performed by cue.   For  example,  the
following will behave as expected, producing a sequence of two sounds:

    play seq(cue(a-snd), cue(a-snd))

This  example  is  correct  because  the second expression will shift the sound
stored in a-snd to start at the end time of the first expression.

  The lesson here is very important: sounds are not behaviors!   Behaviors  are
computations  that generate sounds according to the transformation environment.
Once a sound has been generated, it can  be  stored,  copied,  added  to  other
sounds,  and  used  in  many  other  operations,  but sounds are not subject to
transformations.  To transform a sound,  use  cue,  sound,  or  control.    The
differences  between  these operations are discussed later.  For now, here is a
``cue sheet'' style score that plays 4 copies of a-snd:
    ; use sim and at to place sounds in time
    ;
    play sim(cue(a-snd) @ 0.0,
             cue(a-snd) @ 0.7,
             cue(a-snd) @ 1.0,
             cue(a-snd) @ 1.2)

3.5. The At Transformation
  The second concept introduced by the previous example  is  the  @  operation,
which shifts the *warp* component of the environment.  For example,

    cue(a-snd) @ 0.7

can  be explained operationally as follows: modify *warp* by shifting it by 0.7
and evaluate cue(a-snd).  Return the resulting sound after restoring *warp*  to
its  original  value.    Notice  how @ is used inside a sim construct to locate
copies of a-snd in time.  This is the standard way to represent a note-list  or
a cue-sheet in Nyquist.

  This also explains why sounds need to be cue'd in order to be shifted in time
or arranged in sequence.  If this were not the case, then sim would take all of
its  parameters  (a  set of sounds) and line them up to start at the same time.
But cue(a-snd) @ 0.7 is just a sound, so sim would ``undo'' the  effect  of  @,
making all of the sounds in the previous example start simultaneously, in spite
of the @!  Since sim respects the intrinsic starting times of sounds, a special
operation, cue, is needed to create a new sound with a new starting time.

3.6. Nested Transformations
  Transformations can be combined using nested expressions.  For example,

    sim(cue(a-snd),
        loud(6.0, cue(a-snd) @ 3))

scales the amplitude as well as shifts the second entrance of a-snd.

  Why  use loud instead of simply multiplying a-snd by some scale factor? Using
loud gives the behavior the chance to implement the abstract property  loudness
in  an  appropriate  way,  e.g. by including timbral changes. In this case, the
behavior is cue, which implements loudness by simple amplitude scaling, so  the
result is equivalent to multiplication by db-to-linear(6.0).

  Transformations can also be applied to groups of behaviors:

    loud(6.0, sim(cue(a-snd) @ 0.0,
                  cue(a-snd) @ 0.7))

3.7. Defining Behaviors
  Groups  of  behaviors  can  be named using define (we already saw this in the
definitions of note and note-env).  Here  is  another  example  of  a  behavior
definition and its use.  The definition has one parameter:

    define function snds(dly)
      return sim(cue(a-snd) @ 0.0,
                 cue(a-snd) @ 0.7,
                 cue(a-snd) @ 1.0,
                 cue(a-snd) @ (1.2 + dly))

    play snds(0.1)
    play loud(0.25, snds(0.3) ~ 0.9)

In  the  last  line, snds is transformed: the transformations will apply to the
cue behaviors within snds.  The loud transformation will scale  the  sounds  by
0.25,  and  the  stretch (~) will apply to the shift (@) amounts 0.0, 0.7, 1.0,
and 1.2 + dly.  The sounds themselves (copies of a-snd) will not  be  stretched
because cue never stretches sounds.

  Section 7.3 describes the full set of transformations.

3.8. Sample Rates
  The  global  environment  contains  *sound-srate*  and *control-srate*, which
determine the sample rates of  sounds  and  control  signals.    These  can  be
overridden   at   any   point   by   the  transformations  sound-srate-abs  and
control-srate-abs; for example,

    sound-srate-abs(44100.0, osc(c4)

will compute a tone using a 44.1Khz sample rate even if the default rate is set
to something different.

  As  with  other  components  of  the  environment,  you  should  never change
*sound-srate*  or  *control-srate*  directly.    The  global   environment   is
determined  by  two  additional  variables: *default-sound-srate* and *default-
control-srate*.  You can add lines like the following to your init.lsp file  to
change the default global environment:

    (setf *default-sound-srate* 44100.0)
    (setf *default-control-srate* 1102.5)

You can also do this using preferences in jNyqIDE.  If you have already started
Nyquist and want to change the  defaults,  the  preferences  or  the  following
functions can be used:

    exec set-control-srate(1102.5)exec set-sound-srate(22050.0)

These modify the default values and reinitialize the Nyquist environment.
4. Continuous Transformations and Time Warps
  Nyquist  transformations  were  discussed in the previous chapter, but all of
the examples used scalar values.  For example, we saw the  loud  transformation
used  to  change  loudness  by  a  fixed  amount.  What if we want to specify a
crescendo, where the loudness changes gradually over time?

  It turns out that all transformations can accept signals as well as  numbers,
so  transformations  can be continuous over time.  This raises some interesting
questions about how to interpret continuous transformations.  Should a loudness
transformation  apply  to  the  internal  details  of a note or only affect the
initial loudness?  It might seem unnatural for a decaying piano note to perform
a  crescendo.    On  the  other hand, a sustained trumpet sound should probably
crescendo continuously.  In the case of time warping (tempo changes), it  might
be  best  for  a  drum  roll  to maintain a steady rate, a trill may or may not
change rates with tempo, and a run of sixteenth notes will  surely  change  its
rate.

  These  issues  are  complex,  and Nyquist cannot hope to automatically do the
right thing in all cases.   However,  the  concept  of  behavioral  abstraction
provides  an  elegant  solution.    Since  transformations  merely  modify  the
environment, behaviors are not forced to  implement  any  particular  style  of
transformation.    Nyquist  is  designed  so that the default transformation is
usually the right one, but it  is  always  possible  to  override  the  default
transformation to achieve a particular effect.

4.1. Simple Transformations
  The  ``simple''  transformations affect some parameter, but have no effect on
time itself.  The simple transformations  that  support  continuously  changing
parameters are: sustain, loud, and transpose.

  As  a first example, Let us use transpose to create a chromatic scale.  First
define a sequence of tones at a steady pitch.  The  seqrep  ``function''  works
like  seq  except that it creates copies of a sound by evaluating an expression
multiple times. Here, i takes on 16 values from 0 to 15, and the expression for
the  sound  could  potentially  use  i.    Technically,  seqrep is not really a
function but an abbreviation for a special kind of loop construct.

    define function tone-seq()
      return seqrep(i, 16,
                    osc-note(c4) ~ 0.25)

Now define a linearly increasing ramp to serve  as  a  transposition  function:
define function pitch-rise() return sustain-abs(1.0, 16 * ramp() ~ 4) This ramp
has a duration of 4 seconds, and over that interval  it  rises  from  0  to  16
(corresponding  to the 16 semitones we want to transpose). The ramp is inside a
sustain-abs transformation, which prevents a sustain transformation from having
any effect on the ramp. (One of the drawbacks of behavioral abstraction is that
built-in behaviors sometimes do the  wrong  thing  implicitly,  requiring  some
explicit  correction  to turn off the unwanted transformation.) Now, pitch-rise
is used to  transpose  tone-seq:    define  function  chromatic-scale()  return
transpose(pitch-rise(), tone-seq())

  Similar  transformations  can  be constructed to change the sustain or ``duty
factor'' of notes and their loudness.    The  following  expression  plays  the
previously  constructed  chromatic  scale  with increasing note durations.  The
rhythm is unchanged, but the note length changes from staccato to legato:  play
sustain((0.2  +  ramp()) ~ 4, chromatic-scale()) The resulting sustain function
will ramp from 0.2 to 1.2.  A sustain of  1.2  denotes  a  20  percent  overlap
between notes.  The sum has a stretch factor of 4, so it will extend over the 4
second duration of chromatic-scale.

  What do these transformations mean?  How did the system  know  to  produce  a
pitch rise rather than a continuous glissando?  This all relates to the idea of
behavioral abstraction.  It is possible to  design  sounds  that  do  glissando
under  the  transpose  transform,  and  you  can  even  make sounds that ignore
transpose altogether.  As explained in Chapter 3,  the  transformations  modify
the  environment, and behaviors can reference the environment to determine what
signals to generate.  All built-in functions,  such  as  osc,  have  a  default
behavior.

  The  default behavior for sound primitives under transpose, sustain, and loud
transformations is to sample the environment at  the  beginning  of  the  note.
Transposition  is  not  quantized  to  semitones or any other scale, but in our
example, we arranged for the transposition to work out to  integer  numbers  of
semitones, so we obtained a chromatic scale anyway.

  Transposition  only  applies  to  the oscillator and sampling primitives osc,
partial, sampler, sine, fmosc, and amosc.  Sustain applies  to  osc,  env,  and
pwl.  (Note  that  partial,  amosc,  and  fmosc  get  their  durations from the
modulation signal, so they may indirectly  depend  upon  the  sustain.)    Loud
applies to osc, sampler, cue, sound, fmosc, and amosc. (But not pwl or env.)

4.2. Time Warps
  The  most  interesting  transformations  have  to  do  with transforming time
itself.  The warp transformation  provides  a  mapping  function  from  logical
(score)  time to real time.  The slope of this function tells us how many units
of real time are covered by one unit of score time.  This  is  proportional  to
1/tempo.  A higher slope corresponds to a slower tempo.

  To demonstrate warp, we will define a time warp function using pwl:

    define function warper()
      return pwl(0.25, .4, .75, .6, 1.0, 1.0, 2.0, 2.0, 2.0)

This  function has an initial slope of .4/.25 = 1.6.  It may be easier to think
in reciprocal terms: the initial tempo is .25/.4 =  .625.    Between  0.25  and
0.75,  the tempo is .5/.2 = 2.5, and from 0.75 to 1.0, the tempo is again .625.
It is important for warp functions to completely span the interval of  interest
(in  our  case  it will be 0 to 1), and it is safest to extend a bit beyond the
interval, so we extend the function on to 2.0 with a tempo of 1.0.    Next,  we
stretch  and  scale  the warper function to cover 4 seconds of score time and 4
seconds of real time:

    define function warp4()
      return 4 * warper() ~ 4























     Figure 2:  The result of (warp4), intended to map 4 seconds of  score
     time  into  4  seconds  of  real time.  The function extends beyond 4
     seconds (the dashed lines) to make sure the function is  well-defined
     at    location  (4,  4).    Nyquist sounds are ordinarily open on the
     right.


  Figure 2 shows a plot of this warp function.  Now, we can warp the  tempo  of
the tone-seq defined above using warp4:

    play warp(warp4(), tone-seq())

Figure  3 shows the result graphically.  Notice that the durations of the tones
are warped as well as their onsets.  Envelopes are not shown in detail  in  the
figure.  Because of the way env is defined, the tones will have constant attack
and decay times, and the sustain will be adjusted to fit the available time.














     Figure 3:  When (warp4) is applied to (tone-seq-2), the  note  onsets
     and durations are warped.


4.3. Abstract Time Warps
  We  have seen a number of examples where the default behavior did the ``right
thing,'' making the code  straightforward.    This  is  not  always  the  case.
Suppose  we  want to warp the note onsets but not the durations.  We will first
look at an incorrect solution and discuss the error.  Then we will  look  at  a
slightly more complex (but correct) solution.

  The  default  behavior  for  most Nyquist built-in functions is to sample the
time warp function at the nominal  starting  and  ending  score  times  of  the
primitive.    For  many built-in functions, including osc, the starting logical
time is 0 and the ending logical time is  1,  so  the  time  warp  function  is
evaluated  at these points to yield real starting and stopping times, say 15.23
and 16.79.  The difference (e.g. 1.56) becomes the signal duration,  and  there
is  no  internal  time warping.  The pwl function behaves a little differently.
Here, each breakpoint is warped individually, but  the  resulting  function  is
linear between the breakpoints.

  A  consequence  of  the default behavior is that notes stretch when the tempo
slows down.  Returning to our example, recall that we want  to  warp  only  the
note  onset  times  and  not  the duration.  One would think that the following
would work:

    define function tone-seq-2 ()
      return seqrep(i, 16,
                    osc-note(c4) ~~ 0.25)

    play warp(warp4(), tone-seq-2())

Here, we have redefined tone-seq, renaming it to tone-seq-2  and  changing  the
stretch (~) to absolute stretch (~~).  The absolute stretch should override the
warp function and produce a fixed duration.

  If you play the example,  you  will  hear  steady  sixteenths  and  no  tempo
changes.   What is wrong?  In a sense, the ``fix'' works too well.  Recall that
sequences (including seqrep) determine the starting time of the next note  from
the  logical  stop  time of the previous sound in the sequence.  When we forced
the stretch to 0.25, we also forced the logical stop time to 0.25 real  seconds
from  the  beginning, so every note starts 0.25 seconds after the previous one,
resulting in a constant tempo.

  Now let us design a proper solution.  The trick is to  use  absolute  stretch
(~~) as before to control the duration, but to restore the logical stop time to
a value that results in the proper inter-onset time interval:

    define function tone-seq-3()
      return seqrep(i, 16,
                    set-logical-stop(osc-note(c4) ~~ 0.25, 0.25))

    play warp(warp4(), tone-seq-3())

Notice the addition of set-logical-stop enclosing  the  absolute  stretch  (~~)
expression to set the logical stop time.  A possible point of confusion here is
that the logical stop time is set to 0.25, the same number given to  ~~!    How
does setting the logical stop time to 0.25 result in a tempo change?  When used
within a warp transformation, the second argument to set-logical-stop refers to
score  time  rather  than  real time.  Therefore, the score duration of 0.25 is
warped into real time, producing tempo changes  according  to  the  enviroment.
Figure 4 illustrates the result graphically.














     Figure 4:  When  (warp4) is applied  to (tone-seq-3), the note onsets
     are warped, but not the duration,   which  remains  a  constant  0.25
     seconds.   In the fast middle section, this  causes notes to overlap.
     Nyquist will sum (mix) them.


4.4. Nested Transformations
  Transformations can be nested.  In particular, a simple  transformation  such
as  transpose can be nested within a time warp transformation.  Suppose we want
to warp our chromatic scale example with the warp4 time warp function.   As  in
the  previous  section, we will show an erroneous simple solution followed by a
correct one.

  The simplest approach to a nested transformation is to  simply  combine  them
and hope for the best:

    play warp(warp4(),
              transpose(pitch-rise(), tone-seq()))

This  example  will  not  work the way you might expect.  Here is why: the warp
transformation applies to the (pitch-rise)  expression,  which  is  implemented
using  the  ramp  function.    The  default  behavior of ramp is to interpolate
linearly (in real time) between two points.  Thus, the ``warped'' ramp function
will  not  truly  reflect the internal details of the intended time warp.  When
the notes are moving faster, they will be closer together  in  pitch,  and  the
result  is  not  chromatic.  What we need is a way to properly compose the warp
and ramp functions.  If we continuously warp the ramp function in the same  way
as  the note sequence, a chromatic scale should be obtained.  This will lead to
a correct solution.

  Here is the modified code to properly warp a transposed sequence.  Note  that
the  original  sequence is used without modification.  The only complication is
producing a properly warped transposition function:

      play warp(warp4(),
                transpose(
                  control-warp(get-warp(),
                               warp-abs(nil, pitch-rise())),
                  tone-seq()))

To properly warp the pitch-rise transposition function,  we  use  control-warp,
which  applies a warp function to a function of score time, yielding a function
of real time.  We need to pass the desired  function  to  control-warp,  so  we
fetch  it  from the environment with get-warp().  Finally, since the warping is
done here, we want to shield the pitch-rise expression from further warping, so
we enclose it in warp-abs(nil, ...).

  An  aside:  This  last  example  illustrates  a  difficulty  in the design of
Nyquist.  To support behavioral abstraction  universally,  we  must  rely  upon
behaviors  to  ``do  the  right  thing.''  In this case, we would like the ramp
function to warp continuously according  to  the  environment.    But  this  is
inefficient  and  unnecessary in many other cases where ramp and especially pwl
are used.  (pwl warps its breakpoints, but still interpolates linearly  between
them.)   Also, if the default behavior of primitives is to warp in a continuous
manner, this makes it difficult to build custom abstract behaviors.  The  final
vote is not in.
5. More Examples
  This  chapter  explores  Nyquist through additional examples.  The reader may
wish to browse through these and move on to Chapter 7,  which  is  a  reference
section describing Nyquist functions.

5.1. Stretching Sampled Sounds
  This  example  illustrates  how  to  stretch  a  sound,  resampling it in the
process.  Because sounds in Nyquist are values that contain  the  sample  rate,
start  time,  etc.,  use  sound  to convert a sound into a behavior that can be
stretched, e.g. sound(a-snd). This behavior stretches a sound according to  the
stretch  factor  in  the  environment,  set  using  stretch.  For  accuracy and
efficiency, Nyquist does  not  resample  a  stretched  sound  until  absolutely
necessary.  The  force-srate function is used to resample the result so that we
end up with a ``normal'' sample rate that is playable on ordinary sound cards.

    ; if a-snd is not loaded, load sound sample:
    ;
    if not(boundp(quote(a-snd))) then
      set a-snd = s-read("demo-snd.aiff")

    ; the SOUND operator shifts, stretches, clips and scales
    ; a sound according to the current environment
    ;
    define function ex23()
      play force-srate(*default-sound-srate*,  sound(a-snd) ~ 3.0)

    define function down()
      return force-srate(*default-sound-srate*,
                         seq(sound(a-snd) ~ 0.2,
                             sound(a-snd) ~ 0.3,
                             sound(a-snd) ~ 0.4,
                             sound(a-snd) ~ 0.6))
    play down()

    ; that was so much fun, let's go back up:
    ;
    define function up()
      return force-srate(*default-sound-srate*,
                         seq(sound(a-snd) ~ 0.5,
                             sound(a-snd) ~ 0.4,
                             sound(a-snd) ~ 0.3,
                             sound(a-snd) ~ 0.2))

    ; and write a sequence
    ;
    play seq(down(), up(), down())

  Notice the use of the sound behavior as opposed to cue.    The  cue  behavior
shifts  and  scales  its  sound according to *warp* and *loud*, but it does not
change the duration or resample the sound.  In contrast, sound not only  shifts
and  scales  its  sound, but it also stretches it by resampling or changing the
effective sample rate according to *warp*.  If *warp* is a  continuous  warping
function,  then  the  sound  will  be  stretched by time-varying amounts.  (The
*transpose* element of the environment is ignored by both cue and sound.)

  Note:  sound  may  use  linear  interpolation  rather  than  a   high-quality
resampling  algorithm.    In  some  cases, this may introduce errors audible as
noise. Use resample (see Section 7.2.2) for high-quality interpolation.

  In the functions up and down, the *warp* is set by stretch (~), which  simply
scales time by a constant scale factor. In this case, sound can ``stretch'' the
signal simply by changing the sample rate without any further computation. When
seq  tries  to  add  the signals together, it discovers the sample rates do not
match and uses linear interpolation to adjust all sample rates to match that of
the  first  sound  in  the  sequence. The result of seq is then converted using
force-srate to convert the sample rate, again using linear interpolation.    It
would be slightly better, from a computational standpoint, to apply force-srate
individually to each stretched sound rather  than  applying  force-srate  after
seq.

  Notice  that  the  overall  duration  of  sound(a-snd) ~ 0.5 will be half the
duration of a-snd.

5.2. Saving Sound Files
  So far, we have used the play command to play a  sound.    The  play  command
works  by  writing a sound to a file while simultaneously playing it.  This can
be done one step at a time, and it is often convenient to save  a  sound  to  a
particular file for later use:

    ; write the sample to a file,
    ;    the file name can be any Unix filename.  Prepending a "./" tells
    ;    s-save to not prepend *default-sf-dir*
    ;
    exec s-save(a-snd, 1000000000, "./a-snd-file.snd")

    ; play a file
    ; play command normally expects an expression for a sound
    ; but if you pass it a string, it will open and play a
    ; sound file
    play "./a-snd-file.snd"

    ; delete the file (do this with care!)
    ; only works under Unix (not Windows)
    exec system("rm ./a-snd-file.snd")

    ; now let's do it using a variable as the file name
    ;
    set my-sound-file = "./a-snd-file.snd"

    exec s-save(a-snd, 1000000000, my-sound-file)

    ; play-file is a function to open and play a sound file
    exec play-file(my-sound-file)

    exec system(strcat("rm ", my-sound-file))

This example shows how s-save can be used to save a sound to a file.

  This  example  also  shows how the system function can be used to invoke Unix
shell commands, such as a command to play a file or remove it.  Finally, notice
that  strcat can be used to concatenate a command name to a file name to create
a complete command that is then passed to system.  (This is convenient  if  the
sound file name is stored in a parameter or variable.)

5.3. Memory Space and Normalization
  Sound  samples take up lots of memory, and often, there is not enough primary
(RAM) memory to hold a complete composition.   For  this  reason,  Nyquist  can
compute  sounds  incrementally,  saving  the  final  result  on disk.  However,
Nyquist can also save sounds in memory so that they can be reused  efficiently.
In  general, if a sound is saved in a global variable, memory will be allocated
as needed to save and reuse it.

  The standard way to compute a sound and write  it  to  disk  is  to  pass  an
expression to the play command:

    play my-composition()

  Often  it  is  nice  to  normalize sounds so that they use the full available
dynamic range of 16 bits.  Nyquist has  an  automated  facility  to  help  with
normalization.  By  default,  Nyquist  computes  up to 1 million samples (using
about 4MB of memory) looking for the peak. The entire sound  is  normalized  so
that  this  peak  will not cause clipping. If the sound has less than 1 million
samples, or if the first million samples are a good indication of  the  overall
peak, then the signal will not clip.

  With  this automated normalization technique, you can choose the desired peak
value by setting *autonorm-target*, which is initialized to 0.9.  The number of
samples  examined  is *autonorm-max-samples*, initially 1 million. You can turn
this feature off by executing:

    exec autonorm-off()

and turn it back on by typing:

    exec autonorm-on()

This  normalization  technique   is   in   effect   when   *autonorm-type*   is
quote(lookahead), which is the default.

  An  alternative  normalization  method  uses the peak value from the previous
call to play. After playing a file, Nyquist can adjust an internal scale factor
so  that  if  you  play  the  same  file  again,  the  peak  amplitude  will be
*autonorm-target*, which is initialized to 0.9. This can be useful if you  want
to  carefully  normalize  a  big  sound  that  does  not have its peak near the
beginning. To select this style of normalization, set  *autonorm-type*  to  the
(quoted) atom quote(previous).

  You  can  also  create  your  own  normalization method in Nyquist.  The peak
function computes the maximum value of  a  sound.    The  peak  value  is  also
returned  from  the  play macro. You can normalize in memory if you have enough
memory; otherwise you can compute the sound twice.    The  two  techniques  are
illustrated here:

    ; normalize in memory.  First, assign the sound to a variable so
    ; it will be retained:
    set mysound = sim(osc(c4), osc(c5))
    ; now compute the maximum value (ny:all is 1 giga-samples, you may want
    ; smaller constant if you have less than 4GB of memory:
    set mymax = snd-max(mysound, NY:ALL)
    display "Computed max", mymax
    ; now write out and play the sound from memory with a scale factor:
    play mysound * (0.9 / mymax)

    ; if you don't have space in memory, here's how to do it:
    define function myscore()
      return sim(osc(c4), osc(c5))
    ; compute the maximum:
    set mymax = snd-max(list(quote(myscore)), NY:ALL)
    display "Computed max", mymax
    ; now we know the max, but we don't have a the sound (it was garbage
    ; collected and never existed all at once in memory).  Compute the soun
    ; again, this time with a scale factor:
    play myscore() * (0.9 / mymax)

  You  can  also write a sound as a floating point file.  This file can then be
converted to 16-bit integer with  the  proper  scaling  applied.    If  a  long
computation  was  involved,  it  should be much faster to scale the saved sound
file than to recompute the sound from scratch.  Although not implemented yet in
Nyquist,  some  header formats can store maximum amplitudes, and some soundfile
player  programs  can  rescale  floating  point  files  on  the  fly,  allowing
normalized  soundfile  playback  without  an extra normalization pass (but at a
cost of twice the disk space of 16-bit  samples).    You  can  use  Nyquist  to
rescale a floating point file and convert it to 16-bit samples for playback.

5.4. Frequency Modulation
  The  next  example  uses  the  Nyquist frequency modulation behavior fmosc to
generate various sounds.  The parameters to fmosc are:

    fmosc(pitch modulator table phase)
Note that pitch is the number of half-steps, e.g. c4 has the value of 60  which
is  middle-C,  and  phase  is  in  degrees.   Only the first two parameters are
required:

    ; make a short sine tone with no frequency modulation
    ;
    play fmosc(c4, pwl(0.1))

    ; make a longer sine tone -- note that the duration of
    ;   the modulator determines the duration of the tone
    ;
    play fmosc(c4, pwl(0.5))

In the example above, pwl (for Piece-Wise Linear) is used  to  generate  sounds
that  are  zero  for  the  durations  of 0.1 and 0.5 seconds, respectively.  In
effect, we are using an FM oscillator with no modulation input, and the  result
is  a sine tone.  The duration of the modulation determines the duration of the
generated tone (when the modulation signal ends, the oscillator stops).

  The next example uses a more interesting modulation  function,  a  ramp  from
zero  to  C ,  expressed  in  hz.    More explanation of pwl is in order.  This
           4
operation  constructs   a   piece-wise   linear   function   sampled   at   the
*control-srate*.    The  first breakpoint is always at (0, 0), so the first two
parameters give the time and value of the second  breakpoint,  the  second  two
parameters  give  the  time  and value of the third breakpoint, and so on.  The
last breakpoint has a value of 0, so only the time of the  last  breakpoint  is
given.    In  this  case,  we  want the ramp to end at C , so we cheat a bit by
                                                        4
having the ramp return to zero ``almost'' instantaneously between times 0.5 and
0.501.

  The  pwl  behavior always expects an odd number of parameters.  The resulting
function  is  shifted  and  stretched  linearly  according  to  *warp*  in  the
environment.  Now, here is the example:

    ; make a frequency sweep of one octave; the piece-wise linear function
    ; sweeps from 0 to (step-to-hz c4) because, when added to the c4
    ; fundamental, this will double the frequency and cause an octave sweep
    ;
    play fmosc(c4, pwl(0.5, step-to-hz(c4),  0.501))

  The  same  idea  can be applied to a non-sinusoidal carrier.  Here, we assume
that *fm-voice* is predefined (the next section shows how to define it):

    ; do the same thing with a non-sine table
    ;
    play fmosc(cs2, pwl(0.5, step-to-hz(cs2), 0.501),
               *fm-voice*, 0.0)

  The next example shows how a function can be used to make a special frequency
modulation contour.  In this case the contour generates a sweep from a starting
pitch to a destination pitch:

    ; make a function to give a frequency sweep, starting
    ; after <delay> seconds, then sweeping from <pitch-1>
    ; to <pitch-2> in <sweep-time> seconds and then
    ; holding at <pitch-2> for <hold-time> seconds.
    ;
    define function sweep(delay, pitch-1, sweep-time,
                          pitch-2, hold-time)
      begin
        with interval = step-to-hz(pitch-2) - step-to-hz(pitch-1)
        return pwl(delay, 0.0,
                   ; sweep from pitch 1 to pitch 2
                   delay + sweep-time, interval,
                   ; hold until about 1 sample from the end
                   delay + sweep-time + hold-time - 0.0005,
                   interval,
                   ; quickly ramp to zero (pwl always does this,
                   ;    so make it short)
                   delay + sweep-time + hold-time)
      end


    ; now try it out
    ;
    play fmosc(cs2, sweep(0.1, cs2, 0.6, gs2, 0.5),
               *fm-voice*, 0.0)

  FM can be used for vibrato as well as frequency sweeps.  Here, we use the lfo
function  to  generate vibrato.  The lfo operation is similar to osc, except it
generates sounds at the *control-srate*, and the parameter is hz rather than  a
pitch:

    play fmosc(cs2, 10.0 * lfo(6.0), *fm-voice*, 0.0)

  What  kind  of manual would this be without the obligatory FM sound?  Here, a
sinusoidal modulator (frequency C ) is multiplied by a slowly  increasing  ramp
                                 4
from zero to 1000.0.

    set modulator = pwl(1.0, 1000.0, 1.0005) *
                    osc(c4)
    ; make the sound
    play fmosc(c4, modulator)

  For  more  simple  examples  of FM in Nyquist, see demos/warble_tutorial.htm.
Another interesting FM sound reminiscent of ``scratching'' can be found with  a
detailed explanation in demos/scratch_tutorial.htm..

5.5. Building a Wavetable
  In  Section 1.6.1, we saw how to synthesize a wavetable.  A wavetable for osc
also can be extracted from any sound.  This is especially  interesting  if  the
sound  is digitized from some external sound source and loaded using the s-read
function.  Recall that a table is a list consisting of a sound,  the  pitch  of
that sound, and T (meaning the sound is periodic).

  In the following, a sound is first read from the file demo-snd.nh.  Then, the
extract function is used to extract the portion of the sound  between  0.110204
and  0.13932  seconds.   (These numbers might be obtained by first plotting the
sound and estimating the beginning and end  of  a  period,  or  by  using  some
software  to  look for good zero crossings.)  The result of extract becomes the
first element of a list.  The next element is the pitch  (24.848422),  and  the
last element is T.  The list is assigned to *fm-voice*.

    if not(boundp(quote(a-snd))) then
      set a-snd = s-read("demo-snd.aiff")

    set *fm-voice* = list(extract(0.110204, 0.13932, cue(a-snd)),
                          24.848422,
                          #T)

  The  file  demos/examples.sal  contains an extensive example of how to locate
zero-crossings, extract a period, build a waveform, and generate  a  tone  from
it.  (See ex37 through ex40 in the file.)

5.6. Filter Examples
  Nyquist provides a variety of filters.  All of these filters take either real
numbers or signals as parameters.  If you pass a signal as a filter  parameter,
the  filter  coefficients  are  recomputed  at  the  sample rate of the control
signal.  Since filter coefficients are generally expensive to compute, you  may
want  to select filter control rates carefully.  Use control-srate-abs (Section
7.3) to specify the default control sample rate, or  use  force-srate  (Section
7.2.2) to resample a signal before passing it to a filter.

  Before presenting examples, let's generate some unfiltered white noise:

    play noise()

Now low-pass filter the noise with a 1000Hz cutoff:

    play lp(noise(), 1000.0)

The high-pass filter is the inverse of the low-pass:

    play hp(noise(), 1000.0)

  Here is a low-pass filter sweep from 100Hz to 2000Hz:

    play lp(noise(), pwl(0.0, 100.0, 1.0, 2000.0, 1.0))

And a high-pass sweep from 50Hz to 4000Hz:

    play hp(noise(), pwl(0.0, 50.0, 1.0, 4000.0, 1.0))

  The  band-pass  filter  takes  a  center frequency and a bandwidth parameter.
This example has a 500Hz center frequency with a 20Hz  bandwidth.    The  scale
factor is necessary because, due to the resonant peak of the filter, the signal
amplitude exceeds 1.0:

    play reson(10.0 * noise(), 500.0, 20.0, 1)

In the next example, the center frequency is swept from 100 to 1000Hz, using  a
constant 20Hz bandwidth:

    play reson(0.04 * noise(),
               pwl(0.0, 200.0, 1.0, 1000.0, 1.0),
               20.0)

  For another example with explanations, see demos/wind_tutorial.htm.

5.7. DSP in Lisp
  In  almost  any  signal  processing  system, the vast majority of computation
takes place in the inner loops of DSP algorithms, and Nyquist  is  designed  so
that  these  time-consuming  inner  loops  are in highly-optimized machine code
rather than relatively  slow  interpreted  lisp  code.  As  a  result,  Nyquist
typically  spends 95% of its time in these inner loops; the overhead of using a
Lisp interpreter is negligible.

  The drawback is that Nyquist must provide the DSP operations you need, or you
are  out  of  luck.  When  Nyquist is found lacking, you can either write a new
primitive signal operation, or you can perform DSP in Lisp code. Neither option
is  recommended  for  inexperienced  programmers.  Instructions  for  extending
Nyquist are given in Appendix I. This section describes the process of  writing
a new signal processing function in Lisp.

  Before  implementing  a new DSP function, you should decide which approach is
best. First, figure out how much of the new function can be  implemented  using
existing  Nyquist  functions.  For example, you might think that a tapped-delay
line would require a new function, but  in  fact,  it  can  be  implemented  by
composing  sound  transformations  to  accomplish  delays,  scale  factors  for
attenuation, and additions to combine the intermediate results.  This  can  all
be  packaged  into a new Lisp function, making it easy to use.  If the function
relies on built-in DSP primitives, it will execute very efficiently.

  Assuming that built-in  functions  cannot  be  used,  try  to  define  a  new
operation  that  will  be  both  simple and general. Usually, it makes sense to
implement only the  kernel  of  what  you  need,  combining  it  with  existing
functions  to  build  a  complete instrument or operation.  For example, if you
want to implement a physical model that requires a varying breath pressure with
noise  and  vibrato,  plan  to  use  Nyquist  functions to add a basic pressure
envelope to noise and vibrato signals to come  up  with  a  composite  pressure
signal.  Pass  that signal into the physical model rather than synthesizing the
envelope, noise, and vibrato within the model. This  not  only  simplifies  the
model,  but  gives  you  the  flexibility to use all of Nyquist's operations to
synthesize a suitable breath pressure signal.

  Having designed the new ``kernel'' DSP operation that  must  be  implemented,
decide  whether to use C or Lisp. (At present, SAL is not a good option because
it has no support for object-oriented programming.)  To use C, you must have  a
C  compiler,  the  full  source  code  for  Nyquist,  and  you must learn about
extending Nyquist by reading Appendix I. This is the more complex approach, but
the  result  will be very efficient. A C implementation will deal properly with
sounds that are not time-aligned or matched in sample rates.  To use Lisp,  you
must  learn  something  about  the  XLISP object system, and the result will be
about 50 times slower than C. Also, it is more  difficult  to  deal  with  time
alignment and differences in sample rates.  The remainder of this section gives
an example of a Lisp version  of  snd-prod  to  illustrate  how  to  write  DSP
functions for Nyquist in Lisp.

  The  snd-prod  function  is  the low-level multiply routine. It has two sound
parameters and returns a sound which is the product of the two. To keep  things
simple,  we  will assume that two sounds to be multiplied have a matched sample
rate and matching start times. The DSP algorithm  for  each  output  sample  is
simply  to  fetch  a  sample  from  each  sound,  multiply them, and return the
product.

  To implement snd-prod in Lisp, three components are required:

   1. An object is used to store the two  parameter  sounds.  This  object
      will be called upon to yield samples of the result sound;

   2. Within  the  object,  the snd-fetch routine is used to fetch samples
      from the two input sounds as needed;

   3. The result must be of type  SOUND,  so  snd-fromobject  is  used  to
      create the result sound.

  The  combined  solution  will  work as follows: The result is a value of type
sound that retains a reference to the object.  When Nyquist needs samples  from
the  sound,  it  invokes the sound's ``fetch'' function, which in turn sends an
XLISP message to the object. The object will use snd-fetch to get a sample from
each stored sound, multiply the samples, and return a result.

  Thus  the  goal  is  to  design  an XLISP object that, in response to a :next
message will return a proper sequence of samples.  When the sound  reaches  the
termination time, simply return NIL.

  The  XLISP manual (see Appendix IV describes the object system, but in a very
terse style, so this example will include some explanation of  how  the  object
system  is  used.  First,  we  need to define a class for the objects that will
compute sound products. Every class is a  subclass  of  class  class,  and  you
create a subclass by sending :new to a class.

    (setf product-class (send class :new '(s1 s2)))

The  parameter  '(s1  s2)  says  that  the  new  class  will  have two instance
variables, s1 and s2. In other words, every object  which  is  an  instance  of
class product-class will have its own copy of these two variables.

  Next, we will define the :next method for product-class:

    (send product-class :answer :next '()
      '((let ((f1 (snd-fetch s1))
              (f2 (snd-fetch s2)))
          (cond ((and f1 f2)
                 (* f1 f2))
                (t nil)))))

The  :answer message is used to insert a new method into our new product-class.
The method is described in three parts: the  name  (:next),  a  parameter  list
(empty  in this case), and a list of expressions to be evaluated. In this case,
we fetch samples from s1 and s2. If both are numbers, we return their  product.
If either is NIL, we terminate the sound by returning nil.

  The  :next  method  assumes  that s1 and s2 hold the sounds to be multiplied.
These must be installed when the object is created.   Objects  are  created  by
sending  :new to a class. A new object is created, and any parameters passed to
:new are then sent in a :isnew message to the new object. Here  is  the  :isnew
definition for product-class:

    (send product-class :answer :isnew '(p1 p2)
      '((setf s1 (snd-copy p1))
        (setf s2 (snd-copy p2))))

Take  careful note of the use of snd-copy in this initialization. The sounds s1
and s2 are modified when accessed by snd-fetch  in  the  :next  method  defined
above,  but  this  destroys  the illusion that sounds are immutable values. The
solution is to copy the sounds before accessing them; the original  sounds  are
therefore  unchanged.    (This copy also takes place implicitly in most Nyquist
sound functions.)

  To make this code safer for general use, we should add checks that s1 and  s2
are  sounds  with  identical  starting  times  and  sample rates; otherwise, an
incorrect result might be computed.

  Now we are  ready  to  write  snd-product,  an  approximate  replacement  for
snd-prod:

    (defun snd-product (s1 s2)
      (let (obj)
        (setf obj (send product-class :new s1 s2))
        (snd-fromobject (snd-t0 s1) (snd-srate s1) obj)))

This  code  first creates obj, an instance of product-class, to hold s1 and s2.
Then, it uses obj to  create  a  sound  using  snd-fromobject.  This  sound  is
returned  from snd-product.  Note that in snd-fromobject, you must also specify
the starting time and sample rate as the first two parameters. These are copied
from  s1, again assuming that s1 and s2 have matching starting times and sample
rates.

  Note that in more elaborate DSP algorithms we could expect the object to have
a  number  of  instance  variables  to  hold  things  such as previous samples,
waveform tables, and other parameters.
6. SAL
  Nyquist supports two languages: XLISP and SAL. In some sense, XLISP  and  SAL
are  the  same language, but with differing syntax. This chapter describes SAL:
how it works, SAL syntax and semantics, and the relationship  between  SAL  and
XLISP, and differences between Nyquist SAL and Common Music SAL.

  Nyquist  SAL  is  based on Rick Taube's SAL language, which is part of Common
Music. SAL offers the power of Lisp but features a simple,  Algol-like  syntax.
SAL  is  implemented  in Lisp: Lisp code translates SAL into a Lisp program and
uses the underlying Lisp  engine  to  evaluate  the  program.  Aside  from  the
translation  time,  which is quite fast, SAL programs execute at about the same
speed as the  corresponding  Lisp  program.  (Nyquist  SAL  programs  run  just
slightly   slower   than  XLISP  because  of  some  runtime  debugging  support
automatically added to user programs by the SAL compiler.)

  From the user's perspective, these implementation details are hidden. You can
enter  SAL  mode from XLISP by typing (SAL) to the XLISP prompt.  The SAL input
prompt (SAL> ) will be displayed. From that  point  on,  you  simply  type  SAL
commands,  and  they  will  be executed. By setting a preference in the jNyqIDE
program, SAL mode will be entered automatically.

  It is  possible  to  encounter  errors  that  will  take  you  from  the  SAL
interpreter  to  an  XLISP prompt. In general, the way to get back to SAL is by
typing (top) to get back to the top  level  XLISP  interpreter  and  reset  the
Nyquist environment. Then type (sal) to restart the SAL interpreter.

6.1. SAL Syntax and Semantics
  The  most  unusual  feature  of SAL syntax is that identifiers are Lisp-like,
including names such as ``play-file''  and  even  ``*warp*.''    In  SAL,  most
operators  must  be  separated  from  identifiers by white space.  For example,
play-file is one identifier, but play - file is an expression for ``play  minus
file,''  where  play  and  file  are  two separate identifiers. Fortunately, no
spaces are needed around commas and parentheses.

  In SAL, whitespace (any sequence of space, newline,  or  tab  characters)  is
sometimes  necessary  to  separate  lexical  tokens,  but otherwise, spaces and
indentation are ignored. To make SAL readable, it is strongly advised that  you
indent  SAL  programs as in the examples here. The jNyqIDE program is purposely
insistent about SAL indentation, so if you use it to edit  SAL  programs,  your
indentation should be both beautiful and consistent.

  As in Lisp (but very unlike C or Java), comments are indicated by semicolons.
Any text from an unquoted semicolon to the end of the line is ignored.

    ; this is a comment
    ; comments are ignored by the compiler
    print "Hello World" ; this is a SAL statement

  As  in  Lisp,  identifiers  are  translated   to   upper-case,   making   SAL
case-insensitive. For example, the function name autonorm can be typed in lower
case or as AUTONORM, AutoNorm, or even AuToNoRm.  All  forms  denote  the  same
function. The recommended approach is to wirte programs in all lower case.

  SAL  is  organized  around  statements, most of which contain expressions. We
will begin with expressions and then look at statements.



6.1.1. Expressions


6.1.1.1. Simple Expressions
  As in XLISP, simple expressions include:

   - integers (FIXNUM's), such as 1215,

   - floats (FLONUM's) such as 12.15,

   - strings (STRING's) such as "Magna Carta", and

   - symbols (SYMBOL's) such as magna-carta. A symbol with a leading colon
     (:)  evaluates  to  itself  as  in  Lisp. Otherwise, a symbol denotes
     either a local variable, a formal parameter, or a global variable. As
     in  Lisp,  variables do not have data types or type declarations. The
     type of a variable is determined at runtime by its value.

  Additional simple expressions in SAL are:

   - lists such as {c 60 e 64}. Note that there are no commas to  separate
     list  elements,  and  symbols in lists are not evaluated as variables
     but stand  for  themselves.  Lists  may  contain  numbers,  booleans,
     symbols, strings, and other lists.

   - Booleans:  SAL  interprets  #t as true and #fas false. (As far as the
     SAL compiler is concerned, t and nil are just variables.  Since these
     are  the  Lisp  versions  of true and false, they are interchangeable
     with #t and #f, respectively.)

A curious property of Lisp and Sal is that false and the  empty  list  are  the
same value. Since SAL is based on Lisp, #f and {} (the empty list) are equal.


6.1.1.2. Operators
  Expressions  can  be  formed  with  unary  and  binary  operators using infix
notation. The operators are:

   - + - addition, including sounds - - subtraction, including sounds *  -
     multiplication,  including sounds / - division (due to divide-by-zero
     problems, does not operate on sounds) % -  modulus  (remainder  after
     division)  ^  -  exponentiation  =  - equal (using Lisp eql) != - not
     equal > - greater than < - less than >= - greater than or equal <=  -
     less  than  or  equal  ~=  -  general equality (using Lisp equal) & -
     logical and | - logical or ! - logical not (unary) @ - time shift  @@
     -  time  shift to absolute time ~ - time stretch ~~ - time stretch to
     absolute stretch factor

Again, remember that operators must be  delimited  from  their  operands  using
spaces  or parentheses. Operator precedence is based on the following levels of
precedence:

    @ @@ ~ ~~
    ^
    / *
    % - +
    ~= <= >= > ~= =
    !
    &
    |


6.1.1.3. Function Calls
  A function call is a function name followed by zero or  more  comma-delimited
argument expressions enclosed within parentheses:

    list()
    piano-note(2.0, c4 + interval, 100)

Some  functions  use  named  parameters, in which case the name of the argument
with a colon precedes the argument expression.

    s-save(my-snd(), ny:all, "tmp.wav", play: #t, bits: 16)


6.1.1.4. Array Notation
  An array reference is a variable identifier followed by an  index  expression
in square brackets, e.g.:

    x[23] + y[i]


6.1.1.5. Conditional Values
  The  special  operator  #?  evaluates  the first argument expression.  If the
result is true, the second expression is evaluated and its value  is  returned.
If  false, the third expression is evaluated and returned (or false is returned
if there is no third expression):

    #?(random(2) = 0, unison, major-third)
    #?(pitch >= c4, pitch - c4) ; returns false if pitch < c4



6.1.2. SAL Statements
  SAL compiles and evaluates statements one at a time. You can type  statements
at the SAL prompt or load a file containing SAL statements.  SAL statements are
described below. The syntax is indicated at the  beginning  of  each  statement
type  description:  this  font  indicates  literal  terms such as keywords, the
italic font indicates a place-holder for some other  statement  or  expression.
Bracket  [like  this]  indicate  optional  (zero or one) syntax elements, while
braces with a plus {like this}+ indicate one or more occurrences  of  a  syntax
element. Braces with a star {like this}* indicate zero or more occurrences of a
syntax element: { non-terminal }* is equivalent to [ {non-terminal}+ ].


6.1.2.1. begin and end
  begin [with-stmt] {statement}+ end

  A begin-end statement consists of a sequence of statements surrounded by  the
begin  and  end  keywords. This form is often used for function definitions and
after then or else where the syntax demands a single statement but you want  to
perform  more than one action. Variables may be declared using an optional with
statement immediately after begin.  For example:

    begin
      with db = 12.0,
           linear = db-to-linear(db)
      print db, "dB represents a factor of", linear
      set scale-factor = linear
    end


6.1.2.2. chdir
  chdir expression

  The chdir statement changes the working directory. This statement is provided
for compatibility with Common Music SAL, but it really should be avoided if you
use jNyqIDE. The expression following the chdir keyword should  evaluate  to  a
string  that is a directory path name. Note that literal strings themselves are
valid expressions.

    chdir "/Users/rbd/tmp"


6.1.2.3. define variable
  [define] variable name [= expression] {, name [= expression]}*

  Global variables can be declared and initialized. A list of  variable  names,
each  with  an  optional  initialization  follows the define variable keywords.
(Since variable is a keyword, define is redundant and optional in Nyquist  SAL,
but  required in Common Music SAL.)  If the initialization part is omitted, the
variable is initialized to false. Global variables do not  really  need  to  be
declared:  just  using  the name implicitly creates the corresponding variable.
However, it is an error to use a global variable that has not been initialized;
define  variable  is  a  good way to introduce a variable (or constant) with an
initial value into your program.

    define variable transposition = 2,
                    print-debugging-info, ; initially false
                    output-file-name = "salmon.wav"


6.1.2.4. define function
  [define] function name ( [parameter], {, parameter}* ) statement

  Before a function be called from an expression (as described above), it  must
be  defined.  A  function  definition  gives  the  function  name,  a  list  of
parameters, and a statement. When a function is called,  the  actual  parameter
expressions  are  evaluated from left to right and the formal parameters of the
function definition are set to these values. Then, statement is evaluated.

  The formal parameters are essentially local variables that exist  only  until
statement  completes  or  a  return statement causes the function evaluation to
end. As in Lisp, parameters are passed by value, so assigning a new value to  a
formal  parameter  has no effect on the actual value. However, lists and arrays
are not copied, so internal changes to a list or array produce observable  side
effects.

  The  parameters  are  meaningful  only  within  the lexical (static) scope of
statement. They are not accessible from within other functions even if they are
called by this function.

  Use  a  begin-end  statement  if the body of the function should contain more
than one statement or  you  need  to  define  local  variables.  Use  a  return
statement to return a value from the function. If statement completes without a
return, the value false is returned.


6.1.2.5. display
  display string {, expression}*

  The display statement  is  handy  for  debugging.  At  present,  it  is  only
implemented  in  Nyquist SAL. When executed, display prints the string followed
by a colon and then, for each expression, the  expression  and  its  value  are
printed, after the last expression, a newline is printed. For example,

    display "In function foo", bar, baz

prints

    In function foo : bar = 23, baz = 5.3

SAL  may  print  the  expressions  using Lisp syntax, e.g. if the expression is
``bar + baz,'' do not be surprised if the output is ``(sum bar baz) = 28.3.''


6.1.2.6. exec
  exec expression

  Unlike most other programming languages, you cannot simply type an expression
as  a  statement.  If you want to evaluate an expression, e.g. call a function,
you must use an exec statement. The statement simply evaluates the  expression.
For example,

    exec set-sound-srate(22050.0) ; change default sample rate


6.1.2.7. if
  if test-expr then true-stmt [else false-stmt]

  An  if  statement  evaluates  the  expression  test-expr.  If  it is true, it
evaluates the statement  true-stmt.  If  false,  the  statement  false-stmt  is
evaluated.  Use  a  begin-end  statement to evaluate more than one statement in
then then or else parts.

    if x < 0 then x = -x ; x gets its absoute value

    if x > upper-bound then
      begin
        print "x too big, setting to", upper-bound
        x = upper-bound
      end
    else
      if x < lower-bound then
        begin
          print "x too small, setting to", lower-bound
          x = lower-bound
        end

Notice in this example that the else part is another if statement.  An  if  may
also  be  the then part of another if, so there could be two possible if's with
which to associate an else. An else clause always associates with  the  closest
previous if that does not already have an else clause.


6.1.2.8. when
  when test statement

  The when statement is similar to if, but there is no else clause.

    when *debug-flag* print "you are here"


6.1.2.9. unless
  unless test statement

  The  unless  statement  is  similar  to  when  (and  if) but the statement is
executed when the test expression is false.

    unless count = 0 set average = sum / count


6.1.2.10. load
  load expression

  The load command loads a file named by expression, which must  evauate  to  a
string path name for the file. To load a file, SAL interprets each statement in
the file, stopping when the end of the file or an error is encountered. If  the
file  ends  in .lsp, the file is assumed to contain Lisp expressions, which are
evaluated by the XLISP interpreter.  In general, SAL files should end with  the
extension .sal.


6.1.2.11. loop
  loop [with-stmt] {stepping}* {stopping* action+ [finally] end

  The loop statement is by far the most complex statement in SAL, but it offers
great flexibility for just about any kind of iteration. The basic function of a
loop  is  to  repeatedly  evaluate a sequence of action's which are statements.
Before the loop begins, local variables may be declared in  with-stmt,  a  with
statement.

  The  stepping  clauses  do  several  things.  They  introduce  and initialize
additional local variables similar to the  with-stmt.    However,  these  local
variables  are  updated  to  new  values after the action's.  In addition, some
stepping clauses have associated stopping conditions, which are tested on  each
iteration before evaluating the action's.

  There  are  also  stopping  clauses that provide additional tests to stop the
iteration. These are  also  evaluated  and  tested  on  each  iteration  before
evaluating the action's.

  When  some  stepping  or stopping condition causes the iteration to stop, the
finally clause is evaluated (if present). Local variables and their values  can
still  be  accessed  in  the finally clause. After the finally clause, the loop
statement completes.

  The stepping clauses are the following:

repeat expression
                Sets the number of iterations to the value of expression, which
                should be an integer (FIXNUM).

for var = expression [ then expr2 ]
                Introduces a new local variable named var and initializes it to
                expression. Before each subsequent iteration, var is set to the
                value  of  expr2.  If  the  then part is omitted, expression is
                re-evaluated and assigned to var on each subsequent  iteration.
                Note  that  this differs from a with-stmt where expressions are
                evaluated and variables are only assigned their values once.

for var in expression
                Evaluates  expression  to obtain a list and creates a new local
                variable initialized to the first element of  the  list.  After
                each  iteration,  var is assigned the next element of the list.
                Iteration stops when var has assumed all values from the  list.
                If  the  list  is  initially  empty,  the loop action's are not
                evaluated (there are zero iterations).

for var [from from-expr] [to | below to-expr] [by step-expr]
                Introduces a new local variable named var and intialized to the
                value of the expression from-expr (with a default value of  0).
                After  each  iteration  of  the loop, var is incremented by the
                value of step-expr (with a default value of 1).  The  iteration
                ends  when var is greater than or equal to the value of to-expr
                if there is a to clause, or when var is less than or  equal  to
                the  value of to-expr when there is a below clause. If there is
                no to or below clause, no interation stop test is  created  for
                this stepping clause.

  The stopping clauses are the following:

while expression
                The iterations are stopped when expression evaluates to  false.
                Anything not false is considered to mean true.

until expression
                The iterations are stopped when expression evaluates to true.

  The finally clause is defined as follows:

finally statement
                The statement is evaluated when one of the stepping or stopping
                clauses ends the loop. As always, statement may be a  begin-end
                statement.  If  an  action  evaluates  a  return statement, the
                finally statement is not executed.

  Loops often fall into common patterns, such as iteratiing a fixed  number  of
times, performing an operation on some range of integers, collecting results in
a list, and linearly searching for a solution. These forms are  illustrated  in
the examples below.
    ; iterate 10 times
    loop
      repeat 10
      print random(100)
    end

    ; print even numbers from 10 to 20
    ; note that 20 is printed. On the next iteration,
    ;   i = 22, so i >= 22, so the loop exits.
    loop
      for i from 10 to 22 by 2
      print i
    end

    ; collect even numbers in a list
    loop
      with lis
      for i = 0 to 10 by 2
      set lis @= i ; push integers on front of list,
                   ; which is much faster than append,
                   ; but list is built in reverse
      finally result = reverse(lis)
    end
    ; now, the variable result has a list of evens

    ; find the first even number in a list
    result = #f ; #f means "false"
    loop
      for elem in lis
      until evenp(elem)
      finally result = elem
    end
    ; result has first even value in lis (or it is #f)


6.1.2.12. print
  print expr {, expr}*

  The  print  statement prints a newline, then evaluates expressions and prints
their values. A blank space is printed after each value.

    print "The value of x is", x


6.1.2.13. return
  return expression

  The return statement can  only  be  used  inside  a  function.  It  evaluates
expression  and  then  the  function returns the value of the expression to its
caller.


6.1.2.14. set
  set var op expression {, var op expression}*

  The set statement changes the value  of  a  variable  var  according  to  the
operator op and the value of the expression. The operators are:

=               The value of expression is assigned to var.

+=              The value of expression is added to var.

*=              The value of var is multiplied by the value of the expression.

&=              The  value of expression is inserted as the last element of the
                list referenced by var. If var is the empty  list  (denoted  by
                #f),  then  var  is  assigned  a  newly constructed list of one
                element, the value of expression.

^=              The value of expression,  a  list,  is  appended  to  the  list
                referenced  by  var.  If var is the empty list (denoted by #f),
                then var is assigned the (list) value of expression.

@=              Pushes the value of expression  onto  the  front  of  the  list
                referenced by var. If var is empty (denoted by #f), then var is
                assigned a newly constructed list of one element, the value  of
                expression.

<=              Sets  the  new  value of var to the minimum of the old value of
                var and the value of expression.

>=              Sets the new value of var to the maximum of the  old  value  of
                var and the value of expression.

    ; example from Rick Taube's SAL description
    loop
      with a, b = 0, c = 1, d = {}, e = {}, f = -1, g = 0
      for i below 5
      set a = i, b += 1, c *= 2, d &= i, e @= i, f <= i, g >= i
      finally display "results", a, b, c, d, e, f, g
    end


6.1.2.15. with
  with var [= expression] {, var [= expression]}*

  The  with  statement  declares and initializes local variables. It can appear
only after begin or loop. If the expression is omitted, the  initial  value  is
false.  The  variables  are visible only inside the begin-end or loop statement
where the with statement appears. Even in loop's the variables  are  intialized
only when the loop is entered, not on each iteration.


6.1.2.16. exit
  exit [nyquist]

  The  exit statement is unique to Nyquist SAL. It returns from SAL mode to the
XLISP interpreter. (Return to SAL mode by typing ``(sal)'').    If  nyquist  is
included in the statement, then the entire Nyquist process will exit.

6.2. Interoperability of SAL and XLISP
  When SAL evaluatas command or loads files, it translates SAL into XLISP.  You
can think of SAL as a program that translates everything you write  into  XLISP
and  entering  it  for  you. Thus, when you define a SAL function, the function
actually exists as an XLISP function (created using Lisp's defun special form).
When  you  set  or evaluate global variables in SAL, these are exactly the same
Lisp global variables.  Thus,  XLISP  functions  can  call  SAL  functions  and
vice-versa. At run time, everything is Lisp.



6.2.1. Function Calls
  In  general,  there  is a very simple translation from SAL to Lisp syntax and
back. A function call is SAL, for example,

    osc(g4, 2.0)

is translated to Lisp by moving the open parenthesis in front of  the  function
name and removing the commas:

    (osc g4 2.0)

Similarly,  if  you want to translate a Lisp function call to SAL, just reverse
the translation.



6.2.2. Playing Tricks On the SAL Compiler
  In many cases, the close coupling between SAL and XLISP gives SAL  unexpected
expressive power. A good example is seqrep. This is a special looping construct
in Nyquist, implemented as a macro in XLISP. In Lisp, you would write something
like:

    (seqrep (i 10) (pluck c4))

One might expect SAL would have to define a special seqrep statement to express
this, but since statements  do  not  return  values,  this  approach  would  be
problematic. The solution (which is already fully implemented in Nyquist) is to
define a new macro sal-seqrep that is equivalent to seqrep except  that  it  is
called as follows:

    (sal-seqrep i 10 (pluck c4))

The  SAL compiler automatically translates the identifier seqrep to sal-seqrep.
Now, in SAL, you can just write

    seqrep(i, 10, pluck(c4))

which is translated in a pretty much semantics-unaware fashion to

    (sal-seqrep i 10 (pluck c4))

and viola!, we have Nyquist control  constructs  in  SAL  even  though  SAL  is
completely unaware that seqrep is actually a special form.
7. Nyquist Functions
  This  chapter  provides  a  language  reference  for Nyquist.  Operations are
categorized by functionality and abstraction level.  Nyquist is implemented  in
two important levels: the ``high level'' supports behavioral abstraction, which
means that operations like stretch and at can be applied.  These functions  are
the  ones  that  typical users are expected to use, and most of these functions
are written in XLISP.

  The ``low-level'' primitives directly operate on sounds, but know nothing  of
environmental  variables  (such  as  *warp*, etc.).  The names of most of these
low-level functions start with ``snd-''.  In general, programmers should  avoid
any  function  with  the  ``snd-''  prefix.    Instead,  use the ``high-level''
functions, which know about the environment and react appropriately.  The names
of high-level functions do not have prefixes like the low-level functions.

  There  are  certain  low-level  operations  that apply directly to sounds (as
opposed to behaviors) and are relatively ``safe'' for ordinary use.  These  are
marked as such.

  Nyquist  uses  both  linear  frequency and equal-temperament pitch numbers to
specify repetition rates.  Frequency is always specified in either  cycles  per
second  (hz),  or  pitch numbers, also referred to as ``steps,'' as in steps of
the chromatic scale.  Steps are floating point numbers such that 60 = Middle C,
61  =  C#,  61.23  is  C# plus 23 cents, etc.  The mapping from pitch number to
frequency is the standard exponential conversion, and fractional pitch  numbers
                                (pitch-69)/12
are  allowed:    frequency=440*2             .  There are many predefined pitch
names.  By default these are tuned in equal temperament, with A4 =  440Hz,  but
these may be changed.  (See Section 1.7).

7.1. Sounds
  A  sound  is a primitive data type in Nyquist.  Sounds can be created, passed
as parameters, garbage collected, printed,  and  set  to  variables  just  like
strings, atoms, numbers, and other data types.



7.1.1. What is a Sound?
  Sounds have 5 components:

   - srate M the sample rate of the sound.

   - samples M the samples.

   - signal-start M the time of the first sample.

   - signal-stop M the time of one past the last sample.

   - logical-stop  M  the  time  at which the sound logically ends, e.g. a
     sound may end at the beginning of a decay.  This  value  defaults  to
     signal-stop, but may be set to any value.

It  may  seem  that  there  should  be logical-start to indicate the logical or
perceptual beginning of a sound as well  as  a  logical-stop  to  indicate  the
logical  ending  of  a  sound.   In practice, only logical-stop is needed; this
attribute tells when the next sound should begin to form a sequence of  sounds.
In  this  respect,  Nyquist  sounds  are  asymmetric: it is possible to compute
sequences forward in time by aligning the logical start of each sound with  the
logical-stop  of  the  previous  one,  but  one  cannot  compute ``backwards'',
aligning the logical end of each sound with the logical start of its successor.
The  root  of this asymmetry is the fact that when we invoke a behavior, we say
when to start, and the result of the behavior tells us  its  logical  duration.
There  is  no  way  to invoke a behavior with a direct specification of when to
stop[Most behaviors will stop at time 1, warped according  to  *warp*  to  some
real time, but this is by convention and is not a direct specification.].

  Note:  there  is no way to enforce the intended ``perceptual'' interpretation
of logical-stop.  As far as Nyquist is concerned, these  are  just  numbers  to
guide the alignment of sounds within various control constructs.



7.1.2. Multichannel Sounds
  Multichannel  sounds  are represented by Lisp arrays of sounds.  To create an
array of sounds the XLISP vector function is useful.   Most  low-level  Nyquist
functions  (the ones starting with snd-) do not operate on multichannel sounds.
Most high-level functions do operate on multichannel sounds.



7.1.3. Accessing and Creating Sound
  Several functions display information concerning a sound and can be  used  to
query  the  components of a sound. There are functions that access samples in a
sound and functions that construct sounds from samples.

sref(sound, time)
     Accesses  sound at the point time, which is a local time. If time does not
     correspond to a  sample  time,  then  the  nearest  samples  are  linearly
     interpolated  to  form  the result.  To access a particular sample, either
     convert the sound to an array (see snd-samples below),  or  use  snd-srate
     and  snd-t0  (see  below)  to  find the sample rate and starting time, and
     compute a time (t) from the sample  number  (n):t=(n/srate)+t0  Thus,  the
                                   th
     lisp  code  to  access  the  n   sample of a sound would look like:  (sref
     sound (global-to-local (+ (/ n (snd-srate sound)) (snd-t0  sound))))  Here
     is why sref interprets its time argument as a local time:

         > (sref (ramp 1) 0.5) ; evaluate a ramp at time 0.5
         0.5
         > (at 2.0 (sref (ramp 1) 0.5)) ; ramp is shifted to start at 2.0
                         ; the time, 0.5, is shifted to 2.5
         0.5

     If you were to use snd-sref, which treats time as global, instead of sref,
     which treats time as local, then the first example above would return  the
     same  answer  (0.5),  but the second example would return 0.  Why? Because
     the (ramp 1) behavior would be shifted to  start  at  time  2.0,  but  the
     resulting  sound  would  be  evaluated at global time 0.5.  By definition,
     sounds have a value of zero before their start time.

sref-inverse(sound, value)
     Search sound for the first point at which it achieves value and return the
     corresponding (linearly interpolated) time.   If  no  inverse  exists,  an
     error  is  raised.  This function is used by Nyquist in the implementation
     of time warping.

snd-from-array(t0, sr, array)
     Converts  a  lisp  array of FLONUMs into a sound with starting time t0 and
     sample rate sr.   Safe  for  ordinary  use.    Be  aware  that  arrays  of
     floating-point  samples use 14 bytes per sample, and an additional 4 bytes
     per sample are allocated by this function to create a sound type.

snd-fromarraystream(t0, sr, object)
     Creates  a  sound for which samples come from object. The starting time is
     t0 (a FLONUM), and the sample rate is sr. The object is  an  XLISP  object
     (see Section IV.11 for information on objects.) A sound is returned.  When
     the sound needs samples, they are generated by sending the  message  :next
     to  object. If object returns NIL, the sound terminates. Otherwise, object
     must return an  array  of  FLONUMs.    The  values  in  these  arrays  are
     concatenated  to  form  the  samples  of the resulting sound.  There is no
     provision for object to specify the logical stop time of the sound, so the
     logical stop time is the termination time.

snd-fromobject(t0, sr, object)
     Creates a sound for which samples come from object. The starting  time  is
     t0  (a  FLONUM),  and the sample rate is sr. The object is an XLISP object
     (see Section IV.11 for information on objects. A sound is returned.   When
     the  sound  needs samples, they are generated by sending the message :next
     to object. If object returns NIL, the sound terminates. Otherwise,  object
     must  return  a  FLONUM.   There is no provision for object to specify the
     logical stop  time  of  the  sound,  so  the  logical  stop  time  is  the
     termination time.

snd-extent(sound, maxsamples)
     Returns a list of  two  numbers:  the  starting  time  of  sound  and  the
     terminate time of sound.  Finding the terminate time requires that samples
     be computed.  Like most Nyquist functions,  this  is  non-destructive,  so
     memory  will  be allocated to preserve the sound samples.  If the sound is
     very long or infinite, this may exhaust  all  memory,  so  the  maxsamples
     parameter specifies a limit on how many samples to compute.  If this limit
     is reached, the terminate time will be (incorrectly) based  on  the  sound
     having maxsamples samples.  This function is safe for ordinary use.

snd-fetch(sound)
     Reads samples sequentially from sound. This returns a  FLONUM  after  each
     call,  or NIL when sound terminates. Note: snd-fetch modifies sound; it is
     strongly recommended to copy sound using snd-copy and access only the copy
     with snd-fetch.

snd-fetch-array(sound, len, step)
     Reads sequential arrays of samples from sound, returning either  an  array
     of  FLONUMs or NIL when the sound terminates. The len parameter, a FIXNUM,
     indicates how many samples should be returned in the result array.   After
     the  array is returned, sound is modified by skipping over step (a FIXNUM)
     samples. If step equals len, then every sample is returned once.  If  step
     is  less  than  len, each returned array will overlap the previous one, so
     some samples will be returned more than once. If step is greater than len,
     then  some samples will be skipped and not returned in any array. The step
     and len may change at each call, but in  the  current  implementation,  an
     internal  buffer  is  allocated for sound on the first call, so subsequent
     calls may not specify a greater len than the first. Note:  snd-fetch-array
     modifies  sound;  it  is strongly recommended to copy sound using snd-copy
     and access only the copy with snd-fetch-array.

snd-flatten(sound, maxlen)
     This  function  is identical to snd-length. You would use this function to
     force samples to be computed in memory. Normally, this is not a good thing
     to do, but here is one appropriate use: In the case of sounds intended for
     wavetables, the unevaluated sound may be larger than  the  evaluated  (and
     typically  short)  one.   Calling snd-flatten will compute the samples and
     allow the unit generators to be freed  in  the  next  garbage  collection.
     Note:  If  a  sound  is  computed  from  many  instances  of  table-lookup
     oscillators, calling snd-flatten  will  free  the  oscillators  and  their
     tables.  Calling  (stats)  will  print  how  many  total  bytes  have been
     allocated to tables.

snd-length(sound, maxlen)
     Counts  the  number  of samples in sound up to the physical stop time.  If
     the sound has more than maxlen samples, maxlen is returned.  Calling  this
     function  will  cause all samples of the sound to be computed and saved in
     memory (about 4 bytes per sample).  Otherwise, this function is  safe  for
     ordinary use.

snd-maxsamp(sound)
     Computes the maximum of the  absolute  value  of  the  samples  in  sound.
     Calling  this  function  will  cause  samples  to be computed and saved in
     memory.    (This  function  should  have  a  maxlen  parameter  to   allow
     self-defense   against   sounds  that  would  exhaust  available  memory.)
     Otherwise, this function is safe for ordinary use.    This  function  will
     probably  be  removed in a future version.  See peak, a replacement ( page
     81).

snd-play(expression)
     Evaluates expression to obtain a sound or array of sounds, computes all of
     the samples (without retaining them in memory),  and  returns.    If  this
     happens  faster  than  real time for interesting sounds, you might want to
     modify Nyquist to actually write the samples directly to an  audio  output
     device.  Meanwhile, since this function does not save samples in memory or
     write them to a disk, it is useful in determining how much time  is  spent
     calculating  samples.    See  s-save (Section 7.5) for saving samples to a
     file, and play (Section 7.5) to play a sound.  This function is  safe  for
     ordinary use.

snd-print-tree(sound)
     Prints  an  ascii  representation  of   the   internal   data   structures
     representing  a  sound.    This  is  useful  for  debugging Nyquist.  This
     function is safe for ordinary use.

snd-samples(sound, limit)
     Converts  the  samples into a lisp array.  The data is taken directly from
     the samples, ignoring shifts.  For example, if the  sound  starts  at  3.0
     seconds, the first sample will refer to time 3.0, not time 0.0.  A maximum
     of limit samples is returned.  This function is safe for ordinary use, but
     like  snd-from-array,  it  requires  a total of slightly over 18 bytes per
     sample.

snd-srate(sound)
     Returns the sample rate of the sound. Safe for ordinary use.

snd-time(sound)
     Returns the start time of the sound.  This will  probably  go  away  in  a
     future version, so use snd-t0 instead.

snd-t0(sound)
     Returns the time of the first sample of the  sound.    Note  that  Nyquist
     operators  such  as add always copy the sound and are allowed to shift the
     copy up to one half sample period in either direction to align the samples
     of two operands.  Safe for ordinary use.

snd-print(expression, maxlen)
     Evaluates expression to yield a sound or an array of sounds,  then  prints
     up to maxlen samples to the screen (stdout).  This is similar to snd-save,
     but samples appear in text on the screen instead of in binary in  a  file.
     This function is intended for debugging.  Safe for ordinary use.

snd-set-logical-stop(sound, time)
     Returns a sound which is sound, except that the logical stop of the  sound
     occurs  at  time.    Note:  do  not  call  this function.  When defining a
     behavior, use set-logical-stop or set-logical-stop-abs instead.

snd-sref(sound, time)
     Evaluates  sound at the global time given by time.  Safe for ordinary use,
     but normally, you should call sref instead.

snd-stop-time(sound)
     Returns the stop time of sound.  Sounds can be ``clipped'' or truncated at
     a particular time.  This function returns that time or MAX-STOP-TIME if he
     programmer has not specified a stop time for the sound.  Safe for ordinary
     use.

soundp(sound)
     Returns true iff sound is a SOUND.  Safe for ordinary use.

stats()
     Prints the memory usage status.  See also the XLISP mem  function.    Safe
     for  ordinary  use.  This  is  the only way to find out how much memory is
     being used by table-lookup oscillator instances.



7.1.4. Miscellaneous Functions
  These are all safe and recommended for ordinary use.

db-to-linear(x)
     Returns  the conversion of x from decibels to linear.  0dB is converted to
     1.  20dB represents a linear factor of 10. If x is a sound, each sample is
     converted  and  a  sound  is returned.  If x is a multichannel sound, each
     channel is converted and a multichannel sound (array) is returned.   Note:
     With  sounds,  conversion  is only performed on actual samples, not on the
     implicit zeros before the beginning  and  after  the  termination  of  the
     sound.  Sample rates, start times, etc. are taken from x.

follow(sound, floor, risetime, falltime, lookahead)
     An envelope follower intended as a commponent for compressor  and  limiter
     functions.  The basic goal of this function is to generate a smooth signal
     that rides on the peaks of the input signal. The  usual  objective  is  to
     produce  an  amplitude  envelope  given  a  low-sample rate (control rate)
     signal representing local RMS measurements.  The  first  argument  is  the
     input  signal.  The floor is the minimum output value. The risetime is the
     time (in seconds) it takes for the output  to  rise  (exponentially)  from
     floor  to unity (1.0) and the falltime is the time it takes for the output
     to fall (exponentially) from unity to floor. The algorithm looks ahead for
     peaks  and  will begin to increase the output signal according to risetime
     in anticipation of a peak. The amount  of  anticipation  (in  seconds)  is
     given  by  lookahead.    The  algorithm is as follows: the output value is
     allowed to  increase  according  to  risetime  or  decrease  according  to
     falltime. If the next input sample is in this range, that sample is simply
     output as the next output sample.  If the next input sample is too  large,
     the algorithm goes back in time as far as necessary to compute an envelope
     that rises according to risetime to meet the new value. The algorithm will
     only  work  backward as far as lookahead.  If that is not far enough, then
     there is a final forward pass computing a rising signal from the  earliest
     output  sample.  In  this  case,  the  output  signal  will  be  at  least
     momentarily  less  than  the  input  signal  and  will  continue  to  rise
     exponentially  until  it  intersects the input signal. If the input signal
     falls faster than indicated by falltime, the  output  fall  rate  will  be
     limited  by  falltime,  and  the  fall in output will stop when the output
     reaches floor.  This algorithm can make two passes througth the buffer  on
     sharply  rising inputs, so it is not particularly fast. With short buffers
     and low sample rates this should not matter. See snd-avg  for  a  function
     that  can  help  to  generate  a  low-sample-rate  input  for follow.  See
     snd-chase in Section 7.6.3 for a related filter.

gate(sound, floor, risetime, falltime, lookahead, threshold)
     Generate   an   exponential   rise  and  decay  intended  for  noise  gate
     implementation. The decay starts when the signal drops below threshold and
     stays  there  for longer than lookahead (a FLONUM in seconds). (The signal
     begins to drop when the signal crosses threshold,  not  after  lookahead.)
     Decay  continues  until the value reaches floor (a FLONUM), at which point
     the decay stops and the output value is held constant. Either  during  the
     decay  or  after the floor is reached, if the signal goes above threshold,
     then the ouptut value will rise to unity (1.0) at  the  point  the  signal
     crosses  the threshold. Because of internal lookahead, the signal actually
     begins to rise  before  the  signal  crosses  threshold.  The  rise  is  a
     constant-rate  exponential  and  set  so  that  a rise from floor to unity
     occurs in risetime. Similary, the fall is a constant-rate exponential such
     that a fall from unity to floor takes falltime.

hz-to-step(freq)
     Returns a step number for freq (in hz), which can be either a number of  a
     SOUND.  The  result has the same type as the argument. See also step-to-hz
     (below).

linear-to-db(x)
     Returns the conversion of x from linear to decibels.  1 is converted to 0.
     0 is converted to -INF (a special IEEE floating point value.)  A factor of
     10  represents  a  20dB change.  If x is a sound, each sample is converted
     and a sound is returned.  If x is a multichannel sound,  each  channel  is
     converted  and  a  multichannel  sound  (array)  is  returned.  Note: With
     sounds, conversion is  only  performed  on  actual  samples,  not  on  the
     implicit  zeros  before  the  beginning  and  after the termination of the
     sound.  Start times, sample rates, etc. are taken from x.

log(x)
     Calculates  the natural log of x (a FLONUM). (See s-log for a version that
     operates on signals.)

set-control-srate(rate)
     Sets  the  default  sampling  rate  for control signals to rate by setting
     *default-control-srate* and reinitializing the environment.  Do  not  call
     this   within   any   synthesis   function   (see   the  control-srate-abs
     transformation, Section 7.3).

set-sound-srate(rate)
     Sets  the  default  sampling  rate  for  audio  signals to rate by setting
     *default-sound-srate* and reinitializing the environment.    Do  not  call
     this    within   any   synthesis   function   (see   the   sound-srate-abs
     transformation, Section 7.3).

set-pitch-names()
     Initializes  pitch variables (c0, cs0, df0, d0, ... b0, c1, ... b7).  A440
     (the default tuning) is represented by the step 69.0, so the  variable  a4
     (fourth  octave  A)  is set to 69.0.  You can change the tuning by setting
     *A4-Hertz*  to  a  value  (in  Hertz)  and  calling   set-pitch-names   to
     reinitialize  the  pitch  variables.    Note  that  this  will  result  in
     non-integer step values.  It does not alter the mapping from  step  values
     to  frequency.    There  is  no built-in provision for stretched scales or
     non-equal temperament, although users can write  or  compute  any  desired
     fractional step values.

step-to-hz(pitch)
     Returns a frequency in hz for  pitch,  a  step  number  or  a  SOUND  type
     representing  a  time-varying step number. The result is a FLONUM if pitch
     is a number, and a SOUND if pitch is a SOUND. See also hz-to-step (above).

get-duration(dur)
     Gets the actual duration of of something starting at a local time of 0 and
     ending at a local time of dur times the current sustain. For  convenience,
     *rslt* is set to the global time corresponding to local time zero.

get-loud()
     Gets the current value of the *loud* environment variable.  If *loud* is a
     signal, it is evaluated at local time 0 and a number (FLONUM) is returned.

get-sustain()
     Gets the  current  value  of  the  *sustain*  environment  variable.    If
     *sustain*  is  a  signal,  it  is  evaluated  at local time 0 and a number
     (FLONUM) is returned.

get-transpose()
     Gets  the  current  value  of  the  *transpose*  environment variable.  If
     *transpose* is a signal, it is evaluated at local  time  0  and  a  number
     (FLONUM) is returned.

get-warp()
     Gets  a  function  corresponding  to  the  current  value  of  the  *warp*
     environment  variable.    For  efficiency, *warp* is stored in three parts
     representing a shift, a scale factor,  and  a  continuous  warp  function.
     Get-warp is used to retrieve a signal that maps logical time to real time.
     This signal combines the information of all  three  components  of  *warp*
     into  a  single  signal.  If the continuous warp function component is not
     present (indicating that the time warp is a simple combination of  at  and
     stretch transformations), an error is raised.  This function is mainly for
     internal  system  use.    In  the  future,  get-warp  will   probably   be
     reimplemented to always return a signal and never raise an error.

local-to-global(local-time)
     Converts a score (local) time to a real (global)  time  according  to  the
     current environment.

osc-enable(flag)
     Enable or disable Open Sound Control. (See Appendix II.)  Enabling creates
     a  socket  and  a  service  that  listens  for  UDP  packets on port 7770.
     Currently, only messages of the form \slider with an integer index  and  a
     floating  point  value  are  accepted.  These  set  internal slider values
     accessed by the snd-slider  function.  Disabling  terminates  the  service
     (polling  for  messages)  and  closes  the  socket.  The previous state of
     enablement is returned, e.g. if OSC is enabled and flag  is  nil,  OSC  is
     disabled  and  T (true) is returned because OSC was enabled at the time of
     the call. This function only  exists  if  Nyquist  is  compiled  with  the
     compiler  flag  OSC. Otherwise, the function exists but always returns the
     symbol DISABLED.  Consider  lowering  the  audio  latency  using  snd-set-
     latency.   Warning: there is the potential for network-based attacks using
     OSC. It is tempting to add the ability to evaluate XLISP expressions  sent
     via  OSC,  but  this  would create unlimited and unprotected access to OSC
     clients. For now, it is unlikely that  an  attacker  could  do  more  than
     manipulate slider values.

snd-set-latency(latency)
     Set the latency requested when Nyquist plays sound to latency,  a  FLONUM.
     The  previous  value  is  returned.  The  default is 0.3 seconds. To avoid
     glitches, the latency should be greater than the time required for garbage
     collection  and message printing and any other system activity external to
     Nyquist.

7.2. Behaviors



7.2.1. Using Previously Created Sounds
  These behaviors take a sound  and  transform  that  sound  according  to  the
environment.   These are useful when writing code to make a high-level function
from a low-level function, or when cuing sounds which were previously created:

cue(sound)
     Applies  *loud*,  the  starting  time  from *warp*, *start*, and *stop* to
     sound.

cue-file(filename)
     Same  as  cue,  except  the  sound comes from the named file, samples from
     which are coerced to the current default *sound-srate* sample rate.

sound(sound)
     Applies *loud*, *warp*, *start*, and *stop* to sound.

control(sound)
     This function is identical to sound, but by convention is used when  sound
     is a control signal rather than an audio signal.



7.2.2. Sound Synthesis
  These  functions  provide musically interesting creation behaviors that react
to their environment; these are the ``unit generators'' of Nyquist:

const(value, [duration])
     Creates  a constant function at the *control-srate*.  Every sample has the
     given value, and the default duration is 1.0.  See also s-rest,  which  is
     equivalent  to  calling const with zero, and note that you can pass scalar
     constants (numbers) to sim, sum, and mult  where  they  are  handled  more
     efficiently than constant functions.

env(t , t , t , l , l , l , [dur])
     1   2   4   1   2   3
     Creates a 4-phase envelope.  t  is the duration of phase i, and l  is  the
                                   i                                  i
     final level of phase i.  t  is implied by the duration dur, and l  is 0.0.
                               3                                      4
     If dur is not supplied, then 1.0 is assumed.  The envelope duration is the
     product  of  dur,  *stretch*,  and  *sustain*.    If t  + t  + 2ms + t  is
                                                           1    2          4
     greater  than  the  envelope  duration,  then  a  two-phase  envelope   is
     substituted  that  has  an attack/release time ratio of t /t .  The sample
                                                              1  4
     rate of the returned sound is  *control-srate*.    (See  pwl  for  a  more
     general piece-wise linear function generator.)  The effect of time warping
     is  to  warp  the  starting  time  and  ending  time.    The  intermediate
     breakpoints are then computed as described above.

exp-dec(hold, halfdec, length)
     This convenient envelope shape is a special  case  of  pwev  (see  Section
     7.2.2.2).  The  envelope  starts at 1 and is constant for hold seconds. It
     then decays with a half life of halfdec seconds until length.  (The  total
     duration  is  length.)  In  other  words, the amplitude falls by half each
     halfdec seconds. When stretched,  this  envelope  scales  linearly,  which
     means the hold time increases and the half decay time increases.

force-srate(srate, sound)
     Returns a sound which is up- or down-sampled to srate.   Interpolation  is
     linear,  and  no  prefiltering  is  applied  in  the  down-sample case, so
     aliasing may occur. See also resample.

lfo(freq, [duration, table, phase])
     Just  like  osc  (below)  except  this computes at the *control-srate* and
     frequency is specified in Hz.    Phase  is  specified  in  degrees.    The
     *transpose*  and  *sustain* is not applied.  The effect of time warping is
     to warp the starting and ending times.  The  signal  itself  will  have  a
     constant unwarped frequency.

fmlfo(freq, [table, phase])
     A low-frequency oscillator that computes at the  *control-srate*  using  a
     sound  to  specify  a  time-varying  frequency in Hz. Phase is a FLONUM in
     degrees. The duration of the result is determined by freq.

maketable(sound)
     Assumes  that  the  samples in sound constitute one period of a wavetable,
     and returns a wavetable suitable for use as the table argument to the  osc
     function (see below).  Currently, tables are limited to 1,000,000 samples.
     This limit is the compile-time constant max_table_len set in sound.h.

build-harmonic(n, table-size)
     Intended  for  constructing  wavetables,  this function returns a sound of
     length table-size samples containing n periods of a sinusoid.   These  can
     be scaled and summed to form a waveform with the desired harmonic content.
     See page 2 for an example.

control-warp(warp-fn, signal, [wrate])
     Applies  a warp function warp-fn to signal using function composition.  If
     wrate is omitted, linear interpolation is used.  warp-fn is a mapping from
     score  (logical)  time  to  real time, and signal is a function from score
     time to real values.  The result is a function  from  real  time  to  real
     values  at  a  sample  rate  of  *control-srate*.  See  sound-warp  for an
     explanation of wrate and high-quality warping.

mult(beh , beh , ...)
        1     2
     Returns  the  product of behaviors.  The arguments may also be numbers, in
     which case simple multiplication is performed.  If a number and sound  are
     mixed,  the  scale function is used to scale the sound by the number. When
     sounds are multiplied, the resulting sample rate  is  the  maximum  sample
     rate of the factors.

prod(beh , beh , ...)
        1     2
     Same as mult.

pan(sound, where)
     Pans sound (a behavior) according to where (another behavior or a number).
     Sound must be monophonic. Where may be a monophonic sound (e.g. (ramp)  or
     simply  a  number (e.g. 0.5). In either case, where should range from 0 to
     1, where 0 means pan completely left, and 1 means  pan  completely  right.
     For  intermediate  values,  the  sound to each channel is scaled linearly.
     Presently, pan does not check its arguments carefully.

prod(beh , beh , ...)
        1     2
     Same as mult.

resample(sound, srate)
     Similar to force-srate,  except  high-quality  interpolation  is  used  to
     prefilter  and  reconstruct  the  signal at the new sample rate. Also, the
     result is scaled by 0.95 to  reduce  problems  with  clipping.  (See  also
     sound-warp.)

scale(scale, sound)
     Scales the amplitude of sound by the factor scale.  Identical function  to
     snd-scale,  except  that  it  handles  multichannel sounds.  Sample rates,
     start times, etc. are taken from sound.

scale-db(db, sound)
     Scales  the  amplitude  of  sound by the factor db, expressed in decibels.
     Sample rates, start times, etc. are taken from sound.

scale-srate(sound, scale)
     Scales  the  sample rate of sound by scale factor.  This has the effect of
     linearly shrinking or stretching time  (the  sound  is  not  upsampled  or
     downsampled).  This is a special case of snd-xform (see Section 7.6.2).

shift-time(sound, shift)
     Shift sound by shift seconds.  If the sound is f(t), then  the  result  is
     f(t-shift).    See  Figure  5.    This is a special case of snd-xform (see
     Section 7.6.2).

sound-warp(warp-fn, signal, [wrate])
     Applies a warp function warp-fn to signal using function composition.   If
     the  optional  parameter  wrate is omitted or NIL, linear interpolation is
     used.  Otherwise, high-quality  sample  interpolation  is  used,  and  the
     result  is  scaled  by 0.95 to reduce problems with clipping (interpolated
     samples can exceed the peak values of the input samples.)   warp-fn  is  a
     mapping  from  score (logical) time to real time, and signal is a function
     from score time to real values.  The result is a function from  real  time
     to real values at a sample rate of *sound-srate*.  See also control-warp.

     If  wrate  is  not  NIL, it must be a number. The parameter indicates that
     high-quality resampling should be used and specifies the sample  rate  for
     the  inverse  of  warp-fn.  Use the lowest number you can.  (See below for
     details.) Note that high-quality resampling is  much  slower  than  linear
     interpolation.

     To  perform  high-quality  resampling  by  a  fixed ratio, as opposed to a





















     Figure 5:  The shift-time function shifts a sound in time   according
     to its shift argument.


     variable ratio allowed in sound-warp, use scale-srate to stretch or shrink
     the sound, and then resample to restore the original sample rate.

     Sound-warp  and  control-warp  both  take  the inverse of warp-fn to get a
     function from real time to score time. Each sample of this inverse is thus
     a  score time; signal is evaluated at each of these score times to yield a
     value, which is the desired result. The sample rate of  the  inverse  warp
     function  is  somewhat  arbitrary.  With linear interpolation, the inverse
     warp function sample rate is taken to be the  output  sample  rate.  Note,
     however,  that  the  samples  of  the  inverse warp function are stored as
     32-bit  floats,  so  they  have  limited  precision.  Since  these  floats
     represent  sample  times, rounding can be a problem. Rounding in this case
     is equivalent to adding jitter to the sample times. Nyquist  ignores  this
     problem  for  ordinary  warping,  but for high-quality warping, the jitter
     cannot be ignored.

     The solution is to use a rather low  sample  rate  for  the  inverse  warp
     function.  Sound-warp  can  then  linearly  interpolate  this signal using
     double-precision floats to minimize jitter  between  samples.  The  sample
     rate  is  a  compromise:  a low sample rate minimizes jitter, while a high
     sample  rate  does  a  better  job  of  capturing   detail   (e.g.   rapid
     fluctuations) in the warp function. A good rule of thumb is to use at most
     1,000 to 10,000 samples for the inverse warp function. For example, if the
     result  will  be 1 minute of sound, use a sample rate of 3000 samples / 60
     seconds = 50 samples/second. Because Nyquist has  no  advance  information
     about  the  warp  function,  the inverse warp function sample rate must be
     provided as a parameter.  When in doubt, just try something and  let  your
     ears be the judge.

integrate(signal)
     Computes the integral of signal. The start time,  sample  rate,  etc.  are
     taken from signal.

slope(signal)
     Computes the first derivative (slope) of signal.  The start  time,  sample
     rate, etc. are taken from signal.


7.2.2.1. Oscillators

osc(pitch, [duration, table, phase])
     Returns a sound which is the table  oscillated  at  pitch  for  the  given
     duration,  starting  with the phase (in degrees).  Defaults are:  duration
     1.0 (second), table *table*, phase 0.0.  The default value of *table* is a
     sinusoid.  Duration  is  stretched  by  *warp* and *sustain*, amplitude is
     nominally 1, but scaled by *loudness*, the start time is logical  time  0,
     transformed  by  *warp*, and the sample rate is *sound-srate*.  The effect
     of time-warping is to warp the starting and ending times only; the  signal
     has a constant unwarped frequency.  Note 1: table is a list of the form

         (sound pitch-number periodic)

     where  the  first element is a sound, the second is the pitch of the sound
     (this is not redundant, because the sound  may  represent  any  number  of
     periods),  and  the  third  element  is  T if the sound is one period of a
     periodic signal, or nil if the sound  is  a  sample  that  should  not  be
     looped.  The maximum table size is set by max_table_len in sound.h, and is
     currently set to 1,000,000.  Note 2: in the current implementation, it  is
     assumed  that  the output should be periodic.  See snd-down and snd-up for
     resampling one-shot sounds to a desired sample rate.  A future version  of
     osc  will  handle  both  cases.    Note  3:  When osc is called, memory is
     allocated for the table, and samples are copied from the sound (the  first
     element  of  the  list which is the table parameter) to the memory.  Every
     instance of osc has a private copy of the table, so the total storage  can
     become  large  in  some cases, for example in granular synthesis with many
     instances of osc. In some cases, it may make sense to use snd-flatten (see
     Section  7.1.3)  to  cause the sound to be fully realized, after which the
     osc and its table memory can  be  reclaimed  by  garbage  collection.  The
     partial  function  (see  below) does not need a private table and does not
     use much space.

partial(pitch, env)
     Returns a sinusoid at the indicated pitch; the sound is multiplied by env.
     The start time and duration are taken from env, which is of course subject
     to  transformations.    The  sample  rate  is  *sound-srate*.  The partial
     function is faster than osc.

sine(pitch, [duration])
     Returns   a  sinusoid  at  the  indicated  pitch.    The  sample  rate  is
     *sound-srate*.  This function is like osc with respect to transformations.
     The sine function is faster than osc.

hzosc(hz, [table, phase])
     Returns a sound which is the table oscillated  at  hz  starting  at  phase
     degrees.  The  default  table is *table* and the default phase is 0.0. The
     default duration is 1.0, but this is stretched as in osc (see above).  The
     hz  parameter  may be a SOUND, in which case the duration of the result is
     the duration of hz. The sample rate is *sound-srate*.

osc-saw(hz)
     Returns  a  sawtooth  waveshape at the indicated frequency (in Hertz). The
     sample rate is *sound-srate*. The hz parameter may be a sound as in  hzosc
     (see above).

osc-tri(hz)
     Returns a triangle waveshape at the indicated frequency  (in  Hertz).  The
     sample  rate is *sound-srate*. The hz parameter may be a sound as in hzosc
     (see above).

osc-pulse(hz, bias, [compare-shape])
     Returns  a square pulse with variable width at the indicated frequency (in
     Hertz). The bias parameter controls the pulse width and should be  between
     -1  and +1, giving a pulse width from 0% (always at -1) to 100% (always at
     +1). When bias is zero, a square wave is generated. Bias may be a SOUND to
     create  varying  pulse width. If bias changes rapidly, strange effects may
     occur. The optional compare-shape defaults to a hard  step  at  zero,  but
     other  shapes  may  be  used  to  achieve non-square pulses. The osc-pulse
     behavior is written in terms of other behaviors and defined  in  the  file
     nyquist.lsp using just a few lines of code. Read the code for the complete
     story.

amosc(pitch, modulation, [table, phase])
     Returns  a  sound  which  is  table  oscillated  at  pitch.  The output is
     multiplied by  modulation  for  the  duration  of  the  sound  modulation.
     osc-table  defaults  to  *table*, and phase is the starting phase (default
     0.0 degrees) within osc-table.  The sample rate is *sound-srate*.

fmosc(pitch, modulation, [table, phase])
     Returns a sound which is table oscillated at pitch plus modulation for the
     duration of the sound modulation.   osc-table  defaults  to  *table*,  and
     phase  is  the starting phase (default 0.0 degrees) within osc-table.  The
     modulation is expressed in hz, e.g. a sinusoid modulation signal  with  an
     amplitude  of  1.0  (2.0  peak to peak), will cause a +/N 1.0 hz frequency
     deviation in sound.  Negative frequencies  are  correctly  handled.    The
     sample rate is *sound-srate*.

fmfb(pitch, index, [dur])
     Returns a sound generated by feedback FM synthesis.  The  pitch  parameter
     (given  in  the usual half-step units) controls the fundamental frequency.
     The index is the amount of feedback, which may be a SOUND or a FLONUM.  If
     index  is  a  FLONUM,  dur  must  be  provided  (a  FLONUM) to specify the
     duration. Otherwise, dur  is  ignored  if  present  and  the  duration  is
     determined by that of index. The sample rate is *sound-srate*.  A sinusoid
     table is used.  If index is below  1.1,  this  generates  a  sawtooth-like
     waveform.

buzz(n, pitch, modulation)
     Returns a sound with n harmonics of equal amplitude and a total  amplitude
     of  1.0,  using a well-known function of two cosines. If n (an integer) is
     less than 1, it is set to 1. Aliasing will occur if n is too large.    The
     duration is determined by the duration of the sound modulation, which is a
     frequency modulation term expressed in Hz (see Section 7.2.2.1).  Negative
     frequencies are correctly handled.  The sample rate is *sound-srate*.

pluck(pitch, [duration,] [final-amplitude])
     Returns a sound at the given pitch created using a modified Karplus-Strong
     plucked  string  algorithm. The tone decays from an amplitude of about 1.0
     to about final-amplitude in duration seconds. The default  values  are  to
     decay to 0.001 (-60dB) in 1 second. The sample rate is *sound-srate*.

siosc(pitch, modulation, tables)
     Returns a sound constructed  by  interpolating  through  a  succession  of
     periodic  waveforms.  The  frequency  is given (in half steps) by pitch to
     which a modulation signal (in hz) is  added,  exactly  as  in  fmosc.  The
     tables  specify  a  list of waveforms as follows: (table0 time1 table2 ...
     timeN tableN), where each table is a sound representing one  period.  Each
     time  is  a  time  interval  measured  from the starting time. The time is
     scaled  by  the  nominal   duration   (computed   using   (local-to-global
     (get-sustain)))  to  get  the  actual  time. Note that this implies linear
     stretching rather than continuous timewarping of the interpolation or  the
     breakpoints.  The  waveform  is  table0 at the starting time, table1 after
     time1 (scaled as described), and so on. The duration and logical stop time
     is given by modulation. If modulation is shorter than timeN, then the full
     sequence of waveforms is not used.  If modulation is  longer  than  timeN,
     tableN is used after timeN without further interpolation.

sampler(pitch, modulation, [sample, npoints])
     Returns a sound constructed by reading a sample from beginning to end  and
     then  splicing  on  copies of the same sound from a loop point to the end.
     The pitch and modulation parameters are used as in fmosc described  above.
     The  optional  sample  (which defaults to the global variable *table* is a
     list of the form

         (sound pitch-number loop-start)
     where the first element is a sound containing the sample,  the  second  is
     the  pitch  of  the  sample, and the third element is the time of the loop
     point. If the loop point is not in the bounds of the sound, it is  set  to
     zero.    The optional npoints specifies how many points should be used for
     sample interpolation.  Currently this parameter defaults  to  2  and  only
     2-point (linear) interpolation is implemented.  It is an error to modulate
     such that the frequency is negative. Note also that the loop point may  be
     fractional.  The sample rate is *sound-srate*.


7.2.2.2. Piece-wise Approximations
  There  are  a  number  of  related behaviors for piece-wise approximations to
functions.  The simplest of these, pwl was mentioned earlier in the manual.  It
takes  a  list of breakpoints, assuming an initial point at (0, 0), and a final
value of 0.  An analogous piece-wise exponential function,  pwe,  is  provided.
Its  implicit  starting and stopping values are 1 rather than 0.  Each of these
has variants.  You can specify the initial and final values (instead of  taking
the  default).  You can specify time in intervals rather than cummulative time.
Finally, you can pass a list rather than an argument list.  This  leads  to  16
versions:

    Piece-wise Linear Functions:
        Cummulative Time:
            Default initial point at (0, 0), final value at 0:
                pwl
                pwl-list
            Explicit initial value:
                pwlv
                pwlv-list
        Relative Time:
            Default initial point at (0, 0), final value at 0:
                pwlr
                pwlr-list
            Explicit initial value:
                pwlvr
                pwlvr-list
    Piece-wise Exponential Functions:
        Cummulative Time:
            Default initial point at (0, 1), final value at 1:
                pwe
                pwe-list
            Explicit initial value:
                pwev
                pwev-list
        Relative Time:
            Default initial point at (0, 1), final value at 1:
                pwer
                pwer-list
            Explicit initial value:
                pwevr
                pwevr-list

All of these functions are implemented in terms of pwl (see nyquist.lsp for the
implementations.    There  are  infinite  opportunities  for  errors  in  these
functions:  if  you  leave  off  a data point, try to specify points in reverse
order, try to create an exponential that goes to zero or  negative  values,  or
many  other  bad  things, the behavior is not well-defined.  Nyquist should not
crash, but Nyquist does not necessarily attempt to report errors at this time.

pwl(t , l , t , l , ... t )
     1   1   2   2       n
     Creates a piece-wise linear envelope with breakpoints at (0, 0), (t , l ),
                                                                        1   1
     (t , l ), ... (t , 0).  The breakpoint times are scaled  linearly  by  the
       2   2         n
     value  of  *sustain* (if *sustain* is a SOUND, it is evaluated once at the
     starting time of the envelope).   Each  breakpoint  time  is  then  mapped
     according  to  *warp*.    The  result is a linear interpolation (unwarped)
     between the breakpoints.  The sample rate is *control-srate*.   Breakpoint
     times  are  quantized  to  the nearest sample time.  If you specify one or
     more breakpoints withing one sample period, pwl attempts to  give  a  good
     approximation   to   the  specified  function.    In  particular,  if  two
     breakpoints are simultaneous, pwl will move one of  them  to  an  adjacent
     sample,  producing  a  steepest  possible  step  in the signal.  The exact
     details of this ``breakpoint munging'' is  subject  to  change  in  future
     versions.   Please report any cases where breakpoint lists give unexpected
     behaviors.  The  author  will  try  to  apply  the  ``principle  of  least
     surprise'' to the design.  Note that the times are relative to 0; they are
     not durations of each envelope segment.

pwl-list(breakpoints)
     If  you  have  a  list  of breakpoints, you can use apply to apply the pwl
     function to the breakpoints, but if the list is  very  long  (hundreds  or
     thousands  of  points), you might get a stack overflow because XLISP has a
     fixed-size argument stack.  Instead, call pwl-list, passing one  argument,
     the list of breakpoints.

pwlv(l , t , l , t , t , ... t , l )
      1   2   2   3   3       n   n
     Creates a piece-wise linear envelope with breakpoints  at  (0,  l ),  (t ,
                                                                      1      2
     l ),  etc.,  ending with (t , l .  Otherwise, the behavior is like that of
      2                         n   n
     pwl.

pwlv-list(breakpoints)
     A version of pwlv that takes a single list of breakpoints as its argument.
     See pwl-list above for the rationale.

pwlr(i , l , i , l , ... i )
      1   1   2   2       n
     Creates a piece-wise linear envelope with breakpoints at (0, 0), (t , l ),
                                                                        1   1
     (t , l ), ... (t , 0), where t  is the sum of i  through  i .    In  other
       2   2         n             j                1           j
     words,  the  breakpoint  times  are specified in terms of intervals rather
     than cummulative time.  Otherwise, the behavior is like that of pwl.

pwlr-list(breakpoints)
     A version of pwlr that takes a single list of breakpoints as its argument.
     See pwl-list above for the rationale.

pwlvr(l , i , l , i , i , ... i , l )
       1   2   2   3   3       n   n
     Creates  a  piece-wise  linear  envelope with breakpoints at (0, l ), (t ,
                                                                       1     2
     l ), etc., ending with (t , l , where t  is the sum of i  through i .   In
      2                       n   n         j                2          j
     other  words,  the  breakpoint  times  are specified in terms of intervals
     rather than cummulative time.  Otherwise, the behavior  is  like  that  of
     pwlv.

pwlvr-list(breakpoints)
     A version of pwlvr  that  takes  a  single  list  of  breakpoints  as  its
     argument.  See pwl-list above for the rationale.

pwe(t , l , t , l , ...  t )
     1   1   2   2        n
     Creates a piece-wise exponential envelope with breakpoints at (0, 1), (t ,
                                                                             1
     l ),  (t , l ), ... (t , 1).  Exponential segments means that the ratio of
      1      2   2         n
     values from sample to sample is constant within the segment.  (The current
     implementation actually takes the log of each value, computes a piece-wise
     exponential from the points using pwl, then exponentiates  each  resulting
     sample.    A  faster  implementation  is  certainly possible!)  Breakpoint
     values (l ) must be greater  than  zero.    Otherwise,  this  function  is
              j
     similar  to  pwl,  including  stretch  by  *sustain*, mapping according to
     *warp*, sample rate based on  *control-srate*,  and  "breakpoint  munging"
     (see  pwl  described  above).    Default  initial  and final values are of
     dubious value with exponentials.  See pwev below for the function you  are
     probably looking for.

pwe-list(breakpoints)
     A version of pwe that takes a single list of breakpoints as its  argument.
     See pwl-list above for the rationale.

pwev(l , t , l , t , t , ... t , l )
      1   2   2   3   3       n   n
     Creates a piece-wise exponential envelope with  breakpoints  at  (0,  l ),
                                                                            1
     (t , l ), etc., ending with (t , l .  Otherwise, the behavior is like that
       2   2                       n   n
     of pwe.

pwev-list(breakpoints)
     A version of pwev that takes a single list of breakpoints as its argument.
     See pwl-list above for the rationale.

pwer(i , l , i , l , ... i )
      1   1   2   2       n
     Creates a piece-wise exponential envelope with breakpoints at (0, 1), (t ,
                                                                             1
     l ), (t , l ), ... (t , 1), where t  is the sum of  i   through  i .    In
      1     2   2         n             j                 1            j
     other  words,  the  breakpoint  times  are specified in terms of intervals
     rather than cummulative time.  Otherwise, the behavior  is  like  that  of
     pwe.  Consider using pwerv instead of this one.

pwer-list(breakpoints)
     A version of pwer that takes a single list of breakpoints as its argument.
     See pwl-list above for the rationale.

pwevr(l , i , l , i , i , ... i , l )
       1   2   2   3   3       n   n
     Creates a piece-wise exponential envelope with  breakpoints  at  (0,  l ),
                                                                            1
     (t , l ), etc., ending with (t , l , where t  is the sum of i  through i .
       2   2                       n   n         j                2          j
     In other words, the breakpoint times are specified in terms  of  intervals
     rather  than  cummulative  time.   Otherwise, the behavior is like that of
     pwev.  Note that this is similar to the csound GEN05 generator.  Which  is
     uglier, GEN05 or pwevr?

pwevr-list(breakpoints)
     A version of pwevr  that  takes  a  single  list  of  breakpoints  as  its
     argument.  See pwl-list above for the rationale.


7.2.2.3. Filter Behaviors

alpass(sound, decay, hz, [minhz])
     Applies an all-pass filter to sound.  This all-pass filter creates a delay
     effect  without  the  resonances  of  a comb filter. The decay time of the
     filter is given by decay.  The hz parameter must  be  a  number  or  sound
     greater  than zero.  It is used to compute delay, which is then rounded to
     the nearest integer number of samples (so  the  frequency  is  not  always
     exact.    Higher sampling rates yield better delay resolution.)  The decay
     may be a sound or a number.  In either case, it  must  also  be  positive.
     (Implementation  note:  an  exponentiation is needed to convert decay into
     the   feedback   parameter,   and   exponentiation   is   typically   more
     time-consuming than the filter operation itself.  To get high performance,
     provide decay at a low sample rate.)  The resulting sound  will  have  the
     start  time, sample rate, etc. of sound. If hz is of type SOUND, the delay
     may be time-varying. Linear interpolation  is  then  used  for  fractional
     sample  delay,  but it should be noted that linear interpolation implies a
     low-pass transfer function. Thus, this filter may behave differently  with
     a  constant SOUND than it does with a FLONUM value for hz. In addition, if
     hz is of type SOUND, then minhz is required.  The  hz  parameter  will  be
     clipped  to  be  greater  than  minhz, placing an upper bound on the delay
     buffer length.

comb(sound, decay, hz)
     Applies  a  comb filter to sound.  A comb filter emphasizes (resonates at)
     frequencies that are multiples of a hz. The decay time of the resonance is
     given  by  decay.  This is a variation on feedback-delay (see below).  The
     hz parameter must be a number greater than zero.  It is  used  to  compute
     delay,  which is then rounded to the nearest integer number of samples (so
     the frequency is not always exact.  Higher  sampling  rates  yield  better
     delay resolution.)  The decay may be a sound or a number.  In either case,
     it must also be positive.   (Implementation  note:  an  exponentiation  is
     needed  to  convert  decay into the feedback parameter for feedback-delay,
     and exponentiation  is  typically  more  time-consuming  than  the  filter
     operation  itself.  To get high performance, provide decay at a low sample
     rate.)  The resulting sound will have the start time, sample rate, etc. of
     sound.

congen(gate, risetime, falltime)
     Implements an analog synthesizer-style contour generator. The  input  gate
     normally  goes  from 0.0 to 1.0 to create an attack and from 1.0 to 0.0 to
     start a release.  During the attack (output  is  increasing),  the  output
     converges  half-way  to  gate  in  risetime (a FLONUM) seconds. During the
     decay, the half-time is falltime seconds. The  sample  rate,  start  time,
     logical  stop,  and  terminate time all come from gate. If you want a nice
     decay, be sure that the gate goes to  zero  and  stays  there  for  awhile
     before  gate  terminates,  because  congen  (and  all  Nyquist  sounds) go
     immediately to zero at termination time.  For example, you can use pwl  to
     build a pulse followed by some zero time:

         (pwl 0 1 duty 1 duty 0 1)

     Assuming  duty  is  less  than  1.0, this will be a pulse of duration duty
     followed by zero for a total duration of 1.0.

         (congen (pwl 0 1 duty 1 duty 0 1) 0.01 0.05)

     will have a duration of 1.0 because that is the termination  time  of  the
     pwl  input.  The  decaying  release  of  the  resulting  envelope  will be
     truncated to zero at time 1.0. (Since the decay is theoretically infinite,
     there  is  no  way  to  avoid  truncation,  although you could multiply by
     another envelope that smoothly truncates to zero in the  last  millisecond
     or  two  to get both an exponential decay and a smooth final transition to
     zero.)

convolve(sound, response)
     Convolves  two  signals.  The first can be any length, but the computation
     time per sample and the total  space  required  are  proportional  to  the
     length of response.

feedback-delay(sound, delay, feedback)
     Applies feedback delay to sound.  The delay must be a number (in seconds).
     It  is rounded to the nearest sample to determine the length of the delay.
     The sample rate is the maximum from sound and  feedback  (if  feedback  is
     also a sound).  The amound of feedback should be less than one to avoid an
     exponential increase in amplitude.  The start  time  and  stop  time,  and
     logical  stop time are taken from sound.  Since output is truncated at the
     stop time of sound, you may want to append some silence to sound  to  give
     the filter time to decay.

lp(sound, cutoff)
     Filters sound using a first-order Butterworth low-pass filter.  Cutoff may
     be  a  float or a signal (for time-varying filtering) and expresses hertz.
     Filter coefficients (requiring  trig  functions)  are  recomputed  at  the
     sample  rate  of  cutoff.  The resulting sample rate, start time, etc. are
     taken from sound.

tone(sound, cutoff)
     No  longer defined; use lp instead, or define it by adding (setfn tone lp)
     to your program.

hp(sound, cutoff)
     Filters  sound  using  a first-order Butterworth high-pass filter.  Cutoff
     may be a float or a signal  (for  time-varying  filtering)  and  expresses
     hertz.    Filter coefficients (requiring trig functions) are recomputed at
     the sample rate of cutoff.  This filter is an exact complement of lp.

atone(sound, cutoff)
     No longer defined; use hp instead, or define it by adding (setfn atone hp)
     to your program.

reson(sound, center, bandwidth, n)
     Apply  a  resonating  filter  to  sound  with  center frequency center (in
     hertz), which may be a float  or  a  signal.    Bandwidth  is  the  filter
     bandwidth  (in  hertz),  which  may also be a signal.  Filter coefficients
     (requiring trig functions) are recomputed at each  new  sample  of  either
     center  or  bandwidth,  and  coefficients  are not interpolated.  The last
     parameter n specifies the type of normalization as in Csound: A value of 1
     specifies  a peak amplitude response of 1.0; all frequencies other than hz
     are attenuated.  A value of 2 specifies  the  overall  RMS  value  of  the
     amplitude response is 1.0; thus filtered white noise would retain the same
     power.  A value of zero specifies no scaling.  The resulting sample  rate,
     start time, etc. are taken from sound.

One  application  of  reson is to simulate resonances in the human vocal tract.
     See demos/voice_synthesis.htmfor sample code and documentation.

areson(sound, center, bandwidth, n)
     The  areson  filter  is an exact complement of reson such that if both are
     applied to the same signal with  the  same  parameters,  the  sum  of  the
     results yeilds the original signal.

shape(signal, table, origin)
     A waveshaping function.  Use table as a function; apply  the  function  to
     each  sample  of signal to yield a new sound.  Signal should range from -1
     to +1.  Anything beyond these bounds is clipped.  Table is also  a  sound,
     but  it  is  converted  into  a  lookup  table  (similar  to  table-lookup
     oscillators).  The origin is a FLONUM and gives the time which  should  be
     considered  the  origin of table.  (This is important because table cannot
     have values at negative times, but signal will often have negative values.
     The  origin gives an offset so that you can produce suitable tables.)  The
     output at time t is:

         table(origin + clip(signal(t))

     where clip(x) = max(1, min(-1, x)).  (E.g. if table is  a  signal  defined
     over  the  interval [0, 2], then origin should be 1.0.  The value of table
     at time 1.0 will be output when the input signal is zero.)  The output has
     the same start time, sample rate, etc. as signal.  The shape function will
     also accept multichannel signals and tables.

Further discussion and examples can be  found  in  demos/distortion.htm.    The
     shape  function  is  also  used to map frequency to amplitude to achieve a
     spectral envelope for Shepard tones in demos/shepard.lsp.

biquad(signal, b0, b1, b2, a0, a1, a2)
     A  fixed-parameter biquad filter. All filter coefficients are FLONUMs. See
     also  lowpass2,  highpass2,  bandpass2,  notch2,  allpass2,   eq-lowshelf,
     eq-highshelf,  eq-band,  lowpass4,  lowpass6,  highpass4, and highpass8 in
     this section for convenient variations  based  on  the  same  filter.  The
     equations for the filter are: z  = s  + a1 * z    + a2 * z   , and y  = z 
                                    n    n         n-1         n-2       n    n
     * b0 + z    * b1 + z    * b2.
             n-1         n-2
biquad-m(signal, b0, b1, b2, a0, a1, a2)
     A  fixed-parameter  biquad filter with Matlab sign conventions for a0, a1,
     and a2. All filter coefficients are FLONUMs.

lowpass2(signal, hz, [q])
     A  fixed-parameter,  second-order  lowpass filter based on snd-biquad. The
     cutoff frequency is given by hz (a FLONUM) and an  optional  Q  factor  is
     given by q (a FLONUM).

highpass2(signal, hz, [q])
     A fixed-parameter, second-order highpass filter based on  snd-biquad.  The
     cutoff  frequency  is  given  by hz (a FLONUM) and an optional Q factor is
     given by q (a FLONUM).

bandpass2(signal, hz, [q])
     A  fixed-parameter,  second-order bandpass filter based on snd-biquad. The
     center frequency is given by hz (a FLONUM) and an  optional  Q  factor  is
     given by q (a FLONUM).

notch2(signal, hz, [q])
     A fixed-parameter, second-order notch  filter  based  on  snd-biquad.  The
     center  frequency  is  given  by hz (a FLONUM) and an optional Q factor is
     given by q (a FLONUM).

allpass2(signal, hz, [q])
     A  fixed-parameter,  second-order  allpass filter based on snd-biquad. The
     frequency is given by hz (a FLONUM) and an optional Q factor is given by q
     (a FLONUM).

eq-lowshelf(signal, hz, gain, [slope])
     A fixed-parameter, second-order bass  shelving  equalization  (EQ)  filter
     based  on  snd-biquad.  The hz parameter (a FLONUM)is the halfway point in
     the transition, and gain (a FLONUM) is the bass boost (or cut) in dB.  The
     optional slope (a FLONUM) is 1.0 by default, and response becomes peaky at
     values greater than 1.0.

eq-highshelf(signal, hz, gain, [slope])
     A  fixed-parameter,  second-order treble shelving equalization (EQ) filter
     based on snd-biquad. The hz parameter (a FLONUM)is the  halfway  point  in
     the  transition,  and  gain (a FLONUM) is the treble boost (or cut) in dB.
     The optional slope (a FLONUM) is 1.0  by  default,  and  response  becomes
     peaky at values greater than 1.0.

eq-band(signal, hz, gain, width)
     A fixed- or variable-parameter, second-order  midrange  equalization  (EQ)
     filter  based  on  snd-biquad,  snd-eqbandcv  and  snd-eqbandvvv.  The  hz
     parameter (a FLONUM) is the center frequency, gain (a FLONUM) is the boost
     (or  cut)  in  dB, and width (a FLONUM) is the half-gain width in octaves.
     Alternatively, hz, gain, and width may be SOUNDs, but they must  all  have
     the  same  sample rate, e.g. they should all run at the control rate or at
     the sample rate.

lowpass4(signal, hz)
     A  four-pole  Butterworth  lowpass  filter.  The cutoff frequency is hz (a
     FLONUM).

lowpass6(signal, hz)
     A  six-pole  Butterworth  lowpass  filter.  The  cutoff frequency is hz (a
     FLONUM).

lowpass8(signal, hz)
     An  eight-pole  Butterworth  lowpass filter. The cutoff frequency is hz (a
     FLONUM).

highpass4(signal, hz)
     A  four-pole  Butterworth  highpass  filter. The cutoff frequency is hz (a
     FLONUM).

highpass6(signal, hz)
     A  six-pole  Butterworth  highpass  filter.  The cutoff frequency is hz (a
     FLONUM).

highpass8(signal, hz)
     An  eight-pole  Butterworth highpass filter. The cutoff frequency is hz (a
     FLONUM).

tapv(sound, offset, vardelay, maxdelay)
     A  delay line with a variable position tap.  Identical to snd-tapv. See it
     for details (7.6.2).


7.2.2.4. Effects

nrev(sound, decay, mix)

jcrev(sound, decay, mix)

prcrev(sound,  decay,  mix)  These  reverbs  (nrev,  jcrev,  and  prcrev)   are
     implemented  in  STK  (running  within  Nyquist). nrev derives from Common
     Music's NRev, which consists of 6  comb  filters  followed  by  3  allpass
     filters,  a  lowpass filter, and another allpass in series followed by two
     allpass filters in parallel. jcrev is the John Chowning reverberator which
     is  based on the use of networks of simple allpass and comb delay filters.
     This reverb implements  three  series  allpass  units,  followed  by  four
     parallel  comb  filters,  and two decorrelation delay lines in parallel at
     the output. prcrev is a Perry Cook's reverberator which is  based  on  the
     Chowning/Moorer/Schroeder  reverberators  using networks of simple allpass
     and comb delay filters.  This one implements two series allpass units  and
     two   parallel   comb   filters.    The  sound  input  may  be  single  or
     multi-channel. The decay time is in seconds, and mix sets the  mixture  of
     input  sound  reverb sound, where 0.0 means input only (dry) and 1.0 means
     reverb only (wet).

stkchorus(sound, depth, freq, mix, [delay])
     Chorus implemented in STK. The input sound can be single or multi-channel.
     The FLONUM parameters depth and freq set the modulation depth from 0 to  1
     and  modulation frequency (in Hz), and mix sets the mixture of input sound
     and chorused sound, where 0.0 means input sound only (dry) and  1.0  means
     chorused  sound  only  (wet). The parameter delay is a FIXNUM representing
     the median desired delay length in samples.

pitshift(sound, shift, mix)
     A  pitch  shifter implemented in STK. The input sound, a single-channel or
     multi-channel SOUND is pitch-shifted by shift, a FLONUM ratio. A value  of
     1.0  means  no  shift.    The  parameter mix sets the mixture of input and
     shifted sounds. A value of 0.0 means input only (dry) and a value  of  1.0
     means shifted sound only (wet).


7.2.2.5. Physical Models

clarinet(step, breath-env)
     A physical model of a clarinet from STK. The step parameter  is  a  FLONUM
     that  controls  the tube length, and the breath-env (a SOUND) controls the
     air pressure and also determines the length of the  resulting  sound.  The
     breath-env signal should range from zero to one.

clarinet-freq(step, breath-env, freq-env)
     A variation of  clarinet  that  includes  a  variable  frequency  control,
     freq-env,  which  specifies frequency deviation in Hz. The duration of the
     resulting sound is the minimum duration of breath-env and freq-env.  These
     parameters may be of type FLONUM or SOUND. FLONUMs are coerced into SOUNDs
     with a nominal duration arbitrarily set to 30.

clarinet-all(step,   breath-env,    freq-env,    vibrato-freq,    vibrato-gain,
     reed-stiffness, noise)
     A variation of clarinet-freq that includes controls vibrato-freq (a FLONUM
     for  vibrato frequency in Hertz), vibrato-gain (a FLONUM for the amount of
     amplitude vibrato), reed-stiffness (a FLONUM  or  SOUND  controlling  reed
     stiffness in the clarinet model), and noise (a FLONUM or SOUND controlling
     noise amplitude in the input air pressure). The vibrato-gain is  a  number
     from  zero  to  one,  where zero indicates no vibrato, and one indicates a
     plus/minus 50% change in breath  envelope  values.  Similarly,  the  noise
     parameter  ranges from zero to one where zero means no noise and one means
     white noise with a peak amplitude of plus/minus 40% of the breath-env. The
     reed-stiffness  parameter  varies  from  zero to one.  The duration of the
     resulting  sound  is  the  minimum  duration  of   breath-env,   freq-env,
     reed-stiffness,  and noise. As with clarinet-freq, these parameters may be
     either FLONUMs or SOUNDs, and FLONUMs are coerced to sounds with a nominal
     duration of 30.

sax(step, breath-env)
     A physical model of a sax from STK. The step parameter is  a  FLONUM  that
     controls the tube length, and the breath-env controls the air pressure and
     also determines the length of the resulting sound. The  breath-env  signal
     should range from zero to one.

sax-freq(step, breath-env, freq-env)
     A variation of sax that includes a variable frequency  control,  freq-env,
     which  specifies  frequency deviation in Hz. The duration of the resulting
     sound is the minimum duration of breath-env and freq-env. These parameters
     may  be  of  type  FLONUM or SOUND. FLONUMs are coerced into SOUNDs with a
     nominal duration arbitrarily set to 30.

sax-all(step, breath-env, freq-env, vibrato-freq, vibrato-gain, reed-stiffness,
     noise, blow-pos, reed-table-offset)
     A variation of sax-freq that includes controls vibrato-freq (a FLONUM  for
     vibrato  frequency  in  Hertz),  vibrato-gain  (a FLONUM for the amount of
     amplitude vibrato), reed-stiffness (a SOUND controlling reed stiffness  in
     the  sax  model),  noise (a SOUND controlling noise amplitude in the input
     air pressure), blow-pos (a SOUND controlling the point  of  excitation  of
     the air column), and reed-table-offset (a SOUND controlling a parameter of
     the reed model). The vibrato-gain is a number from zero to one, where zero
     indicates  no vibrato, and one indicates a plus/minus 50% change in breath
     envelope values. Similarly, the noise parameter ranges from  zero  to  one
     where  zero means no noise and one means white noise with a peak amplitude
     of plus/minus 40% of the breath-env.  The  reed-stiffness,  blow-pos,  and
     reed-table-offset  parameters  all vary from zero to one.  The duration of
     the resulting sound is  the  minimum  duration  of  breath-env,  freq-env,
     reed-stiffness,  noise,  breath-env,  blow-pos,  and reed-table-offset. As
     with sax-freq, these parameters may  be  either  FLONUMs  or  SOUNDs,  and
     FLONUMs are coerced to sounds with a nominal duration of 30.

flute(step, breath-env)
     A physical model of a flute from STK.  The step parameter is a FLONUM that
     controls the tube length, and the breath-env controls the air pressure and
     also determines the starting time and length of the resulting  sound.  The
     breath-env signal should range from zero to one.

flute-freq(step, breath-env, freq-env)
     A variation of flute that includes a variable frequency control, freq-env,
     which  specifies  frequency deviation in Hz. The duration of the resulting
     sound is the minimum duration of breath-env and freq-env. These parameters
     may  be  of  type  FLONUM or SOUND. FLONUMs are coerced into SOUNDs with a
     nominal duration arbitrary set to 30.

flute-all(step, breath-env, freq-env,  vibrato-freq,  vibrato-gain,  jet-delay,
     noise)
     A variation of clarinet-freq that includes controls vibrato-freq (a FLONUM
     for  vibrato  frequency  in  Hz), vibrato-gain (a FLONUM for the amount of
     amplitude vibrato), jet-delay (a FLONUM or SOUND controlling jet delay  in
     the flute model), and noise (a FLONUM or SOUND controlling noise amplitude
     in the input air pressure). The vibrato-gain is a number from zero to  one
     where  zero means no vibrato, and one indicates a plus/minus 50% change in
     breath envelope values. Similarly, the noise parameter ranges from zero to
     one,  where  zero  means  no  noise  and one means white noise with a peak
     amplitude of plus/minus 40% of the breath-env. The jet-delay  is  a  ratio
     that  controls  a  delay  length  from  the  flute model, and therefore it
     changes the pitch of the resulting sound. A value of 0.5 will maintain the
     pitch indicated by the step parameter. The duration of the resulting sound
     is the minimum duration of breath-env,  freq-env,  jet-delay,  and  noise.
     These  parameters may be either FLONUMs or SOUNDs, and FLONUMs are coerced
     to sounds with a nominal duration of 30.

bowed(step, bowpress-env)
     A physical model of a bowed string instrument from STK. The step parameter
     is a FLONUM that controls the string length, and the bowpress-env controls
     the  bow pressure and also determines the duration of the resulting sound.
     The bowpress-env signal should range from zero to one.

bowed-freq(step, bowpress-env, freq-env)
     A variation of bowed that includes a variable frequency control, freq-env,
     which specifies frequency deviation in Hz. The duration of  the  resulting
     sound  is  the  minimum  duration  of  bowpress-env  and  freq-env.  These
     parameters may be of type FLONUM or  SOUND.    FLONUMs  are  coerced  into
     SOUNDs with a nominal duration arbitrarily set to 30s.

mandolin(step, dur, &optional detune)
     A physical model of a plucked double-string instrument from STK. The  step
     parameter  is  a  FLONUM  wich  specifies the desired pitch, dur means the
     duration of the resulting sound and detune is a FLONUM that  controls  the
     relative  detune  of  the  two  strings.  A value of 1.0 means unison. The
     default value is 4.0.  Note: body-size (see snd-mandolin does not seem  to
     work correctly, so a default value is always used by mandolin.

wg-uniform-bar(step, bowpress-env)

wg-tuned-bar(step, bowpress-env)

wg-glass-harm(step, bowpress-env)

wg-tibetan-bowl(step, bowpress-env)
     These sounds are presets for a Banded  Wave  Guide  Percussion  instrument
     implemented  in  STK.    The  parameter step is a FLONUM that controls the
     resultant pitch, and bowpress-env is a SOUND ranging from zero to one that
     controls  a  parameter  of the model. In addition, bowpress-env determines
     the duration of the resulting sound.  (Note:  The  bowpress-env  does  not
     seems influence the timbral quality of the resulting sound).

modalbar(preset, step, dur)
     A physical model of a  struck  bar  instrument  implemented  in  STK.  The
     parameter  preset  is one of 'MARIMBA, 'VIBRAPHONE, 'AGOGO, 'WOOD1, 'RESO,
     'WOOD2, 'BEATS, 'TWO-FIXED, or 'CLUMP. The parameter step is a FLONUM that
     sets the pitch, and dur is the duration.

sitar(step, dur)
     A sitar physical model implemented in STK.  The parameter step is a FLONUM
     that sets the pitch, and dur is the duration.


7.2.2.6. More Behaviors

clip(sound, peak)
     Hard limit sound to the given peak, a  positive  number.  The  samples  of
     sound  are constrained between an upper value of peak and a lower value of
     N()peak. If sound is a number, clip will return sound limited by peak.  If
     sound  is  a  multichannel  sound, clip returns a multichannel sound where
     each channel is clipped.  The result has the type, sample  rate,  starting
     time, etc. of sound.

s-abs(sound)
     A generalized absolute value function. If sound is a  SOUND,  compute  the
     absolute  value  of  each  sample.  If sound is a number, just compute the
     absolute value. If sound is a multichannel sound,  return  a  multichannel
     sound  with s-abs applied to each element. The result has the type, sample
     rate, starting time, etc. of sound.

s-sqrt(sound)
     A  generalized  square  root  function.  If  sound is a SOUND, compute the
     square root of each sample. If sound is a number, just compute the  square
     root.  If  sound is a multichannel sound, return a multichannel sound with
     s-sqrt applied to each element. The result  has  the  type,  sample  rate,
     starting  time,  etc. of sound. In taking square roots, if an input sample
     is less than zero, the corresponding output sample is zero. This  is  done
     because the square root of a negative number is undefined.

s-exp(sound)
                                                                         x
     A generalized exponential function.  If sound is a SOUND, compute  e   for
                                                              x
     each  sample  x.   If sound is a number x, just compute e .  If sound is a
     multichannel sound, return a multichannel sound with s-exp applied to each
     element.    The  result  has the type, sample rate, starting time, etc. of
     sound.

s-log(sound)
     A  generalized  natural  log function.  If sound is a SOUND, compute ln(x)
     for each sample x.  If sound is a number x, just compute ln(x).  If  sound
     is a multichannel sound, return a multichannel sound with s-log applied to
     each element.  The result has the type, sample rate, starting  time,  etc.
     of sound.  Note that the ln of 0 is undefined (some implementations return
     negative infinity), so use this function with care.

s-max(sound1, sound2)
     Compute  the  maximum  of  two functions, sound1 and sound2. This function
     also accepts numbers and multichannel sounds and returns the corresponding
     data  type. The start time of the result is the maximum of the start times
     of sound1 and sound2. The logical stop time and physical stop time of  the
     result  is  the  minimum  of  the  logical  stop  and  physical stop times
     respectively of sound1 and sound2. Note, therefore, that the result  value
     is zero except within the bounds of both input sounds.

s-min(sound1, sound2)
     Compute the minimum of two functions, sound1  and  sound2.  This  function
     also accepts numbers and multichannel sounds and returns the corresponding
     data type. The start time of the result is the maximum of the start  times
     of  sound1 and sound2. The logical stop time and physical stop time of the
     result is the  minimum  of  the  logical  stop  and  physical  stop  times
     respectively  of sound1 and sound2. Note, therefore, that the result value
     is zero except within the bounds of both input sounds.

osc-note(pitch, [duration, env, loud, table])
     Same  as osc, but osc-note multiplies the result by env.  The env may be a
     sound, or a list supplying (t  t  t  l  l  l ).  The result has  a  sample
                                  1  2  4  1  2  3
     rate of *sound-srate*.

quantize(sound, steps)
     Quantizes sound as follows: sound is multiplied by steps  and  rounded  to
     the  nearest integer. The result is then divided by steps. For example, if
     steps is 127, then a signal that ranges from -1 to +1 will be quantized to
     255  levels  (127 less than zero, 127 greater than zero, and zero itself).
     This would match the quantization Nyquist performs when writing  a  signal
     to an 8-bit audio file. The sound may be multi-channel.

ramp( [duration])
     Returns a linear ramp from 0 to 1 over  duration  (default  is  1).    The
     function  actually  reaches  1  at  duration,  and therefore has one extra
     sample, making the total duration be duration +  1/*Control-srate*.    See
     Figure   6   for   more  detail.    Ramp  is  unaffected  by  the  sustain
     transformation.  The effect of time warping is to warp  the  starting  and
     ending times only.  The ramp itself is unwarped (linear).  The sample rate
     is *control-srate*.

rms(sound, [rate, window-size])
     Computes  the  RMS of sound using a square window of size window-size. The
     result has a sample rate of rate. The default value of rate is 100 Hz, and
     the default window size is 1/rate seconds (converted to samples). The rate
     is a FLONUM and window-size is a FIXNUM.

















     Figure 6:  Ramps generated by pwl and  ramp  functions.    The    pwl
     version  ramps  toward  the  breakpoint  (1, 1), but in order to ramp
     back to zero at breakpoint (1, 0),  the  function  never  reaches  an
     amplitude    of  1.  If used at the beginning of a seq construct, the
     next sound  will begin at time 1.  The ramp version actually  reaches
     breakpoint   (1, 1); notice that it is one sample longer than the pwl
     version.  If  used in a sequence, the next  sound  after  ramp  would
     start at time 1 +  P, where P is the sample period.


recip(sound)
     A generalized reciprocal function.  If sound is a SOUND, compute  1/x  for
     each  sample  x.  If sound is a number x, just compute 1/x.  If sound is a
     multichannel sound, return a multichannel sound with recip applied to each
     element.    The  result  has the type, sample rate, starting time, etc. of
     sound.  Note that the reciprocal of 0 is undefined  (some  implementations
     return  infinity),  so use this function with care on sounds.  Division of
     sounds is accomplished by  multiplying  by  the  reciprocal.    Again,  be
     careful not to divide by zero.

s-rest( [duration])
     Create silence (zero samples) for the given duration at  the  sample  rate
     *sound-srate*.   Default duration is 1.0 sec, and the sound is transformed
     in time according to *warp*.  Note:  rest  is  a  Lisp  function  that  is
     equivalent to cdr.  Be careful to use s-rest when you need a sound!

noise( [duration])
     Generate noise with the given duration.   Duration  (default  is  1.0)  is
     transformed according to *warp*.  The sample rate is *sound-srate* and the
     amplitude is +/- *loud*.

yin(sound, minstep, maxstep, stepsize)
     Fundamental  frequency  estimation (pitch detection. Use the YIN algorithm
     to estimate the fundamental frequency of sound, which  must  be  a  SOUND.
     The  minstep,  a  FLONUM,  is the minimum frequency considered (in steps),
     maxstep, a FLONUM, is the maximum frequency  considered  (in  steps),  and
     stepsize,  a  FIXNUM, is the desired hop size.  The result is a ``stereo''
     signal, i.e. an array of two SOUNDs, both at the same sample  rate,  which
     is  approximately the sample rate of sound divided by stepsize.  The first
     SOUND consists of frequency estimates. The second sound consists of values
     that  measure  the confidence or reliability of the frequency estimate.  A
     small value (less than 0.1) indicates fairly  high  confidence.  A  larger
     value  indicates lower confidence. This number can also be thought of as a
     ratio of non-periodic power to periodic power. When the number is low,  it
     means  the  signal is highly periodic at that point in time, so the period
     estimate will be reliable.  Hint #1: See Alain  de  Cheveigne  and  Hideki
     Kawahara's  article "YIN, a Fundamental Frequency Estimator for Speech and
     Music" in the Journal of the Acoustic Society of America, April  2002  for
     details  on the yin algorithm.  Hint #2: Typically, the stepsize should be
     at least the expected  number  of  samples  in  one  period  so  that  the
     fundamental  frequency  estimates  are  calculated at a rate far below the
     sample rate of the signal. Frequency does not change rapidly and  the  yin
     algorithm is fairly slow. To optimize speed, you may want to use less than
     44.1 kHz sample rates for input sounds. Yin uses interpolation to  achieve
     potentially  fractional-sample-accurate  estimates, so higher sample rates
     do not necessarily help the algorithm and definitely  slow  it  down.  The
                              2
     computation  time  is O(n ) per estimate, where n is the number of samples
     in the longest period considered. Therefore, each increase of  minstep  by
     12  (an  octave) gives you a factor of 4 speedup, and each decrease of the
     sample rate of sound by a factor of two gives  you  another  factor  of  4
     speedup.  Finally,  the  number  of estimates is inversely proportional to
     stepsize.  Hint #3: Use snd-srate (see Section 7.1.3)  to  get  the  exact
     sample  rate of the result, which will be the sample rate of sound divided
     by stepsize.  E.g. (snd-srate (aref yin-output 0)), where yin-output is  a
     result returned by yin, will be the sample rate of the estimates.

7.3. Transformations
  These  functions  change  the  environment  that  is seen by other high-level
functions.  Note that  these  changes  are  usually  relative  to  the  current
environment.    There  are  also  ``absolute''  versions of each transformation
function, with the exception of seq, seqrep, sim, and simrep.  The ``absolute''
versions  (starting  or  ending  with  ``abs'')  do  not  look  at  the current
environment, but rather set an environment variable to a specific  value.    In
this way, sections of code can be insulated from external transformations.

abs-env(beh)
     Compute beh in the default environment.   This  is  useful  for  computing
     waveform  tables  and  signals that are ``outside'' of time.  For example,
     (at 10.0 (abs-env (my-beh))) is equivalent to (abs-env  (my-beh))  because
     abs-env forces the default environment.

at(time, beh)
     Evaluate beh with *warp* shifted by time.

at-abs(time, beh)
     Evaluate beh with *warp* shifted so that local time 0 maps to time.

continuous-control-warp(beh)
     Applies the current warp environment to the signal returned  by  beh.  The
     result  has  the  default  control  sample  rate  *control-srate*.  Linear
     interpolation is currently used. Implementation: beh  is  first  evaluated
     without  any  shifting, stretching, or warping. The result is functionally
     composed with the inverse of the environment's warp function.

continuous-sound-warp(beh)
     Applies  the  current  warp environment to the signal returned by beh. The
     result  has  the  default  sound   sample   rate   *sound-srate*.   Linear
     interpolation   is   currently   used.   See  continuous-control-warp  for
     implementation notes.

control-srate-abs(srate, beh)
     Evaluate beh with *control-srate*set to sample rate srate.  Note: there is
     no ``relative'' version of this function.

extract(start, stop, beh)
     Returns  a sound which is the portion of beh between start and stop.  Note
     that this is done relative to the current *warp*.  The result  is  shifted
     to  start according to *warp*, so normally the result will start without a
     delay of start.

extract-abs(start, stop, beh)
     Returns  a  sound  which  is  the  portion  of beh between start and stop,
     independent of the current  *warp*.    The  result  is  shifted  to  start
     according to *warp*.

loud(volume, beh)
     Evaluates beh with *loud* incremented by volume. (Recall that *loud* is in
     decibels, so increment is the proper operation.)

loud-abs(volume, beh)
     Evaluates beh with *loud* set to volume.

sound-srate-abs(srate, beh)
     Evaluate  beh with *sound-srate* set to sample rate srate.  Note: there is
     no ``relative'' version of this function.

stretch(factor, beh)
     Evaluates  beh with *warp* scaled by factor.  The effect is to ``stretch''
     the result of beh (under the current environment) by factor.  See  Chapter
     4 for more information.

stretch-abs(factor, beh)
     Evaluates beh with *warp* set to a linear time transformation  where  each
     unit  of logical time maps to factor units of real time.  The effect is to
     stretch the nominal behavior of beh (under the default global environment)
     by factor.  See Chapter 4 for more information.

sustain(factor, beh)
     Evaluates  beh  with  *sustain*  scaled  by  factor.  The  effect  is   to
     ``stretch''  the  result of beh (under the current environment) by factor;
     however, the logical stop times are not stretched. Therefore, the  overall
     duration  of a sequence is not changed, and sounds will tend to overlap if
     *sustain* is greater than one (legato) and  be  separated  by  silence  if
     *sustain* is less than one.

sustain-abs(factor, beh)
     Evaluates beh with *sustain* set to factor. (See sustain, above.)

transpose(amount, beh)
     Evaluates  beh with *transpose* shifted by amount.  The effect is relative
     transposition by amount semitones.

transpose-abs(amount, beh)
     Evaluates  beh  with  *transpose*  set  to  amount.    The  effect  is the
     transposition of the nominal pitches in  beh  (under  the  default  global
     environment) by amount.

warp(fn, beh)
     Evaluates beh with *warp* modified by fn.  The idea is that beh and fn are
     written  in  the  same time system, and fn warps that time system to local
     time.  The current environment already contains a mapping from local  time
     to  global  (real)  time.    The  value  of  *warp*  in effect when beh is
     evaluated is the functional composition of the initial *warp* with fn.

warp-abs(fn, beh)
     Evaluates  beh  with *warp* set to fn.  In other words, the current *warp*
     is ignored and not composed with fn to form the new *warp*.

7.4. Combination and Time Structure
  These  behaviors  combine  component  behaviors  into  structures,  including
sequences  (melodies),  simultaneous  sounds  (chords), and structures based on
iteration.

seq(beh , [beh , ...])
       1      2
     Evaluates  the first behavior beh  according to *time* and each successive
                                      1
     behavior at the logical-stop time of the previous one.   The  results  are
     summed  to form a sound whose logical-stop is the logical-stop of the last
     behavior in the sequence.  Each behavior  can  result  in  a  multichannel
     sound,  in  which  case,  the  logical  stop  time is considered to be the
     maximum logical stop time of any channel.  The number of channels  in  the
     result  is  the  number  of  channels  of  the  first  behavior.  If other
     behaviors return fewer  channels,  new  channels  are  created  containing
     constant  zero  signals until the required number of channels is obtained.
     If other behaviors return a simple sound rather than multichannel  sounds,
     the sound is automatically assigned to the first channel of a multichannel
     sound that is then filled out with zero  signals.    If  another  behavior
     returns  more  channels than the first behavior, the error is reported and
     the computation is stopped.  Sample rates are  converted  up  or  down  to
     match the sample rate of the first sound in a sequence.

seqrep( (var, limit) beh)
     Iteratively evaluates beh with the atom var set  with  values  from  0  to
     limit-1, inclusive.  These sounds are placed sequentially in time as if by
     seq. The symbol var is a read-only local variable to beh. Assignments  are
     not restricted or detected, but may cause a run-time error or crash.

sim( [beh , beh , ...])
         1     2
     Returns a sound which is the sum of the  given  behaviors  evaluated  with
     current value of *warp*.  If behaviors return multiple channel sounds, the
     corresponding channels are added.  If the  number  of  channels  does  not
     match,  the  result  has the maximum.  For example, if a two-channel sound
     [L, R] is added to a four-channel sound [C1, C2, C3, C4], the result is [L
     +  C1,  R  +  C2,  C3, C4].  Arguments to sim may also be numbers.  If all
     arguments are numbers, sim is equivalent  (although  slower  than)  the  +
     function.   If a number is added to a sound, snd-offset is used to add the
     number to each sample of the sound.  The result of adding a number to  two
     or  more  sounds  with  different  durations is not defined.  Use const to
     coerce a number to  a  sound  of  a  specified  duration.    An  important
     limitation  of sim is that it cannot handle hundreds of behaviors due to a
     stack size limitation in XLISP.   To  compute  hundreds  of  sounds  (e.g.
     notes) at specified times, see timed-seq, below.  See also sum below.

simrep( (var, limit) beh)
     Iteratively evaluates beh with the atom var set  with  values  from  0  to
     limit-1,  inclusive.   These sounds are then placed simultaneously in time
     as if by sim.

trigger(s, beh)
     Returns  a  sound  which  is the sum of instances of the behavior beh. One
     instance is created each time SOUND s makes a transition from less than or
     equal  to  zero to greater than zero. (If the first sample of s is greater
     than zero, an instance is created immediately.) The sample rate of  s  and
     all  behaviors  must  be  the same, and the behaviors must be (monophonic)
     SOUNDs.  This function is particularly designed to allow behaviors  to  be
     invoked in real time by making s a function of a Nyquist slider, which can
     be controlled by a graphical interface or by OSC messages. See  snd-slider
     in Section 7.6.1.

set-logical-stop(beh, time)
     Returns a sound with time as the logical stop time.

sum(a, [b, c, ...])
     Returns  the  sum  of  a,  b,  c,  ..., allowing mixed addition of sounds,
     multichannel sounds and numbers.  Identical to sim.

mult(a, [b, c, ...])
     Returns  the  product  of  a,  b, c, ..., allowing mixed multiplication of
     sounds, multichannel sounds and numbers.

diff(a, b)
     Returns the difference between a and b. This function is defined as (sum a
     (prod -1 b)).

timed-seq(score)
     Computes  sounds  from a note list or ``score.'' The score is of the form:
     `((time1 stretch1 beh1) (time2 stretch2 beh2) ...),  where  timeN  is  the
     starting  time,  stretchN is the stretch factor, and behN is the behavior.
     Note that score is normally a quoted list! The times must be in increasing
     order, and each behN is evaluated using lisp's eval, so the behN behaviors
     cannot refer to local parameters or local variables. The advantage of this
     form  over seq is that the behaviors are evaluated one-at-a-time which can
     take much less stack space and overall memory.  One  special  ``behavior''
     expression  is  interpreted  directly  by  timed-seq: (SCORE-BEGIN-END) is
     ignored, not evaluated as a function. Normally, this special  behavior  is
     placed  at  time  0  and  has two parameters: the score start time and the
     score end time. These are used in Xmusic functions. If the behavior has  a
     :pitch keyword parameter which is a list, the list represents a chord, and
     the expression is replaced by a set of behaviors, one for each note in the
     chord.    It follows that if :pitch is nil, the behavior represents a rest
     and is ignored.

7.5. Sound File Input and Output

play(sound)
     Play the sound through the DAC.  The play function writes a file and plays
     it.  The details of this are system-dependent, but play is defined in  the
     file  system.lsp.    The  variable *default-sf-dir* names a directory into
     which to save a sound file.

By default, Nyquist will try to normalize sounds  using  the  method  named  by
     *autonorm-type*,  which  is  'lookahead  by default.  The lookahead method
     precomputes and buffers *autonorm-max-samples*  samples,  finds  the  peak
     value,   and  normalizes  accordingly.  The  'previous  method  bases  the
     normalization of the current sound on  the  peak  value  of  the  (entire)
     previous  sound.  This  might  be good if you are working with long sounds
     that start rather softly. See Section 5.3 for more details.

If you want precise control over output levels, you should  turn  this  feature
     off by typing:

         (autonorm-off)

     Reenable the automatic normalization feature by typing:
         (autonorm-on)

Play  normally produces real-time output.  The default is to send audio data to
     the DAC as it is computed in addition to saving samples in  a  file.    If
     computation is slower than real-time, output will be choppy, but since the
     samples end up in a file, you can type (r) to  replay  the  stored  sound.
     Real-time playback can be disabled by:

         (sound-off)

     and reenabled by:

         (sound-on)

     Disabling real-time playback has no effect on (play-file) or (r).

play-file(filename)
     Play the contents of a sound file named by filename. The  s-read  function
     is  used  to read the file, and unless filename specifies an absolute path
     or starts with ``.'', it will be read from *default-sf-dir*.

autonorm-on()
     Enable  automatic  adjustment of a scale factor applied to sounds computed
     using the play command.

autonorm-off()
     Disable  automatic adjustment of a scale factor applied to sounds computed
     using the play command.

sound-on()
     Enable  real-time  audio  output  when  sound  is computed by the the play
     command.

sound-off()
     Disable  real-time  audio  output  when  sound is computed by the the play
     command.

s-save(expression, maxlen, filename, [format:  format,]  [mode:  mode,]  [bits:
     bits,] [swap: flag,] [play: play])
     Evaluates the expression, which should result in a sound or  an  array  of
     sounds, and writes the result to the given filename.  A FLONUM is returned
     giving the maximum absolute value of all samples written. (This is  useful
     for normalizing sounds and detecting sample overflow.) If play is not NIL,
     the sound will be output  through  the  computer's  audio  output  system.
     (:play  is  not  implemented  on  all  systems;  if it is implemented, and
     filename is NIL, then this will play  the  file  without  also  writing  a
     file.)   The latency (length of audio buffering) used to play the sound is
     0.3s by default, but see snd-set-latency.  If a multichannel sound (array)
     is written, the channels are up-sampled to the highest rate in any channel
     so that all channels have the same sample rate.   The  maximum  number  of
     samples  written  per channel is given by maxlen, which allows writing the
     initial part of a very  long  or  infinite  sound.  A  header  is  written
     according  to  format,  samples  are encoded according to mode, using bits
     bits/sample, and bytes are swapped if swap is not NIL.  Defaults for these
     are  *default-sf-format*,  *default-sf-mode*,  and  *default-sf-bits*. The
     default for swap is NIL.  The bits parameter may be 8, 16,  or  32.    The
     values for the format and mode options are described below:

  Format

snd-head-none       No header.

snd-head-AIFF       AIFF format header.

snd-head-IRCAM      IRCAM format header.

snd-head-NeXT       1024-byte  NeXT/SUN  format header followed by IRCAM header
                    ala  CMIX.    Note  that  the   NeXT/SUN   format   has   a
                    header-length  field, so it really is legal to have a large
                    header, even though the normal minimal header  is  only  24
                    bytes.    The  additional  space  leaves  room  for maximum
                    amplitudes, which can be  used  for  normalizing  floating-
                    point  soundfiles, and for other data.  Nyquist follows the
                    CMIX  convention  of  placing  an   IRCAM   format   header
                    immediately after the NeXT-style header.

snd-head-Wave       Microsoft Wave format header.

  Mode

snd-head-mode-adpcm ADPCM mode (not supported).

snd-head-mode-pcm   signed binary PCM mode.

snd-head-mode-ulaw  8-bit U-Law mode.

snd-head-mode-alaw  8-bit A-Law mode (not supported).

snd-head-mode-float 32-bit floating point mode.

snd-head-mode-upcm  unsigned binary PCM mode.

  The defaults for format, mode, and bits are as follows:

NeXT and Sun machines:
                    snd-head-NeXT, snd-head-mode-pcm, 16

SGI and Macintosh machines:
                    snd-head-AIFF, snd-head-mode-pcm, 16

s-read(filename,  [time-offset:  offset,]  [srate:    sr,] [dur: dur,] [nchans:
     chans,] [format: format,] [mode: mode,] [bits: n,] [swap: flag])
     Reads a sound from a file.  If a header is detected, the header is used to
     determine the format of the file, and header information overrides  format
     information provided by keywords (except for :time-offset and :dur).

         (s-read "mysound.snd" :srate 44100)

     specifies  a  sample  rate  of  44100  hz,  but  if  the file has a header
     specifying 22050 hz, the  resulting  sample  rate  will  be  22050.    The
     parameters are:

        - :time-offset  M the amount of time (in seconds) to skip from the
          beginning of the file.  The default is 0.0.

        - :srate M the sample rate of the samples in the file.  Default is
          *default-sf-srate* , which is normally 44100.

        - :dur  M  the  maximum  duration  in seconds to read.  Default is
          10000.

        - :nchans M the number of channels to read.  It  is  assumed  that
          samples from each channel are interleaved.  Default is 1.

        - :format  M  the header format.  See s-save for details.  Default
          is *default-sf-format*, although  this  parameter  is  currently
          ignored.

        - :mode  M  the  sample  representation,  e.g.  PCM or float.  See
          s-save for details.  Default is *default-sf-format*.

        - :bits M the number of bits per sample.  See s-save for  details.
          Default is *default-sf-bits*.

        - :swap  M  (T  or NIL) swap byte order of each sample. Default is
          NIL.

     If there is an error, for example if  :time-offset  is  greater  than  the
     length  of the file, then NIL is returned rather than a sound. Information
     about the sound is also returned by s-read through *rslt*[Since XLISP does
     not  support  multiple value returns, multiple value returns are simulated
     by having the function assign additional return values in a  list  to  the
     global  variable *rslt*. Since this is a global, it should be inspected or
     copied immediately after the function return to insure that return  values
     are  not overwritten by another function.]. The list assigned to *rslt* is
     of  the  form:  (format  channels  mode  bits  samplerate  duration  flags
     byte-offset), which are defined as follows:

        - format M the header format. See s-save for details.

        - channels M the number of channels.

        - mode  M the sample representation, e.g. PCM or float. See s-save
          for details.

        - bits M the number of bits per sample.

        - samplerate M the sample rate, expressed as a FLONUM.

        - duration M the duration of the sound, in seconds.

        - flags M The values for format, channels, mode, bits, samplerate,
          and  duration  are  initially  just  the  values  passed  in  as
          parameters or default values to s-read.  If a value is  actually
          read  from the sound file header, a flag is set.  The flags are:
          snd-head-format,  snd-head-channels,  snd-head-mode,   snd-head-
          bits, snd-head-srate, and snd-head-dur.  For example,

              (let ((flags (caddr (cddddr  *rslt*))))
                (not (zerop (logand flags snd-head-srate))))

          tells  whether  the  sample  rate was specified in the file. See
          also sf-info below.

        - byte-offset M the byte offset into the file of the first  sample
          to  be  read  (this  is  used  by  the  s-overwrite and s-add-to
          functions).

s-add-to(expression, maxlen, filename, [offset])
     Evaluates  the  expression,  which should result in a sound or an array of
     sounds, and adds the result to the given filename.  The sample rate(s)  of
     expression  must  match  those of the file.  The maximum number of samples
     written per channel is given by maxlen, which allows writing  the  initial
     part  of  a  very long or infinite sound.  If offset is specified, the new
     sound is added to the file beginning at an offset from the  beginning  (in
     seconds).    The  file  is  extended  if  necessary to accommodate the new
     addition, but if offset falls outside of the original file,  the  file  is
     not modified. (If necessary, use s-add-to to extend the file with zeros.)

s-overwrite(expression, maxlen, filename, [offset])
     Evaluates the expression, which should result in a sound or  an  array  of
     sounds, and replaces samples in the given filename.  A FLONUM is returned,
     giving the maximum absolute value  of  all  samples  written.  The  sample
     rate(s) of expression must match those of the file.  The maximum number of
     samples written per channel is given by maxlen, which allows  writing  the
     initial  part  of  a very long or infinite sound.  If offset is specified,
     the new sound is written to the file  beginning  at  an  offset  from  the
     beginning  (in  seconds). The file is extended if necessary to accommodate
     the new insert, but if offset falls outside of the original file, the file
     is  not  modified.  (If  necessary,  use  s-add-to to extend the file with
     zeros.)

sf-info(filename)
     Prints information about a sound file. The parameter filename is a string.
     The file is assumed to be in *default-sf-dir*  (see  soundfilename  below)
     unless  the  filename  begins  with  ``.''  or  ``/''. The source for this
     function is in the runtime and provides an example  of  how  to  determine
     sound file parameters.

soundfilename(name)
     Converts a string name to a soundfile name.  If name begins with ``.''  or
     ``/'',  the  name is returned without alteration.  Otherwise, a path taken
     from *default-sf-dir* is prepended to  name.    The  s-plot,  s-read,  and
     s-save functions all use soundfilename translate filenames.

s-plot(sound, n)
     Plots sound in a window.  This function was designed to run a plot program
     on  a  Unix workstation, but now is primarily used with jNyqIDE, which has
     self-contained plotting. Normally, time/value pairs in ascii  are  written
     to  points.dat and system-dependent code (or the jNyqIDE program) takes it
     from there. The data file used is:

     *default-plot-file* The file  containing  the  data  points,  defaults  to
                         "points.dat".

s-print-tree(sound)
     Prints  an  ascii  representation  of   the   internal   data   structures
     representing a sound.  This is useful for debugging Nyquist.  Identical to
     snd-print-tree.

7.6. Low-level Functions
  Nyquist includes many low-level functions that  are  used  to  implement  the
functions and behaviors described in previous sections. For completeness, these
functions are described here.  Remember that these are low-level functions that
are not intended for normal use.  Unless you are trying to understand the inner
workings of Nyquist, you can skip this section.



7.6.1. Creating Sounds
  The basic operations that create sounds are described here.

snd-const(value, t0, srate, duration)
     Returns  a  sound  with  constant  value,  starting  at  t0 with the given
     duration, at the sample rate srate.   You  might  want  to  use  pwl  (see
     Section 7.2.2.2) instead.

snd-read(filename, offset, t0, format, channels, mode, bits, swap, sr, dur)
     Loads a sound from a file with  name  filename.    Files  are  assumed  to
     consist  of a header followed by frames consisting of one sample from each
     channel.  The format specifies the type of header, but this information is
     currently  ignored.    Nyquist  looks  for  a number of header formats and
     automatically figures out which format to  read.    If  a  header  can  be
     identified,  the  header  is  first  read  from  the file.  Then, the file
     pointer is advanced by the indicated offset (in seconds).  If there is  an
     unrecognized  header,  Nyquist will assume the file has no header.  If the
     header  size  is  a  multiple  of   the   frame   size   (bytes/sample   *
     number-of-channels),  you can use offset to skip over the header.  To skip
     N bytes, use an offset of:

         (/ (float N) sr (/ bits 8) channels)

     If the header is not a multiple of the frame size, either write  a  header
     or  contact  the  author  (dannenberg@cs.cmu.edu) for assistance.  Nyquist
     will round offset to the nearest sample.  The resulting sound  will  start
     at  time t0.  If a header is found, the file will be interpreted according
     to the header information.  If no header was  found,  channels  tells  how
     many  channels  there  are, the samples are encoded according to mode, the
     sample length is bits, and sr is the sample rate.  The swap flag is  0  or
     1,  where  1  means  to  swap  sample  bytes.  The duration to be read (in
     seconds) is given by dur.  If dur is longer than the  data  in  the  file,
     then  a  shorter  duration  will  be  returned.   If the file contains one
     channel, a sound is returned.  If the file contains 2 or more channels, an
     array  of sounds is returned.  Note: you probably want to call s-read (see
     Section 7.5) instead of snd-read.  Also, see Section 7.5  for  information
     on the mode and format parameters.

snd-save(expression, maxlen, filename, format, mode, bits, swap, play)
     Evaluates the expression, which should result in a sound or  an  array  of
     sounds,  and  writes  the result to the given filename.  If a multichannel
     sound (array) is written, the channels are up-sampled to the highest  rate
     in  any  channel  so  that  all  channels  have the same sample rate.  The
     maximum number of samples written per channel is given  by  maxlen,  which
     allows writing the initial part of a very long or infinite sound. A header
     is written according to format, samples are  encoded  according  to  mode,
     using  bits  bits/sample,  and  swapping  bytes if swap is 1 (otherwise it
     should be 0).  If play is not null, the audio is played in real  time  (to
     the  extent  possible) as it is computed.  Note: you probably want to call
     s-save (see Section 7.5) instead.  The  format  and  mode  parameters  are
     described in Section 7.5.

snd-overwrite(expression,  maxlen, filename, byte-offset, mode, bits, swap, sr,
     channels)
     Evaluates  the  expression,  which should result in a sound or an array of
     sounds, and replaces samples in the given filename.  The sample rate(s) of
     expression  must match those of the file and the parameter sr. The file is
     not read to determine its format, so it is essential to specify the proper
     parameters:  byte-offset  is the offset in bytes of the first sound sample
     to be written, mode is the representation  (see  snd-save),  bits  is  the
     number  of  bits  per sample, swap is 0 or 1, where 1 means to swap sample
     bytes, sr is the sample rate, and channels is the number of  channels.  If
     these do not match the parameters for filename, it is likely that filename
     will be corrupted. Up to a maximum of maxlen samples will be  written  per
     channel.  Use  s-add-to  (in  Section  7.5  or s-overwrite (in Section 7.5
     instead of this function.

snd-coterm(s1, s2)
     Returns  a  copy  of s1, except the start time is the maximum of the start
     times of s1 and s2, and the termination time is the minimum of s1 and  s2.
     (After  the  termination time, the sound is zero as if s1 is gated by s2.)
     Some rationale follows: In order to implement s-add-to, we  need  to  read
     from  the  target sound file, add the sounds to a new sound, and overwrite
     the result back into the file.  We only want to write as many samples into
     the  file as there are samples in the new sound. However, if we are adding
     in samples read from the file, the result of a  snd-add  in  Nyquist  will
     have  the maximum duration of either sound.  Therefore, we may read to the
     end of the file.  What we need is a way  to  truncate  the  read,  but  we
     cannot  easily do that, because we do not know in advance how long the new
     sound will be. The solution is to use snd-coterm, which will allow  us  to
     truncate  the  sound  that  is  read  from  the file (s1) according to the
     duration of the new sound (s2).  When this truncated sound is added to the
     new  sound,  the  result will have only the duration of the new sound, and
     this can be used to overwrite the file.  This  function  is  used  in  the
     implementation of s-add-to, which is defined in runtime/fileio.lsp.

(snd-from-array ...)
     See page 16.

snd-white(t0, sr, d)
     Generate white noise, starting at t0, with sample rate sr, and duration d.
     You probably want to use noise (see Section 7.2.2.6).

snd-zero(t0, srate)
     Creates a sound that is zero everywhere, starts at t0, and has sample rate
     srate.  The logical stop time is immediate, i.e. also at t0.  You probably
     want to use pwl (see Section 7.2.2.2) instead.

get-slider-value(index)
     Return the current value of the slider named by index  (an  integer  index
     into  the array of sliders).  Note that this ``slider'' is just a floating
     point value in an array. Sliders can  be  changed  by  OSC  messages  (see
     osc-enable)  and  by  sending  character  sequences  to Nyquist's standard
     input. (Normally,  these  character  sequences  would  not  be  typed  but
     generated  by  the jNyqIDE interactive development environment, which runs
     Nyquist as a sub-process,  and  which  present  the  user  with  graphical
     sliders.)

snd-slider(index, t0, srate, duration)
     Create a sound controlled by the slider named by index (an  integer  index
     into  the  array  of  sliders; see get-slider-value for more information).
     The function returns a sound. Since Nyquist sounds are computed in  blocks
     of  samples,  and  each block is computed at once, each block will contain
     copies of the current slider value. To obtain  reasonable  responsiveness,
     slider sounds should have high (audio) sample rates so that the block rate
     will be reasonably high. Also, consider lowering the audio  latency  using
     snd-set-latency. To ``trigger'' a Nyquist behavior using slider input, see
     the trigger function in Section 7.4.



7.6.2. Signal Operations
  This next set of functions take sounds as arguments,  operate  on  them,  and
return a sound.

snd-abs(sound)
     Computes a new sound where each  sample  is  the  absolute  value  of  the
     corresponding sample in sound. You should probably use s-abs instead. (See
     Section 7.2.2.6.)

snd-sqrt(sound)
     Computes  a  new  sound  where  each  sample  is  the  square  root of the
     corresponding sample in sound. If a sample is negative, it is taken to  be
     zero  to  avoid  raising  a  floating point error. You should probably use
     s-sqrt instead. (See Section 7.2.2.6.)

snd-add(sound1, sound)
     Adds  two  sounds.    The  resulting  start time is the minimum of the two
     parameter start times, the logical stop time is the  maximum  of  the  two
     parameter  stop  times,  and  the  sample  rate  is the maximum of the two
     parameter sample rates.  Use sim or sum instead of  snd-add  (see  Section
     7.4).

snd-offset(sound, offset)
     Add an offset to a sound. The resulting start  time,  logical  stop  time,
     stop  time,  and  sample  rate  are  those  of sound. Use sum instead (see
     Section 7.4).

snd-avg(sound, blocksize, stepsize, operation)
     Computes  the  averages  or  peak values of blocks of samples. Each output
     sample is an average or peak of blocksize (a fixnum) adjacent samples from
     the  input  sound.    After  each  average  or peak is taken, the input is
     advanced by  stepsize,  a  fixnum  which  may  be  greater  or  less  than
     blocksize.    The  output  sample  rate  is  the sound (input) sample rate
     divided  by  stepsize.     This   function   is   useful   for   computing
     low-sample-rate  rms  or  peak  amplitude signals for input to snd-gate or
     snd-follow.    To  select  the  operation,  operation  should  be  one  of
     OP-AVERAGE  or  OP-PEAK.    (These  are  global lisp variables; the actual
     operation parameter is an  integer.)  For  RMS  computation,  see  rms  in
     Section 7.2.2.6.

snd-clip(sound, peak)
     Hard limit sound to the given peak, a  positive  number.  The  samples  of
     sound  are constrained between an upper value of peak and a lower value of
     N()peak. Use clip instead (see Section 7.2.2.6).

snd-compose(f, g)
     Compose two signals, i.e.  compute f(g(t)), where f and g are sounds. This
     function is used primarily to implement time warping, but it can  be  used
     in  other applications such as frequency modulation.  For each sample x in
     g, snd-compose looks up the value of f(x) using linear interpolation.  The
     resulting  sample rate, start time, etc. are taken from g.  The sound f is
     used  in  effect  as  a  lookup  table,  but  it  is  assumed  that  g  is
     non-decreasing,  so that f is accessed in time order.  This allows samples
     of f to be computed and discarded incrementally.  If in fact g  decreases,
     the  current  sample  of g is replaced by the previous one, forcing g into
     compliance with the non-decreasing restriction.  See also sref, shape, and
     snd-resample.

For  an extended example that uses snd-compose for variable pitch shifting, see
     demos/pitch_change.htm.

snd-tapv(sound, offset, vardelay, maxdelay)
     A  variable  delay:  sound  is  delayed  by the sum of offset (a FIXNUM or
     FLONUM) and vardelay (a SOUND).  The specified delay is adjusted to lie in
     the  range  of zero to maxdelay seconds to yield the actual delay, and the
     delay  is  implemented  using  linear  interpolation.  This  function  was
     designed  specifically  for  use  in a chorus effect: the offset is set to
     half of maxdelay, and the vardelay input is a slow sinusoid.  The  maximum
     delay is limited to maxdelay, which determines the length of a fixed-sized
     buffer.

snd-tapf(sound, offset, vardelay, maxdelay)
     A variable delay like snd-tapv except there is no linear interpolation. By
     eliminating interpolation, the output is an exact copy of the  input  with
     no  filtering  or  distortion.  On  the other hand, delays jump by samples
     causing samples to double or skip even when the delay is changed smoothly.

snd-copy(sound)
     Makes  a  copy  of sound.  Since operators always make (logical) copies of
     their sound parameters, this  function  should  never  be  needed.    This
     function is here for debugging.

snd-down(srate, sound)
     Linear interpolation of samples down to the given sample rate srate, which
     must  be  lower than the sample rate of sound.  Do not call this function.
     Nyquist performs sample-rate conversion automatically as needed.   If  you
     want to force a conversion, call force-srate (see Section 7.2.2).

snd-exp(sound)
     Compute the exponential of each sample of sound. Use  s-exp  instead  (see
     Section 7.2.2.6).

snd-follow(sound, floor, risetime, falltime, lookahead)
     An envelope follower. The basic goal of this function  is  to  generate  a
     smooth  signal  that  rides  on  the  peaks of the input signal. The usual
     objective is to produce an amplitude  envelope  given  a  low-sample  rate
     (control  rate)  signal  representing  local  RMS  measurements. The first
     argument is the input signal. The floor is the minimum output  value.  The
     risetime  is  the  time  (in  seconds)  it  takes  for  the output to rise
     (exponentially) from floor to unity (1.0) and the falltime is the time  it
     takes  for  the  output  to  fall (exponentially) from unity to floor. The
     algorithm looks ahead for peaks and will  begin  to  increase  the  output
     signal  according  to  risetime  in  anticipation of a peak. The amount of
     anticipation (in sampless) is given by lookahead.   The  algorithm  is  as
     follows:  the output value is allowed to increase according to risetime or
     decrease according to falltime. If the next input sample is in this range,
     that sample is simply output as the next output sample.  If the next input
     sample is too large, the algorithm goes back in time as far  as  necessary
     to  compute  an  envelope that rises according to risetime to meet the new
     value. The algorithm will only work backward as far as lookahead.  If that
     is  not  far enough, then there is a final forward pass computing a rising
     signal from the earliest output sample. In this case,  the  output  signal
     will  be at least momentarily less than the input signal and will continue
     to rise exponentially until it intersects the input signal. If  the  input
     signal  falls faster than indicated by falltime, the output fall rate will
     be limited by falltime, and the fall in output will stop when  the  output
     reaches  floor.  This algorithm can make two passes througth the buffer on
     sharply rising inputs, so it is not particularly fast. With short  buffers
     and  low  sample  rates  this  should  not matter. See snd-avg above for a
     function that can help to generate a low-sample-rate input for snd-follow.
     See snd-chase in Section 7.6.3 for a related filter.

snd-gate(sound, lookahead, risetime, falltime, floor, threshold)
     This function generates an exponential rise and decay intended  for  noise
     gate  implementation.  The  decay  starts  when  the  signal  drops  below
     threshold and stays there for longer than lookahead. Decay continues until
     the  value  reaches  floor,  at which point the decay stops and the output
     value is held constant. Either during the decay  or  after  the  floor  is
     reached,  if  the  signal goes above threshold, then the output value will
     rise to unity (1.0) at the point the signal crosses the threshold.  Again,
     look-ahead  is used, so the rise actually starts before the signal crosses
     the threshold. The rise is a constant-rate exponential and set so  that  a
     rise  from  floor  to  unity occurs in risetime.  Similarly, the fall is a
     constant-rate exponential such that a  fall  from  unity  to  floor  takes
     falltime.  The  result  is  delayed  by  lookahead,  so  the output is not
     actually synchronized with the input. To compensate, you should  drop  the
     initial lookahead of samples. Thus, snd-gate is not recommended for direct
     use. Use gate instead (see Section 7.1.4).

snd-inverse(signal, start, srate)
     Compute  the  function  inverse of signal, that is, compute g(t) such that
     signal(g(t)) = t.  This function assumes that signal is non-decreasing, it
     uses  linear  interpolation,  the  resulting sample rate is srate, and the
     result is shifted to have a starting time of start.  If signal  decreases,
     the  true inverse may be undefined, so we define snd-inverse operationally
     as follows: for each output time point t, scan ahead in signal  until  the
     value of signal exceeds t.  Interpolate to find an exact time point x from
     signal and output x at time t.  This function  is  intended  for  internal
     system use in implementing time warps.

snd-log(sound)
     Compute the natural logorithm of each sample of sound. Use  s-log  instead
     (see Section 7.2.2.6).

peak(expression, maxlen)
     Compute the maximum absolute value of the amplitude of a sound.  The sound
     is created by evaluating expression (as in s-save).  Only the first maxlen
     samples are evaluated. The expression is automatically quoted (peak  is  a
     macro), so do not quote this parameter.  If expression is a variable, then
     the global binding of that  variable  will  be  used.    Also,  since  the
     variable retains a reference to the sound, the sound will be evaluated and
     left in memory.  See Section 5.3 on page 10 for examples.

snd-max(expression, maxlen)
     Compute the maximum absolute value of the amplitude of a sound.  The sound
     is created by evaluating expression (as in snd-save), which  is  therefore
     normally  quoted by the caller.  At most maxlen samples are computed.  The
     result is the maximum of the absolute values of the samples.  Notes: It is
     recommended  to  use  peak  (see  above) instead.  If you want to find the
     maximum of a sound bound to a local variable and it is acceptable to  save
     the  samples  in  memory,  then  this  is  probably  the function to call.
     Otherwise, use peak.

snd-maxv(sound1, sound2)
     Compute  the maximum of sound1 and sound2 on a sample-by-sample basis. The
     resulting sound has its start time at the maximum of the input start times
     and a logical stop at the minimum logical stop of the inputs. The physical
     stop time is the minimum of the physical stop times  of  the  two  sounds.
     Note that this violates the ``normal'' interpretation that sounds are zero
     outside their start and stop times. For example, even  if  sound1  extends
     beyond sound2 and is greater than zero, the result value in this extension
     will be zero because it will be after the physical stop time,  whereas  if
     we  simply  treated sound2 as zero in this region and took the maximum, we
     would get a non-zero result. Use s-max instead (see Section 7.2.2.6).

snd-normalize(sound)
     Internally,  sounds  are  stored  with  a scale factor that applies to all
     samples of the sound.  All operators that take sound arguments  take  this
     scale  factor into account (although it is not always necessary to perform
     an actual multiply per sample), so you should  never  need  to  call  this
     function.    This  function multiplies each sample of a sound by its scale
     factor, returning a sound that represents the same signal, but whose scale
     factor is 1.0.

snd-oneshot(sound, threshold, ontime)
     Computes a new sound that is zero except where  sound  exceeds  threshold.
     From  these  points, the result is 1.0 until sound remains below threshold
     for ontime (in seconds).  The result has the same sample rate, start time,
     logical stop time, and duration as sound.

snd-prod(sound1, sound2)
     Computes the product of sound1 and sound2.  The resulting  sound  has  its
     start  time  at the maximum of the input start times and a logical stop at
     the minimum logical stop of the inputs.  Do not use this  function.    Use
     mult  or  prod instead (see Section 7.2.2).  Sample rate, start time, etc.
     are taken from sound.

snd-pwl(t0, sr, lis)
     Computes a piece-wise linear function according to the breakpoints in lis.
     The starting time is t0, and the sample rate is sr.  The  breakpoints  are
     passed  in  an  XLISP list (of type LVAL) where the list alternates sample
     numbers (FIXNUMs, computed in  samples  from  the  beginning  of  the  pwl
     function)  and  values (the value of the pwl function, given as a FLONUM).
     There is an implicit starting point of (0, 0).  The list must  contain  an
     odd  number  of  points, the omitted last value being implicitly zero (0).
     The list is assumed to be well-formed.  Do not call this  function.    Use
     pwl instead (see Section 7.2.2.2).

snd-quantize(sound, steps)
     Quantizes a sound. See Section 7.2.2.6 for details.

snd-recip(sound)
     Compute  the  reciprocal  of  each sample of sound. Use recip instead (see
     Section 7.2.2.6).

snd-resample(f, rate)
     Resample  sound  f  using high-quality interpolation, yielding a new sound
     with the specified rate. The result is scaled by 0.95  because  often,  in
     resampling,  interpolated  values  exceed  the original sample values, and
     this could lead to clipping.  The resulting start  time,  etc.  are  taken
     from f. Use resample instead.

snd-resamplev(f, rate, g)
     Compose two signals, i.e.  compute f(g(t)), where f and g are sounds.  The
     result  has  sample  rate given by rate.  At each time t (according to the
     rate), g is linearly interpolated  to  yield  an  increasing  sequence  of
     high-precision  score-time values. f is then interpolated at each value to
     yield a result sample. If in fact g decreases, the current sample of g  is
     replaced  by  the  previous  one,  forcing  g  into  compliance  with  the
     non-decreasing restriction.  The result is scaled by 0.95  because  often,
     in  resampling, interpolated values exceed the original sample values, and
     this could lead to clipping. Note that if g has a high sample  rate,  this
     may  introduce  unwanted  jitter  into  sample times. See sound-warp for a
     detailed discussion. See snd-compose for a fast,  low-quality  alternative
     to  this  function.    Normally, you should use sound-warp instead of this
     function.

snd-scale(scale, sound)
     Scales the amplitude of sound by the factor scale.  Use scale instead (see
     Section 7.2.2).

snd-shape(signal, table, origin)
     A  waveshaping function.  This is the primitive upon which shape is based.
     The snd-shape function is like shape except that signal and table must  be
     (single-channel) sounds.  Use shape instead (see Section 7.2.2.3).

snd-up(srate, sound)
     Increases sample rate by linear interpolation.  The sound is the signal to
     be  up-sampled,  and  srate  is  the output sample rate.  Do not call this
     function.    Nyquist  performs  sample-rate  conversion  automatically  as
     needed.   If you want to force a conversion, call force-srate (see Section
     7.2.2).

snd-xform(sound, sr, time, start, stop, scale)
     Makes  a copy of sound and then alters it in the following order:  (1) the
     start time (snd-t0) of the sound is shifted to  time,  (1)  the  sound  is
     stretched  as a result of setting the sample rate to sr (the start time is
     unchanged by this), (3) the sound is clipped from start to  stop,  (4)  if
     start  is greater than time, the sound is shifted shifted by time - start,
     so that the start time is time, (5) the sound is  scaled  by  scale.    An
     empty  (zero)  sound  at time will be returned if all samples are clipped.
     Normally, you  should  accomplish  all  this  using  transformations.    A
     transformation  applied  to  a sound has no effect, so use cue to create a
     transformable sound (see Section 7.2.1).

snd-yin(sound, minstep, maxstep, rate)
     Identical to yin. See Section 7.2.2.6.



7.6.3. Filters
  These are also ``Signal Operators,'' the subject of the previous section, but
there are so many  filter  functions,  they  are  documented  in  this  special
section.

  Some  filters  allow  time-varying  filter  parameters.   In these functions,
filter coefficients are calculated at the sample rate of the filter  parameter,
and coefficients are not interpolated.

snd-alpass(sound, delay, feedback)
     An all-pass filter.  This produces a repeating  echo  effect  without  the
     resonances  of  snd-delay.   The feedback should be less than one to avoid
     exponential amplitude blowup.  Delay is rounded  to  the  nearest  sample.
     You should use alpass instead (see Section 7.2.2.3).

snd-alpasscv(sound, delay, feedback)
     An all-pass filter with variable feedback.  This is just  like  snd-alpass
     except  feedback  is  a sound.  You should use alpass instead (see Section
     7.2.2.3).

snd-alpassvv(sound, delay, feedback, maxdelay)
     An  all-pass  filter  with  variable feedback and delay. This is just like
     snd-alpass  except  feedback  and  delay  are  sounds,  and  there  is  an
     additional  FLONUM  parameter,  maxdelay, that gives an upper bound on the
     value of delay. Note: delay must remain between zero and maxdelay. If not,
     results  are  undefined,  and  Nyquist  may  crash.  You should use alpass
     instead (see Section 7.2.2.3).

snd-areson(sound, hz, bw, normalization)
     A  notch  filter  modeled  after the areson unit generator in Csound.  The
     snd-areson filter is an exact complement of snd-reson such  that  if  both
     are  applied  to  the same signal with the same parameters, the sum of the
     results  yeilds  the  original  signal.    Note  that  because   of   this
     complementary  design,  the  power is not normalized as in snd-reson.  See
     snd-reson for details on normalization.  You  should  use  areson  instead
     (see Section 7.2.2.3).

snd-aresoncv(sound, hz, bw, normalization)
     This function  is  identical  to  snd-areson  except  the  bw  (bandwidth)
     parameter  is a sound.  Filter coefficients are updated at the sample rate
     of bw.  The ``cv'' suffix stands for Constant, Variable,  indicating  that
     hz  and  bw  are constant (a number) and variable (a sound), respectively.
     This naming convention is used throughout.  You should use areson  instead
     (see Section 7.2.2.3).

snd-aresonvc(sound, hz, bw, normalization)
     This function is identical to snd-areson except the hz (center  frequency)
     parameter  is a sound.  Filter coefficients are updated at the sample rate
     of hz.  You should use areson instead (see Section 7.2.2.3).

snd-aresonvv(sound, hz, bw, normalization)
     This function is identical to snd-areson except both hz (center frequency)
     and bw (bandwidth) are sounds.  Filter coefficients  are  updated  at  the
     next  sample  of  either  hz  or  bw.   You should use areson instead (see
     Section 7.2.2.3).

snd-atone(sound, hz)
     A  high-pass filter modeled after the atone unit generator in Csound.  The
     snd-atone filter is an exact complement of snd-tone such that if both  are
     applied  to  the  same  signal  with  the  same parameters, the sum of the
     results yeilds the original signal.    You  should  use  hp  instead  (see
     Section 7.2.2.3).

snd-atonev(sound, hz)
     This is just like snd-atone except that  the  hz  cutoff  frequency  is  a
     sound.    Filter  coefficients  are updated at the sample rate of hz.  You
     should use hp instead (see Section 7.2.2.3).

snd-biquad(sound, b0, b1, b2, a1, a2, z1init, z2init)
     A general second order IIR filter, where a0 is assumed to be unity. For a1
     and a2, the sign convention is opposite to that of Matlab. All  parameters
     except  the input sound are of type FLONUM. You should probably use one of
     lowpass2,  highpass2,  bandpass2,  notch2,  allpass2,   eq-lowshelf,   eq-
     highshelf, eq-band, lowpass4, lowpass6, lowpass8, highpass4, highpass6, or
     highpass8, which are all based on  snd-biquad  and  described  in  Section
     7.2.2.3.  For  completeness,  you  will  also  find  biquad  and  biquad-m
     described in that section.

snd-chase(sound, risetime, falltime)
     A  slew  rate limiter. The output ``chases'' the input at rates determined
     by risetime and falltime.  If the input changes too fast, the output  will
     lag behind the input. This is a form of lowpass filter, but it was created
     to turn hard-switching square waves into  smoother  control  signals  that
     could  be  used  for linear crossfades. If the input switches from 0 to 1,
     the output will linearly rise to 1  in  risetime  seconds.  If  the  input
     switches  from  1  to  0,  the  output will linearly fall to 0 in falltime
     seconds.  The generated slope is constant; the transition is linear;  this
     is  not  an  exponential  rise or fall.  The risetime and falltime must be
     scalar constants; complain to the author if  this  is  not  adequate.  The
     snd-chase  function  is  safe  for ordinary use. See snd-follow in Section
     7.6.2 for a related function.

snd-congen(gate, risetime, falltime)
     A  simple ``contour generator'' based on analog synthesizers.  The gate is
     a sound that normally steps from 0.0 to 1.0 at the start of an envelop and
     goes from 1.0 back to 0.0 at the beginning of the release. At each sample,
     the output converges to the input exponentially.  If gate is greater  than
     the  output,  e.g.  the  attack, then the output converges half-way to the
     output in risetime.  If the gate is less than the output, the half-time is
     falltime.     The  sample  rate,  starting  time,  logical-stop-time,  and
     terminate time are taken from gate. You should  use  congen  instead  (see
     Section 7.2.2.3.

snd-convolve(sound, response)
     Convolves sound by response using a simple O(N x M) algorithm.  The  sound
     can be any length, but the response is computed and stored in a table. The
     required compuation time per sample and total space  are  proportional  to
     the length of response. Use convolve instead (see Section 7.2.2.3).

snd-delay(sound, delay, feedback)
     Feedback delay.  The output, initially sound, is  recursively  delayed  by
     delay,  scaled  by  feedback,  and added to itself, producing an repeating
     echo effect.  The feedback should be less than one  to  avoid  exponential
     amplitude blowup.  Delay is rounded to the nearest sample.  You should use
     feedback-delay instead (see Section 7.2.2.3)

snd-delaycv(sound, delay, feedback)
     Feedback delay with variable feedback.  This is just like snd-delay except
     feedback is a sound.  You should use feedback-delay instead  (see  Section
     7.2.2.3).

snd-reson(sound, hz, bw, normalization)
     A second-order resonating (bandpass) filter with center frequency  hz  and
     bandwidth  bw,  modeled  after  the  reson  unit generator in Csound.  The
     normalization parameter must be an integer and (like in Csound)  specifies
     a  scaling  factor.    A value of 1 specifies a peak amplitude response of
     1.0; all frequencies other than hz are attenuated.  A value of 2 specifies
     the  overall  RMS  value  of  the amplitude response is 1.0; thus filtered
     white noise would retain the same power.  A value  of  zero  specifies  no
     scaling.   The result sample rate, start time, etc. are takend from sound.
     You should use reson instead (see Section 7.2.2.3).

snd-resoncv(sound, hz, bw, normalization)
     This  function is identical to snd-reson except bw (bandwidth) is a sound.
     Filter coefficients are updated at the sample rate of bw.  You should  use
     reson instead (see Section 7.2.2.3).

snd-resonvc(sound, hz, bw, normalization)
     This function is identical to snd-reson except hz (center frequency) is  a
     sound.    Filter  coefficients  are updated at the sample rate of hz.  You
     should use reson instead (see Section 7.2.2.3).

snd-resonvv(sound, hz, bw, normalization)
     This function is identical to snd-reson except botth hz (center frequency)
     and bw (bandwidth) are sounds.  Filter coefficients  are  updated  at  the
     next  sample  from  either  hz  or  bw.  You should use reson instead (see
     Section 7.2.2.3).

snd-stkchorus(sound, delay, depth, freq, mix, sr)
     A  chorus implemented in STK. The parameter delay is a FIXNUM representing
     the median desired delay length in samples. A typical value is  6000.  The
     FLONUM  parameters  depth  and freq set the modulation depth (from 0 to 1)
     and modulation frequency (in Hz), mix sets the mixture of input sound  and
     chorused  sound,  where  a value of 0.0 means input sound only (dry) and a
     value of 1.0 means chorused sound only (wet).  The  parameter  sr  is  the
     desired  sample  rate  of  the  resulting sound[This is probably a mistake
     since sample rate is implied by sound. This parameter may be removed in  a
     future release.] You should use pitshift instead (see Section 7.2.2.4).

snd-stkpitshift(sound, shift, mix, sr)
     A pitch shifter implemented in STK. The  sound  is  shifted  in  pitch  by
     shift,  a  FLONUM  representing  the shift factor. A value of 1.0 means no
     shift.  The parameter mix sets the mixture of input and shifted sounds.  A
     value of 0.0 means input only (dry) and a value of 1.0 means shifted sound
     only (wet). The sr is the desired sampling frequency.[This is  probably  a
     mistake  since  sample  rate  is  implied  by sound. This parameter may be
     removed in a future release.] You should use pitshift instead (see Section
     7.2.2.4).

snd-stkrev(rev-type, sound, decay, mix, sr)
     A reverb implemented in STK. The parameter rev-type is  a  FIXNUM  ranging
     from  zero  to two and selects the type of reverb. Zero selects NRev type,
     one selects JCRev, and two selects PRCRev. The input sound is processed by
     the  reverb  with  a  decay time in seconds (a FLONUM). The mix, a FLONUM,
     sets the mixture of dry input and reverb output.  A  value  of  0.0  means
     input  only  (dry)  and a value of 1.0 means reverb only (wet). The sample
     rate is sr[This is probably a mistake since  sample  rate  is  implied  by
     sound.  This parameter may be removed in a future release.] You should use
     nrev, jcrev or prcrev instead (see Section 7.2.2.4).

snd-tone(sound, hz)
     A  first-order recursive low-pass filter, based on the tone unit generator
     of Csound.  The hz parameter is the cutoff frequency, the response curve's
     half-power  point.    The  result sample rate, start time, etc. are takend
     from sound.  You should use lp instead (see Section 7.2.2.3).

snd-tonev(sound, hz)
     This  function  is identical to snd-tone except hz (cutoff frequency) is a
     sound.  The filter coefficients are updated at the sample rate of hz.  You
     should use lp instead (see Section 7.2.2.3).



7.6.4. Table-Lookup Oscillator Functions
  These  functions  all  use  a  sound  to  describe  one  period of a periodic
waveform.  In the current implementation, the sound samples are  copied  to  an
array (the waveform table) when the function is called.  To make a table-lookup
oscillator generate a specific  pitch,  we  need  to  have  several  pieces  of
information:

   - A  waveform  to  put  into  the  table.    This  comes from the sound
     parameter.

   - The length (in samples) of the waveform.  This is obtained by reading
     samples  (starting at the sound's start time, not necessarily at time
     zero) until the physical stop time of the sound.  (If  you  read  the
     waveform from a file or generate it with functions like sim and sine,
     then the physical and logical stop times will be the  same  and  will
     correspond  to  the  duration  you  specified, rounded to the nearest
     sample.)

   - The intrinsic sample rate of the  waveform.    This  sample  rate  is
     simply the sample rate property of sound.

   - The  pitch  of  the waveform.  This is supplied by the step parameter
     and indicates the pitch (in steps) of sound.  You might  expect  that
     the pitch would be related to the period (length) of sound, but there
     is the interesting case that synthesis based on sampling often  loops
     over  multiple periods.  This means that the fundamental frequency of
     a generated tone may be some  multiple  of  the  looping  rate.    In
     Nyquist,  you  always specify the perceived pitch of the looped sound
     if the sound is played at the sound's own sample rate.

   - The desired pitch.  This is specified by the hz  parameter  in  Hertz
     (cycles  per second) in these low-level functions.  Note that this is
     not necessarily the ``loop'' rate at  which  the  table  is  scanned.
     Instead,  Nyquist  figures  what  sample  rate  conversion  would  be
     necessary to ``transpose'' from the step which specifies the original
     pitch  of  sound to hz, which gives the desired pitch.  The mixed use
     of steps and Hertz came about because it seemed  that  sample  tables
     would  be  tagged  with  steps  (``I  sampled  a middle-C''), whereas
     frequency deviation in the fmosc function is linear, thus calling for
     a specification in Hertz.

   - The desired sample rate.  This is given by the sr parameter in Hertz.

  Other parameters common to all of these oscillator functions are:

   - t0, the starting time, and

   - phase,  the  starting  phase  in  degrees.    Note  that  if the step
     parameter indicates that the table holds more  than  one  fundamental
     period,  then  a  starting  phase  of  360  will  be different than a
     starting phase of 0.

snd-amosc(sound, step, sr, hz, t0, am, phase)
     An  oscillator  with  amplitude  modulation.    The sound am specifies the
     amplitude and the logical stop time.  The physical stop time is also  that
     of am.  You should use amosc instead (see Section 7.2.2.1).

snd-fmosc(s, step, sr, hz, t0, fm, phase)
     A Frequency Modulation oscillator.    The  sound  fm  specifies  frequency
     deviation  (in  Hertz) from hz.  You should use fmosc instead (see Section
     7.2.2.1).

(snd-fmfb t0 hz sr index dur)
     A  Feedback  FM  oscillator.  The  resulting  sound  starts  at  t0, has a
     fundamental frequency of hz, a sample rate of sr, and a  duration  of  dur
     seconds.  The index is a FLONUM that specifies the amount of feedback. You
     should use fmfb instead (see Section 7.2.2.1).

(snd-fmfbv t0 hz sr index)
     A  Feedback  FM  oscillator.  The  resulting  sound  starts  at  t0, has a
     fundamental frequency of hz, and a sample rate of sr. The index is a SOUND
     that  specifies  the  amount of feedback and determines the duration.  You
     should use fmfb instead (see Section 7.2.2.1).

snd-buzz(n, sr, hz, t0, fm)
     A buzz oscillator, which generates n harmonics of equal amplitude.  The fm
     specifies frequency deviation (in Hertz) from hz.   You  should  use  buzz
     instead (see Section 7.2.2.1).

snd-pluck(sr, hz, t0, d, final-amp)
     A  Karplus-Strong  plucked  string  oscillator  with   sample   rate   sr,
     fundamental  frequency hz, starting time t0, duration d, initial amplitude
     approximately 1.0 (not exact because the string is initialized with random
     values)  and final amplitude approximately final-amp. You should use pluck
     instead (see Section 7.2.2.1).

snd-osc(s, step, sr, hz, t0, d, phase)
     A  simple table lookup oscillator with fixed frequency.  The duration is d
     seconds.  You should use osc instead (see Section 7.2.2.1).

snd-partial(sr, hz, t0, env)
     This  is a special case of snd-amosc that generates a sinusoid starting at
     phase 0 degrees.  The env  parameter  gives  the  envelope  or  any  other
     amplitude  modulation.    You  should  use  partial  instead  (see Section
     7.2.2.1).

snd-sine(t0, hz, sr, d)
     This  is  a  special case of snd-osc that always generates a sinusoid with
     initial phase of 0 degrees.  You should  use  sine  instead  (see  Section
     7.2.2.1).

snd-siosc(tables, sr, hz, t0, fm)
     A Spectral Interpolation Oscillator with frequency modulation. The  tables
     is  a  list  of sounds and sample counts as follows: (table0 count1 table1
     ... countN tableN). The initial waveform is  given  by  table0,  which  is
     interpolated linearly to table1 over the first count1 samples. From count1
     to count2 samples, the waveform is interpolated from table1 to table2, and
     so  on.  If more than countN samples are generated, tableN is used for the
     remainder of the sound. The duration and logical stop time of the sound is
     taken  from fm, which specified frequency modulation (deviation) in Hertz.
     You should use siosc instead (see Section 7.2.2.1).



7.6.5. Physical Model Functions
  These functions perform some sort of physically-based modeling synthesis.

(snd-bandedwg freq bowpress-env preset sr)
     A  Banded  Wave  Guide  Percussion  instrument  implemented  in  STK.  The
     parameter freq is a FLONUM in Hz, bowpress-env is a SOUND that ranges from
     zero  to one, preset is a FIXNUM, and sr is the desired sample rate in Hz.
     Currently,  there  are  four  presets:  uniform-bar  (0),  tuned-bar  (1),
     glass-harmonica  (2), and tibetan-bowl (3). You should use wg-uniform-bar,
     wg-tuned-bar,  wg-glass-harm,  or  wg-tibetan-bowl  instead  (see  Section
     7.2.2.5).

snd-bowed(freq, bowpress-env, sr)
     A bowed string instrument implemented in STK. The  freq  is  a  FLONUM  in
     Hertz,  bowpress-env  is  a SOUND that ranges from z ero to one, and sr is
     the desired sample rate (a FLONUM).  You should  use  bowed  instead  (see
     Section 7.2.2.5).

snd-bowed-freq(freq, bowpress-env, freq-env, sr)
     A bowed model just like snd-bowed but with  an  additional  parameter  for
     continuous  frequency  control.  You  should  use  bowed-freq instead (see
     Section 7.2.2.5).

snd-clarinet(freq, breath-env, sr)
     A  clarinet  model  implemented  in  STK.  The  freq is a FLONUM in Hertz,
     breath-env is a SOUND that ranges from zero to one, and sr is the  desired
     sample  rate  (a  FLONUM).  You  should  use clarinet instead (see Section
     7.2.2.5).

snd-clarinet-freq(freq, breath-env, freq-env, sr)
     A  clarinet  model just like snd-clarinet but with an additional parameter
     for continuous frequency control. You  should  use  clarinet-freq  instead
     (see Section 7.2.2.5).

snd-clarinet-all(freq,   vibrato-freq,   vibrato-gain,   freq-env,  breath-env,
     reed-stiffness, noise, sr)
     A   clarinet   model  just  like  snd-clarinet-freq  but  with  additional
     parameters for vibrato generation and continuous control of reed stiffness
     and  breath  noise.  You  should  use  clarinet-all  instead  (see Section
     7.2.2.5).

snd-flute(freq, breath-env, sr)
     A flute implemented in STK. The freq is a FLONUM in Hertz, breath-env is a
     SOUND that ranges from zero to one, and sr is the desired sample  rate  (a
     FLONUM). You should use flute instead (see Section 7.2.2.5).

snd-flute-freq(freq, breath-env, freq-env, sr)
     A flute model just like snd-flute but with  an  additional  parameter  for
     continuous  frequency  control.  You  should  use  flute-freq instead (see
     Section 7.2.2.5).

snd-flute-all(freq,   vibrato-freq,   vibrato-gain,    freq-env,    breath-env,
     jet-delay, noise, sr)
     A flute model just like snd-flute-freq but with additional parameters  for
     vibrato  generation and continuous control of breath noise. You should use
     flute-all instead (see Section 7.2.2.5).

snd-mandolin(t0, freq, dur, body-size, detune, sr)
     A  plucked  double-string  instrument  model  implemented  in  STK. The t0
     parameter is the starting time (in seconds),  freq  is  a  FLONUM  in  Hz,
     body-size  and  detune are FLONUMs, and sr is the desired sample rate. You
     should use mandolin instead (see Section 7.2.2.5).

snd-modalbar(t0, freq, preset, dur, sr)
     Struck  bar  instrument  model implemented in STK. The parameter t0 is the
     starting time (in seconds), freq is a FLONUM in Hz,  preset  is  a  FIXNUM
     ranging  from  0 to 8, dur is a FLONUM that sets the duration (in seconds)
     and sr is the desired sample rate. You should use  modalbar  instead  (see
     Section 7.2.2.5).

snd-sax(freq, breath-env, sr)
     A sax model implemented in STK. The freq is a FLONUM in Hertz,  breath-env
     is a SOUND that ranges from zero to one, and sr is the desired sample rate
     (a FLONUM). You should use sax instead (see Section 7.2.2.5).

snd-sax-freq(freq, freq-env, breath-env, sr)
     A  sax  model  just  like  snd-sax  but  with  an additional parameter for
     continuous frequency control. You should use sax-freq instead (see Section
     7.2.2.5).

snd-sax-all(freq,    vibrato-freq,    vibrato-gain,    freq-env,    breath-env,
     reed-stiffness, noise, blow-pos, reed-table-offset, sr)
     A  sax  model  just  like  snd-sax-freq but with additional parameters for
     vibrato generation and continuous control of reed stiffness, breath noise,
     excitation  position,  and  reed  table  offset.    You should use sax-all
     instead (see Section 7.2.2.5).

snd-sitar(t0, freq, dur, sr)
     A  sitar  model implemented in STK. The parameter t0 is the starting time,
     freq is a FLONUM (in Hz), E dur sets the duration and  sr  is  the  sample
     rate  (in  Hz)  of  the resulting sound. You should use sitar instead (see
     Section 7.2.2.5).



7.6.6. Sequence Support Functions
  The next two functions are used to implement Nyquist's seq construct.

snd-seq(sound, closure)
     This  function  returns sound until the logical stop time of sound.  Then,
     the XLISP closure is evaluated, passing it the logical stop time of  sound
     as  a  parameter.  The closure must return a sound, which is then added to
     sound.  (An add is used so that sound can continue past its  logical  stop
     if desired.)  Do not call this function.  See seq in Section 7.4.

snd-multiseq(array, closure)
     This function is similar to  snd-seq  except  the  first  parameter  is  a
     multichannel  sound  rather  than a single sound.  A multichannel sound is
     simply an XLISP array of sounds.  An array of sounds is returned which  is
     the  sum  of  array  and another array of sounds returned by closure.  The
     closure is passed the logical stop time of the multichannel  sound,  which
     is  the  maximum  logical  stop time of any element of array.  Do not call
     this function.  See seq in Section 7.4.

  snd-trigger(s, closure)
This  is  one  of  the only ways in which a behavior instance can be created by
changes in a signal. When s (a SOUND) makes a  transition  from  less  than  or
equal  to  zero  to greater than zero, the closure, which takes a starting time
parameter, is evaluated. The closure must return a SOUND. The sum of all  these
sounds  is  returned. If there are no sounds, the result will be zero. The stop
time of the result is the maximum stop time of s and all sounds returned by the
closure.  The  sample rate of the return value is the sample rate of s, and the
sounds returned by the closure must all have that same sample rate. Do not call
this function.  See trigger in Section 7.4.

  An  implementation  note:  There  is  no  way  to  have  snd-trigger return a
multichannel sound. An alternative implementation would be a built-in  function
to  scan  ahead  in  a  sound to find the time of the next zero crossing.  This
could be combined with some LISP code similar to seq to sum up instances of the
closure. However, this would force arbitrary look-ahead and therefore would not
work with real-time inputs, which was the motivation  for  snd-trigger  in  the
first place.
8. Nyquist Globals
  There  are many global variables in Nyquist. A convention in Lisp is to place
asterisks (*) around global variables, e.g. *table*. This is only a convention,
and  the  asterisks are just like any other letter as far as variable names are
concerned. Here are some globals users should know about:

*table*             Default table used by osc and other oscillators.

*A4-Hertz*          Frequency  of  A4  in   Hertz..   Note:   you   must   call
                    (set-pitch-names)   to  recompute  pitches  after  changing
                    *A4-Hertz*.

*autonorm*          The normalization factor to be applied to  the  next  sound
                    when  *autonorm-type*  is  'previous.  See Sections 5.3 and
                    7.5.

*autonormflag*      Enables the automatic normalization  feature  of  the  play
                    command.  You  should  use (autonorm-on) and (autonorm-off)
                    rather than setting *autonormflag* directly.  See  Sections
                    5.3 and 7.5.

*autonorm-max-samples*
                    Specifies how many samples will be computed searching for a
                    peak value when *autonorm-type* is 'lookahead. See Sections
                    5.3 and 7.5.

*autonorm-previous-peak*
                    The  peak  of the previous sound generated by play. This is
                    used to compute the scale factor for the  next  sound  when
                    *autonorm-type* is 'previous. See Sections 5.3 and 7.5.

*autonorm-target*   The  target  peak  amplitude  for the autonorm feature. The
                    default value is 0.9. See Sections 5.3 and 7.5.

*autonorm-type*     Determines how the autonorm feature is  implemented.  Valid
                    values  are  'lookahead  (the  default)  and 'previous. See
                    Sections 5.3 and 7.5.

*breakenable*       Controls whether XLISP enters a break loop when an error is
                    encountered. See Section IV.14.

*control-srate*     Part  of  the  environment,  establishes the control sample
                    rate. See Section 3.1 for details.

*default-sf-bits*   The default bits-per-sample for sound files. Typically 16.

*default-sf-dir*    The default sound file directory.  Unless you give  a  full
                    path  for  a  file,  audio  files are assumed to be in this
                    directory.

*default-sf-format* The default sound file format. When you write a file,  this
                    will  be  the  default  format:  AIFF for Mac and most Unix
                    systems, NeXT for NeXT systems, and WAV for Win32.

*default-sf-srate*  The default sample rate for sound files. Typically 44100.0,
                    but often set to 22050.0 for speed in non-critical tasks.

*default-control-srate*
                    Default value for *control-srate*. This value  is  restored
                    when  you  execute (top) to pop out of a debugging session.
                    Change it by calling (set-control-srate value).

*default-sound-srate*
                    Default  value  for  *sound-srate*.  This value is restored
                    when you execute (top) to pop out of a  debugging  session.
                    Change it by calling (set-sound-srate value).

*file-separator*    The  character  that  separates directories in a path, e.g.
                    ``/'' for Unix, ``:'' for Mac, and ``\'' for Win32.    This
                    is normally set in system.lsp.

*rslt*              When  a function returns more than one value, *rslt* is set
                    to  a  list  of  the  ``extra''  values.  This  provides  a
                    make-shift version of the multiple-value-return facility in
                    Common Lisp.

*sound-srate*       Part of the environment, establishes the audio sample rate.
                    See Section 3.1 for details.

*soundenable*       Controls whether writes to a sound file will also be played
                    as audio.  Set  this  variable  by  calling  (sound-on)  or
                    (sound-off).

*tracenable*        Controls  whether XLISP prints a backtrace when an error is
                    encountered.

XLISP variables     See Section IV.14 for a list of global variables defined by
                    XLISP.

Environment variables
                    See Section 3.1 for definitions of variables  used  in  the
                    environment for behaviors. In general, you should never set
                    or access these variables directly.

Various constants   See Section 1.7 for definitions of predefined constants for
                    loudness, duration, and pitch.
9. Time/Frequency Transformation
  Nyquist  provides  functions for FFT and inverse FFT operations on streams of
audio data.  Because sounds can be of any length, but  an  FFT  operates  on  a
fixed  amount  of  data,  FFT  processing  is typically done in short blocks or
windows that move through the audio. Thus, a stream of samples is converted  in
to a sequence of FFT frames representing short-term spectra.

  Nyquist  does not have a special data type corresponding to a sequence of FFT
frames.  This would be nice, but it would  require  creating  a  large  set  of
operations  suitable  for  processing  frame  sequences.  Another approach, and
perhaps  the  most  ``pure''  would  be  to  convert  a  single  sound  into  a
multichannel sound, with one channel per bin of the FFT.

  Instead,  Nyquist  violates  its  ``pure''  functional  model  and resorts to
objects for FFT processing. A sequence of frames is  represented  by  an  XLISP
object. Whenever you send the selector :next to the object, you get back either
NIL, indicating  the  end  of  the  sequence,  or  you  get  an  array  of  FFT
coefficients.

  The  Nyquist  function snd-fft (mnemonic, isn't it?) returns one of the frame
sequence generating objects. You can pass any frame sequence generating  object
to another function, snd-ifft, and turn the sequence back into audio.

  With snd-fft and snd-ifft, you can create all sorts of interesting processes.
The main idea is to create intermediate objects that both accept  and  generate
sequences  of frames.  These objects can operate on the frames to implement the
desired spectral-domain processes. Examples of this can be found  in  the  file
fft_tutorial.htm,   which   is  part  of  the  standard  Nyquist  release.  The
documentation for snd-fft and snd-ifft follows.

snd-fft(sound, length, skip, window)
     This  function performs an FFT on the first samples in sound and returns a
     Lisp array of FLONUMs.  The function modifies  the  sound,  violating  the
     normal  rule  that  sounds are immutable in Nyquist, so it is advised that
     you copy the sound using snd-copy if there are  any  other  references  to
     sound.  The  length of the FFT is specified by length, a FIXNUM (integer).
     After each FFT, the sound is  advanced  by  skip  samples,  also  of  type
     FIXNUM.  Overlapping FFTs, where skip is less than length, are allowed. If
     window is not NIL, it must be a sound.  The first length samples of window
     are  multiplied by length samples of sound before performing the FFT. When
     there are no more samples in sound to  transform,  this  function  returns
     NIL.  The  coefficients  in  the  returned  array,  in  order,  are the DC
     coefficient, the first real, the first imaginary,  the  second  real,  the
     second  imaginary,  etc.  If  the  length  is even, the last array element
     corresponds to the real coefficient at the Nyquist frequency.

snd-ifft(time, srate, iterator, skip, window)
     This  function  performs an IFFT on a sequence of spectral frames obtained
     from iterator and returns a sound. The start time of the sound is given by
     time.  Typically,  this  would be computed by calling (local-to-global 0).
     The sample rate is given by srate. Typically, this would be *sound-srate*,
     but  it might also depend upon the sample rate of the sound from which the
     spectral frames were derived. To obtain each frame, the function sends the
     message :next to the iterator object, using XLISP's primitives for objects
     and message passing. The object should return an array in the same  format
     as obtained from snd-fft, and the object should return NIL when the end of
     the sound is reached. After each frame is  inverse  transformed  into  the
     time  domain, it is added to the resulting sound. Each successive frame is
     added with a sample offset specified by  skip  relative  to  the  previous
     frame. This must be an integer greater than zero. If window is not NIL, it
     must be  a  sound.  This  window  signal  is  multiplied  by  the  inverse
     transformed  frame  before  the  frame  is  added to the output sound. The
     length of each frame should be the same. The  length  is  implied  by  the
     array  returned  by  iterator,  so it does not appear as a parameter. This
     length is also the number of samples used from window. Extra  samples  are
     ignored,  and  window is padded with zeros if necessary, so be sure window
     is the right length. The resulting sound is computed  on  demand  as  with
     other Nyquist sounds, so :next messages are sent to iterator only when new
     frames are needed. One should be careful not to reuse or  modify  iterator
     once it is passed to snd-ifft.
10. MIDI, Adagio, and Sequences
  Nyquist  includes facilities to read and write MIDI files as well as an ASCII
text-based score representation language, Adagio. XLISP and Nyquist can be used
to  generate  MIDI files using compositional algorithms. (See also Section 13.)
A tutorial on using  the  Adadio  representation  and  MIDI  can  be  found  in
demos/midi_tutorial.htm.  The  Adagio  language  is described below. Adagio was
originally developed as part of the CMU MIDI Toolkit, which included a  program
to  record  and  play  MIDI  using  the Adagio representation. Some of the MIDI
features of Adagio may not be useful within Nyquist.

  Nyquist offers a number of different score representations, and you may  find
this  confusing.  In  general,  MIDI  files  are a common way to exchange music
performance data, especially with sequencers and score  notation  systems.  The
demos/midi_tutorial.htm  examples show how to get the most precise control when
generating MIDI data. Adagio  is  most  useful  as  a  text-based  score  entry
language,  and it is certainly more compact than Lisp expressions for MIDI-like
data. The Xmusic library (Chapter 13) is best  for  algorithmic  generation  of
music  and  score  manipulation.  There  are  functions  to convert between the
Adagio, MIDI sequence data, and Xmusic score representations.

  Adagio  is an easy-to-use, non-procedural notation for scores.    In  Adagio,
text commands are used to specify each note.  If you are new to Adagio, you may
want to glance at the examples in Section 10.3  starting  on  page  101  before
reading any further.

  A  note  is described in Adagio by a set of attributes, and any attribute not
specified is ``inherited'' from the previous line.  Attributes  may  appear  in
any  order  and  must be separated by one or more blanks.  An attribute may not
contain any blanks.  The attributes are:  time, pitch, loudness, voice  number,
duration, and articulation.

  Adagio  has  been  used  to  program  a  variety  of  hardware  and  software
synthesizers,  and  the  Adagio  compiler  can  be  easily   adapted   to   new
environments.    Although  not originally intended for MIDI, Adagio works quite
well as a representation for MIDI scores.  Adagio has been  extended  to  allow
MIDI  controller  data  such as modulation wheels, pitch bend, and volume, MIDI
program commands to change timbre, and System Exclusive messages.

  A note command in Adagio must be separated from other notes.  Usually,  notes
are  distinguished  by  writing each one on a separate line.  Notes can also be
separated by using a comma or semicolon as will be described below.

  Besides notes, there are several other types of commands:

   1. An asterisk (*)  in  column  one  (or  immediately  after  a  comma,
      semicolon,  or  space)  indicates  that  the  rest  of the line is a
      comment.  The line is ignored by Adagio, and is therefore a good way
      to insert text to be read by people.  Here are some examples:

          * This is a comment.
          T150 G4  * This is a comment too!
          T150 G4  ;* So is this.

   2. An  empty  command  (a  blank line, for example) is ignored as if it
      were a comment(To be consistent, a blank line ought to specify  zero
      attributes  and  generate a note that inherits all of its attributes
      from the previous one.  Adagio is intentionally inconsistent in this
      respect.).

   3. An exclamation point (!) in column one (or immediately after a comma
      or semicolon) indicates a special command.  A special  command  does
      not  generate  a  note.    Special commands follow the ``!'' with no
      intervening spaces and extend to the end of the line, for example:

          !TEMPO 100

   4. Control change commands are used to control  parameters  like  pitch
      bend, modulation, and program (timbre).  Control change commands can
      be specified along with notes or by  themselves.    A  command  that
      specifies  control  changes  without  specifying  a  pitch  will not
      produce a note.

  Adagio is insensitive to case, thus ``A'' is equivalent to ``a'', and you can
mix upper and lower case letters freely.

10.1. Specifying Attributes
  A  note  is  indicated by a set of attributes.  Attributes are indicated by a
string of  characters  with  no  intervening  spaces  because  spaces  separate
attributes.  The attributes are described below.
                                                 th
  The  default unit of time is a centisecond (100  's), but this can be changed
                      th
to a millisecond (1000  's) using the !MSEC command and reset  to  centiseconds
with  !CSEC  (see  Section 10.4.1).  In the descriptions below, the term ``time
unit'' will be used to mean whichever convention is currently in effect.



10.1.1. Time
  The time attribute specifies when to start the note.  A time is specified  by
a  ``T''  followed  by  a  number  representing  time  units  or  by a duration
(durations are described below).  Examples:

    T150    ** 1.5 sec (or .15 sec)
    TQ3     ** 3 quarter note's duration

If no time is specified, the default time is the sum of the time  and  duration
attributes  of  the  previous note.  (But see Section 10.1.4.) Time is measured
relative to the time of the most recent  Tempo  or  Rate  command.    (See  the
examples in Section 10.3 for some clarification of this point.)



10.1.2. Pitch
  The  pitch  attribute  specifies  what  frequency to produce.  Standard scale
pitches are named by name, using S for sharp, F for flat,  and  (optionally)  N
for  natural.   For example, C and CN represent the same pitch, as do FS and GF
(F sharp and G flat).  Note that there are no bar lines, and accidentals to not
carry forward to any other notes as in common practice notation.

  Octaves are specified by number. C4 is middle C, and B3 is a half step lower.
F5 is the top line of the treble clef, etc.  (Adagio octave  numbering  follows
the  ISO  standard, but note that this is not universal.  In particular, Yamaha
refers to middle C as C3.)  Accidentals can  go  before  or  after  the  octave
number, so FS3 and F3S have the same meaning.

  An alternate notation for pitch is Pn, where n is an integer representing the
pitch.Middle C (C4) is equivalent to P60, CS4 is P61, etc.

  If you do not specify an octave, Adagio will choose one for  you.    This  is
done  by  picking  the  octave that will make the current pitch as close to the
previous pitch as possible.  In the case of  augmented  fourths  or  diminished
fifths, there are two equally good choices.  Adagio chooses the lower octave.



10.1.3. Duration
  Duration  is  specified by a letter indicating a number of beats, followed by
one or several modifiers.  The basic duration codes are:

    W (whole, 4 beats),
    H (half, 2 beats),
    Q (quarter, 1 beat),
    I (eighth, 1/2 beat),
    S (sixteenth, 1/4 beat),
    % (thirtysecond, 1/8 beat), and
    ^ (sixtyfourth, 1/16 beat).

Note that E is a pitch, so eighth-notes use the duration code I.   The  default
tempo  is  100  beats  per  minute  (see  Section 10.1.10).  These codes may be
followed by a T (triplet), indicating a duration of 2/3 the normal.  A dot  (.)
after a duration code extends it by half to 3/2 the normal.  An integer after a
note multiplies its duration by the indicated value (the result is  still  just
one note).  Finally, a slash followed by an integer divides the duration by the
integer.  Like all  attributes,  duration  attributes  may  not  have  embedded
spaces.  Examples:

    Q    1   beat (quarter note)
    QT   2/3 beat (quarter triplet)
    W.   6   beats(dotted whole note)
    ST6  1   beat (6 sixteenth triplets)
    H5   10  beats(5 half notes)
    Q3/7 3/7 beats

                                                                      th
A  duration  may  be noted by Un, where n is an integer indicating 100  's of a
               th
second (or 1000  's), see Section 10.4.1.  For example, U25 is twenty-five time
units.

  Durations may be combined using a plus sign:

    Q+IT        ** a quarter tied to an eighth triplet
    Q/7+W+Q2/7  ** a 7th beat tied to a whole tied to 2/7th beat
    Q+U10       ** a quarter plus 10 time units



10.1.4. Next Time
  The time of the next command (the next command in the Adagio program text) is
normally the time of the current note command plus the duration of the  current
note.  This can be overridden by a field consisting of the letter N followed by
a number indicating time units, or followed by a duration as  described  above.
The next note will then start at the time of the current note plus the duration
specified after N.  If the next note has an explicit time attribute  (T),  then
the specified time will override the one based on the previous note.  Examples:

    N0      ** start the next note at the same time as this one
    N50     ** start the next note 0.5 seconds after this one
    NQT     ** start the next note 2/3 beat after the current one
    NU10+Q  ** start after 0.1 seconds plus a quarter

A  comma  has  an  effect  similar  to  N0  and is explained in Section 10.4.2.
Articulation effects such as staccato can be produced using N, but it  is  more
convenient to use the articulation attribute described in Section 10.1.6.



10.1.5. Rest
  Rests are obtained by including the field R in a note command.  The effect of
an R field is to omit the note that would otherwise occur as the result of  the
current  note  command.    In all other respects, the command is processed just
like any other line.  This means that attributes such  as  duration,  loudness,
and  pitch  can  be  specified, and anything specified will be inherited by the
note in the next command.  Normally, a rest will include just R and a duration.
The fact that a note command specifies a rest is not inherited.  For example:

    R H     ** a half (two beat) rest
    RH      ** illegal, R must be separated from H by space(s)
Because  some  synthesizers  (e.g.  a  DX7)  cannot  change  programs (presets)
rapidly, it may be  desirable  to  change  programs  in  a  rest  so  that  the
synthesizer  will  be ready to play by the end of the rest.  See Section 10.1.9
for an example.



10.1.6. Articulation
  Articulation in Adagio refers to the percentage of time a note is on relative
to  the  indicated  duration.   For example, to play a note staccato, you would
normally play the note about half  of  its  indicated  duration.    In  Adagio,
articulation  is  indicated  by  #  followed  by an integer number indicating a
percentage.  The articulation attribute does not affect the time  of  the  next
command.  This example plays two staccato quarter notes:

    C Q #50
    D

To produce overlapping notes, the articulation may be greater than 100.
Be  aware  that  overlapping  notes on the same pitch can be a problem for some
synthesizers.  The following example illustrates this potential problem:

    !TEMPO 60
    C Q #160   * starts at time 0,   ends at 1.6 sec
    D I        * starts at time 1,   ends at 1.8 sec
    C Q        * starts at time 1.5, ends at 3.1 sec?

At one beat per second (tempo 60), these three notes will start at times 0,  1,
and  1.5 seconds, respectively.  Since these notes have an articulation of 160,
each will be on 160% of its nominal duration, so the first note (C) will remain
on  until  1.6  seconds.  But the third note (another C) will start at time 1.5
seconds.  Thus, the second C  will  be  started  before  the  first  one  ends.
Depending on the synthesizer, this may cancel the first C or play a second C in
unison.  In either case, a note-off message will be sent at time  1.6  seconds.
If  this  cancels the second C, its actual duration will be 0.1 rather than 1.6
seconds as intended.  A final note-off will be sent at time 3.1 seconds.



10.1.7. Loudness
  Loudness is indicated by  an  L  followed  by  a  dynamic  marking  from  the
following:  PPP,  PP, P, MP, MF, F, FF, FFF.  Alternatively, a number from 1 to
127 may be used.  The loudness attribute is the MIDI note velocity.  (Note that
a  MIDI  velocity  of 0 means ``note-off,'' so the minimum loudness is 1.)  The
dynamicmarkings are translated into numbers as follows:

    Lppp    20                    Lmf     58
    Lpp     26                    Lf      75
    Lp      34                    Lff     98
    Lmp     44                    Lfff    127



10.1.8. Voice
  The voice attribute tells which of the 16 MIDI channels to use for the  note.
The voice attribute consists of a V followed by an integer from 1 (the default)
to 16.
There is a limit to how many notes can be played at the same time  on  a  given
voice  (MIDI  channel).    Since the limit depends upon the synthesizer, Adagio
cannot tell you when you exceed the  limit.    Similarly,  Adagio  cannot  tell
whether  your  synthesizer is set up to respond to a given channel, so there is
no guarantee that what you write will actually be heard.



10.1.9. Timbre (MIDI Program)
  A MIDI program (synthesizer preset) can be selected using the  attribute  Zn,
where  n  is the program number (from 1 to 128).  Notice that in MIDI, changing
the program on a given channel will  affect  all  notes  on  that  channel  and
possibly  others.    Adagio  treats  MIDI  program changes as a form of control
change.
For many synthesizers, you will not be able to change programs at the start  of
a  note  or  during  a  note.    Change the program during a rest instead.  For
example:

    R I Z23 V4      ** change MIDI channel 4 to program 23 during rest
    A4              ** play a note on channel 4

Check how your synthesizer  interprets  program  numbers.    For  example,  the
cartridge  programs  on  a  DX7  can  be accessed by adding 32 to the cartridge
program number.  Cartridge program number 10 is specified by Z42.
  As in MIDI, the Adagio timbre is a property of the voice (MIDI  channel),  so
the timbre will not be inherited by notes on a different channel; to change the
timbre on multiple voices (channels), you must explicitly notate each change.



10.1.10. Tempo
  The length of a beat may be changed using a Tempo command:

    !TEMPO n

where n indicates beats per minute.  The exclamation  mark  tells  Adagio  that
this  is  a  special  command  line  rather  than a note definition.  A special
command takes the place of a note specification.  No other attributes should be
written  on  a  line  with a special command.  The !TEMPO command is associated
with a time, computed as if the !TEMPO command were a note.  The time attribute
(T)  of all succeeding notes is now measured relative to the time of the !TEMPO
command.  The new tempo starts at the  !TEMPO  command  time  and  affects  all
succeeding notes.  Durations specified in time units (for example U58, N15) are
not affected by the !TEMPO command, and numerical times (for example T851)  are
computed relative to the time of the last !TEMPO command.

  The  !TEMPO  command  is  fairly clever about default durations.  If the last
duration specified before the !TEMPO command is symbolic (using one of ^,%,  S,
I,  Q,  H,  or  W  ),  then  the default duration for the node after the !TEMPO
command will be modified according to the tempo change.  Consider the following
tempo change:

    !TEMPO 60
    A4 H
    !TEMPO 120
    G

In  this  example,  the first note will last 2 seconds (2 beats at 60 beats per
minute).  The second note inherits the duration (H) from the first note, but at
120 beats per minute, the second note will last only 1 second.  If the duration
had been specified U200 (also a duration of 2 seconds), the second  note  would
also  last  2  seconds  because  the  !TEMPO  command  does not affect times or
durations specified numerically in time units.  If the duration is the sum of a
symbolic  and  a  numeric  specification, the inherited duration after a !TEMPO
command is undefined.



10.1.11. Rate
  The !RATE command scales all times including those specified in hundredths of
seconds.   A rate of 100 means no change, 200 means twice as fast, and 50 means
half as fast.  For example, to make a piece play 10% faster, you  can  add  the
following command at the beginning of the score:

    !RATE 110

!RATE and !TEMPO commands combine, so

    !RATE 200
    !TEMPO 70

will  play  70  beats  per  minute at double the normal speed, or 140 beats per
minute.  Like !TEMPO, the time of the  !RATE  command  is  added  to  the  time
attribute of all following notes up to the next !TEMPO or !RATE command.

  Two  !RATE  commands do not combine, so a !RATE command only affects the rate
until the next !RATE command.

  Although !TEMPO and !RATE can occur in the middle of  a  note  (using  N,  T,
etc.)  they  do  not  affect  a  note  already specified.  This property allows
multiple tempi to exist simultaneously (see Section 10.4.4).

10.2. Default Attributes
  If an attribute is omitted, the previous one is used  by  default  (with  the
exception of the time attribute).  The default values for the first note, which
are inherited by succeeding notes until something else is specified, are  given
below in Adagio notation:

    Time           T0
    Pitch          C4
    Duration       Q
    Articulation   #100
    Loudness       LFFF
    Voice          V1
    Tempo          !TEMPO 100
    Rate           !RATE 100

Control  changes  (including  timbre  or  MIDI program, specified by Z) have no
default value and are only sent as specified in the score.

  Important: the rules for determining when a command will play a note  are  as
follows (and this has changed slightly from previous versions):

   1. If a special (!) command or nothing is specified, e.g. a blank line,
      do not play a note.

   2. If R (for ``rest'') is specified, do not play a note.

   3. Otherwise, if a pitch is specified, do play a note.

   4. Otherwise, if no control changes (or program changes) are  specified
      (so  this  is  a  command  with  non-pitch attributes and no control
      changes), do play a note.

Another way to say this is ``Special commands and commands with  rests  (R)  do
not  play  notes.    Otherwise,  play  a  note if a pitch is specified or if no
control is specified.''

10.3. Examples
  The following plays the first two bars of  ``Happy  Birthday''.    Note  that
Adagio  knows  nothing  of bar lines, so the fact that the first note occurs on
beat 3 or that the meter is three-four is of no consequence:

    *Example 1 ** Happy Birthday tune (C major)
    !TEMPO 120
    G4 I. LF
    G4 S
    A4 Q
    G4
    C5
    B4 H

The time attribute for the first note is zero (0).  The second note will  occur
a  dotted  eighth  later,  etc.    Notice that no timbre or rate was specified.
Adagio will provide reasonable default values of 1 and 100, respectively.

  The following example plays the first four bars of an exercise from  Bartok's
Mikrokosmos  (Vol.    1,  No.    12).  An extra quarter note is inserted at the
beginning of each voice in order to allow time to change MIDI  programs.    The
right  hand  part is played on voice (MIDI channel) 1 and the left hand part on
voice 2.  Notice the specification of the time attribute to indicate that voice
2 starts at time 0.  Also, default octaves are used to reduce typing.

    *Example 2 ** Bartok
    *voice 1, right hand
    R Q Z10 V1   ** extra rest for program change
    A4 H
    B Q
    C
    D H
    C
    D Q
    C
    B
    A
    B
    C
    D
    R

    *voice 2, left hand
    T0 R Q Z15 V2   ** extra rest for program change
    G3 H
    F Q
    E
    D H
    E
    D Q
    E
    F
    G
    F
    E
    D
    R

  The  next  example  is  the  same  piece  expressed  in  a  different manner,
illustrating the interaction between the !TEMPO command and the time attribute.
Recall  that  the  time  attribute is measured relative to the time of the last
!TEMPO command:

    *Example 3 ** 4 measures in 2 sections
    !Tempo 100
    *Voice 1, Measures 1 & 2
    R Q Z10 V1
    A4 H
    B Q
    C
    D H
    C

    *Voice 2, Measures 1 & 2
    T0 R Q Z15 V2
    G3 H
    F Q
    E
    D H
    E H

    !TEMPO 100
    *Voice 1, Measures 3 & 4
    * note that Z10 is still in effect for V1
    V1 D4 Q
    C
    B
    A
    B
    C
    D
    R

    *Voice 2, Measures 3 & 4
    T0 V2 D3 Q
    E
    F
    G
    F
    E
    D
    R

  The piece is written in 4 sections.  The first plays a rest followed  by  two
measures,  starting  at time 0.  The next section changes the time back to zero
and plays two measures of the left hand part  (voice  2).    The  next  command
(!TEMPO  100) sets the tempo to 100 (it already is) and sets the reference time
to be two measures into the piece.  Therefore, the next note  (D4)  will  begin
measure  3.   The D3 that begins the last group of notes has a T0 attribute, so
it will also start at measure 3.  Notice how the !TEMPO command  can  serve  to
divide a piece into sections.

  The last example will show yet another way to express the same piece of music
using the ``Next'' attribute.  Only the first bar of music is given.

    *Example 4 ** use of the Next attribute
    !Tempo 100
    R Q Z10 V1 N0
    R Q Z15 V2

    A4 H V1 N0
    G3   V2

    B4 Q V1 N0
    F3   V2

    C4 Q V1 N0
    E3   V2

Here, each pair of lines represents two simultaneous notes.  The  N0  attribute
forces  the  second  line  to  start at the same time as the first line of each
pair.  Because of the large intervals, octave numbers (3 and 4)  are  necessary
to override the default octave for these pitches.

10.4. Advanced Features
  Beyond  the  simple  notation  described  above,  Adagio supports a number of
features.  (See also the next chapter.)



10.4.1. Time Units and Resolution
                                                                             th
  The default time unit is 10ms (ten milliseconds or one centisecond  or  100  
                                                                          th
of  a second), but it is possible to change the basic unit to 1ms, or 1000   of
a second.  The time unit can be specified by:

                                        th
    !CSEC   centisecond time units = 100  
                                         th
    !MSEC   millisecond time units = 1000  

The time unit remains in effect until the next !CSEC or !MSEC command.



10.4.2. Multiple Notes Per Line
  Notes can be separated by commas or semicolons as well as by starting  a  new
line.    A  comma is equivalent to typing N0 and starting a new line.  In other
words, the next note after a comma will start at the  same  time  as  the  note
before the comma.  In general, use commas to separate the notes of a chord.

  A semicolon is equivalent to starting a new line.  In general, use semicolons
to group notes in a melody.  Here is yet another rendition of the Bartok:

    *Example 5 ** use of semicolons
    !Tempo 100
    R Q Z10 V1
    A4 H; B Q; C; D H; C; D Q; C; B; A; B; C; D; R

    T0 R Q Z15 V2
    G3 H; F Q; E; D H; E; D Q; E; F; G; F; E; D; R

This example is similar to Example 2, except semicolons are  used.    Note  how
semicolons  make the two lines of music stand out.  The next example is similar
to Example 4, except commas are used and four bars  are  notated.    The  music
below  is treated as a sequence of 2-note chords, with each chord on a separate
line:

    *Example 6 ** use of commas
    !Tempo 100
    R Q Z10 V1, R Q Z15 V2
    A4 H V1, G3 V2
    B4 Q V1, F3 V2
    C4   V1, E3 V2
    D4 H V1, D3 V2
    C4   V1, E3 V2
    D4 Q V1, D3 V2
    C4   V1, E3 V2
    B4   V1, F3 V2
    A4   V1, G3 V2
    B4   V1, F3 V2
    C4   V1, E3 V2
    D4   V1, D3 V2
    R



10.4.3. Control Change Commands
  Any control change can be specified using the syntax ``~n(v)'',  where  n  is
the  controller  number (0 - 127), and v is the value.  In addition, Adagio has
some special syntax for some of the commonly used control  changes  (note  that
Pitch  bend,  Aftertouch,  and  MIDI  Program  Change  are technically not MIDI
control changes but have their own special message format and status bytes):

    K    Portamento switch

    M    Modulation wheel

    O    Aftertouch

    X    Volume

    Y    Pitch bend
    Z    Program Change


The letter listed beside each control function is the  Adagio  command  letter.
For example, M23 is the command for setting the modulation wheel to 23.  Except
for pitch bend, the portamento switch, and  MIDI  Program  Change,  all  values
range from 0 to 127.  Pitch bend is ``off'' or centered at 128, and has a range
from 0 to 255 (MIDI allows for more precision, but Adagio does not).   Turn  on
portamento  with  K127  and  off  with  K0.   Programs are numbered 1 to 128 to
correspond to synthesizer displays.

  About volume: Midi volume is just a control, and the Midi standard  does  not
say  what  it  means. Typically it does what the volume pedal does; that is, it
scales the amplitude in a continuously changeable fashion.  In  contrast,  Midi
velocity,  which is controlled by the L (loudness) attribute, is part of a Midi
note-on command and is fixed for the duration of the note. Typically, these two
ways  of  controlling  loudness  and  amplitude  operate independently. In some
low-cost synthesizers the numbers seem to  be  added  together  internally  and
volume changes are ignored after the note starts.

  About  pitch bend: Midi pitch bend is a number from 0 to 16383, where 8192 is
the center position. To convert to Midi, Adagio simply multiplies  your  number
by  64,  giving  values  from  0 to 16320. Note that Y128 translates exactly to
8192. The meaning of pitch bend depends upon your synthesizer and its  setting.
Most  synthesizers  let  you  specify  a  ``pitch  bend range.'' A range of one
semitone means that Y255 will produce a bend of approximately one semitone  up,
and  Y0  will  bend  one semitone down.  If the range is 12 semitones, then the
same Y255 will bend an octave. Typically, pitch bend is  exponential,  so  each
increment in the pitch bend value will bend an equal number of cents in pitch.

  Control  changes  can be part of a note specification or independent.  In the
following example, a middle C is played with a modulation wheel setting  of  50
and  a  pitch  bend  of  120.    Then,  at 10 unit intervals, the pitch bend is
decreased by 10.  The last line sets the portamento time (controller 5) to 80:

    *Example 7
    C4 LMF M50 Y120 U100 N10
    Y110 N10; Y100 N10; Y90 N10; Y80 N10
    Y70 N10; Y60 N10; Y50 N10
    ~5(80)

  See Section 10.2 on page 34 for rules on whether or not a command will play a
note.



10.4.4. Multiple Tempi
  Writing  a  piece with multiple tempi requires no new commands; you just have
to be clever in the use of Tempo and Time.    The  following  plays  a  7  note
diatonic scale on voice 1, and a 12 note chromatic scale on voice 2:

    *Example 8 ** multiple tempi
    !TEMPO 70
    V1 C4; D; E; F; G; A; B
    T0 R N0

    !TEMPO 120
    V2 C4; CS; D; DS; E; F; FS; G; GS; A; AS; B

    !TEMPO 100
    V1 C5, V2 C5

The  third  line  plays  the  7-note  diatonic scale on voice 1.  The next line
contains the tricky part:  notice that the time is set back to zero, there is a
rest,  and  a  next (N) attribute is used to specify that the next default time
will be at the same time as the current one.  This is tricky because  a  !TEMPO
command  cannot  have  a time (T0) attribute, and a T0 by itself would create a
note with a duration.  T0 R N0 says: ``go to time 0, do not play a note, and do
not  advance  the time before the next command''.  Thus, the time of the !TEMPO
120 command is zero.  After the 12 note scale, the tempo is changed to 100  and
a  final  note  is  played on each voice.  A little arithmetic will show that 7
notes at tempo 70 and 12 notes at tempo 120 each take 6 seconds, so  the  final
notes (C5) of each scale will happen at the same time.



10.4.5. MIDI Synchronization
  The  Adagio  program  (but not Nyquist) can synchronize with external devices
using MIDI real time messages. Thus, Adagio has a !CLOCK command. This  command
is currently of no use to Nyquist users but is documented here for completeness
(it's part of the language syntax even if it does not do anything).

  Since Adagio supports multiple tempi, and Midi clock is based on beats, it is
necessary  to  be  explicit in the score about where the clock should start and
what is the duration of a quarter note.  The !CLOCK command in Adagio turns  on
a 24 pulse-per-quarter (PPQ) clock at the current tempo and time:

    !TEMPO 100
    !CLOCK

A  !CLOCK  command  must  also  be inserted for each tempo change that is to be
reflected in the Midi clock.  Typically, each !TEMPO command will  be  followed
by a !CLOCK command.
Clock commands and thus tempo changes can take place at arbitrary times.  It is
                                         th
assumed that tempo changes on an exact 24   of a beat subdivision (for example,
exactly  on  a  beat).  If not, the tempo change will take place on the nearest
        th
exact 24   of a beat subdivision.  This  may  be  earlier  or  later  than  the
requested time.



10.4.6. System Exclusive Messages
  Adagio  has  a  definition  facility  that  makes  it possible to send system
exclusive parameters.  Often, there are parameters on  Midi  synthesizers  that
can  only  be controlled by system exclusive messages.  Examples include the FM
ratio and LFO rate on a DX7 synthesizer.  The following example defines a macro
for  the  DX7 LFO rate and then shows how the macro is used to set the LFO rate
for a B-flat whole note in the  score.    The  macro  definition  is  given  in
hexadecimal,  except v is replaced by the channel (voice) and %1 is replaced by
the first parameter.  A macro is invoked by writing ``~'' followed by the macro
name and a list of parameters:

    !DEF LFO F0 43 0v 01 09 %1 F7
    Bf5 W ~LFO(25)

  In  general,  the !DEF command can define any single MIDI message including a
system exclusive message.  The message must be complete (including  the  status
byte), and each !DEF must correspond to just one message.  The symbol following
!DEF can be any name consisting of alphanumeric characters.  Following the name
is  a  hexadecimal string (with optional spaces), all on one line.  Embedded in
the string may be the following special characters:

v               Insert the 4-bit voice (MIDI channel) number.  If v  occurs  in
                the  place of a high-order hexadecimal digit, replace v with 0v
                so that the channel number is always placed in the low-order  4
                bits  of a data byte.  In other words, v is padded if necessary
                to fall into the low-order bits.

%n              Insert a data byte with  the  low-order  7  bits  of  parameter
                number  n.    Parameters  are  numbered  1  through  9.  If the
                parameter value is greater than 127, the  high-order  bits  are
                discarded.

^n              Insert  a  data byte with bits 7 through 13 of parameter number
                n.  In other words, shift the value right 7 places  then  clear
                all  but  the  first  7  bits.  Note that 14-bit numbers can be
                encoded by referencing the same parameter twice;  for  example,
                %4^4 will insert the low-order followed by the high-order parts
                of parameter 4 into two successive data bytes.

  Parameters are separated by commas, but there may be no spaces.  The  maximum
number of parameters allowed is 9.  Here is an example of definitions to send a
full-resolution pitch bend command and to send a system  exclusive  command  to
change  a  DX7  parameter[My TX816 Owner's Manual gives an incorrect format for
the change parameter sysex command (according to the manual, there is  no  data
in  the  message!)   I am assuming that the data should be the last byte before
the EOX and that there is no byte count.  If you are reading this, assume  that
I have not tested this guess, nor have I tested this example.].

    * Define macro for pitch bend commands:
    !DEF bend Ev %1 ^1

    A ~bend(8192)  ** 8192 is "pitch bend off"

    * Change the LFO SPEED:
    *  SYSEX = F0, Yamaha = 43, Substatus/Channel = 1v,
    *  Group# = 01, Parameter# = 9, Data = 0-99, EOX = F7
    !DEF lfospeed F0 43 1v 01 09 %1 F7

    * now use the definitions:
    G4 ~bend(7567) N40
    ~lfospeed(30) N35




10.4.7. Control Ramps
  The  !RAMP  command  can  specify  a  smooth control change from one value to
another.  It consists of a specification of the starting and ending  values  of
some control change, a duration specifying how often to send a new value, and a
duration specifying the total length of the ramp.

    !RAMP X10 X100 Q W2
    !RAMP ~23(10) ~23(50) U20 W
    !RAMP ~lfo(15) ~lfo(35) U10

The first line says to ramp the volume control (controller number 7) from 10 to
100,  changing  at  each quarter note for the duration of two whole notes.  The
second line says to ramp controller number  23  from  value  10  to  value  50,
sending a new control change message every 20 time units.  The overall duration
of the ramp should be equivalent to a whole note (W).  As shown  in  the  third
line, even system exclusive messages controlled by parameters can be specified.
If the system exclusive message has more than one parameter, only one parameter
may be ``ramped''; the others must remain the same.  For example, the following
would ramp the second parameter:

    !RAMP ~mysysex(4,23,75) ~mysysex(4,100,75) U10 W

A rather curious and extreme use of macros and  ramps  is  illustrated  in  the
following example.  The noteon macro starts a note, and noteoff ends it.  Ramps
can now be used to emit a series of notes with changing pitches or  velocities.
Since  Adagio  has  no idea that these macros are turning on notes, it is up to
the programmer to turn them off!

    !DEF noteon 9v %1 %2
    !DEF noteoff 8v %1 %2
    ~noteon(48,125)
    ~noteoff(48,126)
    * turn on some notes
    !RAMP ~noteon(36,125) ~noteon(60,125) Q W NW
    * turn them off
    !RAMP ~noteoff(60,50) ~noteoff(36,50) Q W NW



10.4.8. The !End Command
  The special command !END marks the end of a score.  Everything beyond that is
ignored, for example:

    * this is a score
    C; D; E; F; G W
    !END
    since the score has ended, this text will be ignored



10.4.9. Calling C Routines
  It  is  possible  to  call  C  routines  from within Adagio scores when using
specially linked versions, but this feature is disabled in Nyquist. The  syntax
is described here for completeness.

  The  !CALL  command  calls  a  C  routine  that  can in turn invoke a complex
sequence of operations.  Below is a  call  to  a  trill  routine,  which  is  a
standard  routine  in  Adagio.  The parameters are the base pitch of the trill,
the total duration of the trill, the interval in  semitones,  the  duration  of
each  note of the trill, and the loudness.  Notice that both numbers and Adagio
notation can be used as parameters:

    !CALL trill(A5,W,2,S,Lmf)  T278 V1

The parameter list should have no  spaces,  and  parameters  are  separated  by
commas.  Following the close parenthesis, you may specify other attributes such
as the starting time and voice as shown in the example above.

  A parameter may be an Adagio pitch  specification,  an  Adagio  duration,  an
Adagio loudness, a number, or an ASCII character within single quotes, e.g. 'a'
is equivalent to 97 because 97 is the decimal encoding of ``a'' in ASCII.

  The !CALL may be followed by a limited set of attributes.    These  are  time
(T), voice (V), and next time (N).  The !CALL is made at the current time if no
time is specified, and the time of the next adagio command is the time  of  the
!CALL unless a next time is specified.  In other words, the default is N0.



10.4.10. Setting C Variables
  In  addition  to calling C routines, there is another way in which scores can
communicate with C. As with !CALL, specific C code must be linked before  these
commands  can be used, and this is not supported in Nyquist.  The !SETI command
sets an integer variable to a value, and the !SETV command sets an  element  of
an  integer  array.   For example, the next line sets the variable delay to 200
and sets transposition[5] to -4 at time 200:

    !SETI delay 200
    !SETV transposition 5 -4  T200

As  with  the  !CALL  command,  these  commands  perform  their  operations  at
particular  times  according to their place in the Adagio score.  This makes it
very easy to implement time-varying parameters that control various aspects  of
an interactive music system.
11. Linear Prediction Analysis and Synthesis
  Nyquist provides functions to perform Linear Prediction Coding (LPC) analysis
and synthesis. In simple terms, LPC analysis assumes that a sound is the result
of an all-pole filter applied to a source with a flat spectrum. LPC is good for
characterizing  the  general  spectral  shape  of  a  signal,  which   may   be
time-varying  as  in speech sounds.  For synthesis, any source can be filtered,
allowing the general spectral shape of one signal  (used  in  analysis)  to  be
applied  to  any  source  (used  in  synthesis).  A  popular  effect is to give
vowel-like spectra to musical  tones,  creating  an  artificial  (or  sometimes
natural) singing voice.

  Examples   of   LPC   analysis  and  synthesis  can  be  found  in  the  file
lpc_tutorial.htm, which is part of the standard Nyquist release.

  As with FFT processing, LPC analysis takes a sound as  input  and  returns  a
stream  of  frames. Frames are returned from an object using the :next selector
just as with FFT frames. An LPC frame is a  list  consisting  of:    RMS1,  the
energy  of  the input signal, RMS2, the energy of the residual signal, ERR, the
square root of RMS1/RMS2, and FILTER-COEFS, an array of filter coefficients. To
make  code  more readable and to avoid code dependence on the exact format of a
frame,  the  functions  lpc-frame-rms1,  lpc-frame-rms2,   lpc-frame-err,   and
lpc-frame-filter-coefs  can  be  applied  to  a  frame to obtain the respective
fields.

  The z transform of the filter is H(z) = 1/A(z), where A(z) is a polynomial of
the  form A(z) = 1 + a z + a z + ... + a z. The FILTER-COEFS array has the form
                      1     2           p
#(a  a    ... a  a  a ).
   p  p-1      3  2  1
  The file lpc.lsp defines some useful classes and functions. The file  is  not
automatically  loaded  with  Nyquist,  so  you must execute (load "lpc") before
using them.

11.1. LPC Classes and Functions

make-lpanal-iterator(sound, framedur, skiptime, npoles)
     Makes  an  iterator  object, an instance of lpanal-class, that returns LPC
     frames from successive frames  of  samples  in  sound.  The  duration  (in
     seconds)  of  each frame is given by framedur, a FLONUM. The skip size (in
     seconds) between successive frames is given by skiptime, a FLONUM. Typical
     values  for  framedur and skiptime are 0.08 and 0.04, giving 25 frames per
     second and a 50% frame overlap. The number of poles is given by npoles,  a
     FIXNUM.  The  result  is  an object that responds to the :next selector by
     returning  a  frame  as  described  above.  NIL  is  returned  when  sound
     terminates.    (Note  that one or more of the last analysis windows may be
     padded with zeros. NIL is only  returned  when  the  corresponding  window
     would begin after the termination time of the sound.)

make-lpc-file-iterator(filename)
     Another way to get LPC frames is to read them from a file.  This  function
     opens  an ASCII file containing LPC frames and creates an iterator object,
     an instance of class lpc-file-class to access them. Create  a  file  using
     save-lpc-file (see below).

save-lpc-file(lpc-iterator, filename)
     Create  a  file  containing  LPC  frames.    This  file  can  be  read  by
     make-lpc-file-iterator (see above).

show-lpc-data(lpc-iterator, iniframe, endframe, [poles?])
     Print values of LPC frames from an LPC  iterator  object.  The  object  is
     lpc-iterator,   which   is   typically  an  instance  of  lpanal-class  or
     lpc-file-class. Frames are numbered from zero, and only files starting  at
     iniframe  (a  FIXNUM)  and  ending  before  endframe  (also  a FIXNUM) are
     printed. By default, only the values for RMS1, RMS2, and ERR are  printed,
     but if optional parameter poles? is non-NIL, then the LPC coefficients are
     also printed.

allpoles-from-lpc(snd, lpc-frame)
     A  single LPC frame defines a filter.  Use allpoles-from-lpc to apply this
     filter to snd, a SOUND. To obtain lpc-frame,  a  LIST  containing  an  LPC
     frame, either send :next to an LPC iterator, or use nth-frame (see below).
     The result is a SOUND whose duration is the same as that of snd.

lpreson(snd, lpc-iterator, skiptime)
     Implements  a time-varying all-pole filter controlled by a sequence of LPC
     frames from an iterator. The SOUND to be filtered is snd, and  the  source
     of  LPC  frames  is lpc-iterator, typically an instance of lpanal-class or
     lpc-file-class. The frame period (in seconds)  is  given  by  skiptime  (a
     FLONUM).    This  number  does not have to agree with the skiptime used to
     analyze the frames. (Greater values will cause the filter  evolution  slow
     down,  and  smaller  values  will  cause  it to speed up.) The result is a
     SOUND. The duration of the result is the minimum of the  duration  of  snd
     and that of the sequence of frames.

lpc-frame-rms1(frame)
     Get the energy of the input signal from a frame.

lpc-frame-rms2(frame)
     Get the energy of the residual from a frame.

lpc-frame-err(frame)
     Get the square root of RMS1/RMS2 from a frame.

lpc-frame-filter-coefs(frame)
     Get the filter coefficients from a frame.

11.2. Low-level LPC Functions
  The lowest-level Nyquist functions for LPC are

   - snd-lpanal for analysis,

   - snd-allpoles, an all-pole filter with fixed coefficients, and

   - snd-lpreson,  an  all-pole  filter  that  takes  frames  from  an LPC
     iterator.

snd-lpanal(samps, npoles)
     Compute an LPC frame with npoles (a FIXNUM) poles from an ARRAY of samples
     (FLONUMS). Note that snd-fetch-array can be used to fetch  a  sequence  of
     frames  from  a  sound.  Ordinarily, you should not use this function. Use
     make-lpanal-iterator instead.

snd-allpoles(snd, lpc-coefs, gain)
     A   fixed  all-pole  filter.  The  input  is  snd,  a  SOUND.  The  filter
     coefficients are given by lpc-coefs (an ARRAY), and  the  filter  gain  is
     given  by  gain,  a  FLONUM.  The result is a SOUND whose duration matches
     that of snd.  Ordinarily, you should use  allpoles-from-lpc  instead  (see
     above).

snd-lpreson(snd, lpc-iterator, skiptime)
     This function is identical to lpreson (see above).
12. Developing and Debugging in Nyquist
  There are a number of tools, functions, and techniques that can help to debug
Nyquist  programs.  Since  these  are  described in many places throughout this
manual, this chapter  brings  together  many  suggestions  and  techniques  for
developing  code  and debugging. You really should read this chapter before you
spend too much time with Nyquist. Many problems that  you  will  certainly  run
into are addressed here.

12.1. Debugging
  Probably  the  most  important  debugging tool is the backtrace. When Nyquist
encounters an error, it suspends execution and prints an error message. To find
out  where  in  the  program the error occurred and how you got there, start by
typing (bt). This will print out the last  several  function  calls  and  their
arguments, which is usually sufficient to see what is going on.

  In  order  for  (bt) to work, you must have a couple of global variables set:
*tracenable* is ordinarily set to NIL.  If it is  true,  then  a  backtrace  is
automatically  printed when an error occurs; *breakenable* must be set to T, as
it enables the execution to be suspended  when  an  error  is  encountered.  If
*breakenable* is NIL (false), then execution stops when an error occurs but the
stack is not saved and you cannot get a backtrace. Finally, bt is just a  macro
to  save  typing.    The  actual backtrace function is baktrace, which takes an
integer argument telling how many levels to print.  All of these things are set
up by default when you start Nyquist.

  Since  Nyquist sounds are executed with a lazy evaluation scheme, some errors
are encountered when samples are being generated.  In this case, it may not  be
clear which expression is in error. Sometimes, it is best to explore a function
or set of functions by examining  intermediate  results.  Any  expression  that
yields a sound can be assigned to a variable and examined using one or more of:
s-plot, snd-print-tree, and of course play. The snd-print-tree function  prints
a  lot  of detail about the inner representaion of the sound. Keep in mind that
if you assign a sound to a global variable and then look at the  samples  (e.g.
with  play  or  s-plot), the samples will be retained in memory. At 4 bytes per
sample, a big sound may use all of your memory and cause a crash.

  Another technique is to use low sample rates so that it  is  easier  to  plot
results or look at samples directly. The calls:

    (set-sound-srate 100)
    (set-control-srate 100)

set  the  default  sample rates to 100, which is too slow for audio, but useful
for examining programs and results. The function

    (snd-samples sound limit)

will convert up to limit samples from sound into a Lisp array. This is  another
way to look at results in detail.

  The trace function is sometimes useful.  It prints the name of a function and
its arguments everytimg the function is called, and the result is printed  when
the function exits.  To trace the osc function, type:

    (trace osc)

and to stop tracing, type (untrace osc).

  If a variable needs a value or a function is undefined, you can fix the error
(by setting the variable or loading the function definition)  and  keep  going.
Use  (co),  short  for  (continue)  to  reevaluate the variable or function and
continue execution.

  When you finish debugging a particular call, you can ``pop'' up  to  the  top
level by typing (top), a short name for (top-level).

12.2. Useful Functions

grindef(name)
     Prints a formatted listing of a lisp function. This  is  often  useful  to
     quickly  inspect  a  function without searching for it in source files. Do
     not forget to quote the name, e.g. (grindef 'prod).

args(name)
     Similar to grindef, this function prints the arguments to a function. This
     may be faster than looking up a function in the documentation if you  just
     need  a  reminder.  For example, (args 'lp) prints ``(LP S C),'' which may
     help you to remember that the arguments are a sound (S)  followed  by  the
     cutoff (C) frequency.

  The  following  functions are useful short-cuts that might have been included
in XLISP. They are so useful that they are defined as part of Nyquist.

incf(symbol)
     Increment  symbol by one. This is a macro, and symbol can be anything that
     can be set by setf. Typically, symbol is a  variable:  ``(incf  i),''  but
     symbol can also be an array element: ``(incf (aref myarray i)).''

decf(symbol)
     Decrement symbol by one. (See incf, above.)

push(val, lis)
     Push  val  onto  lis  (a Lisp list). This is a macro that is equivalent to
     writing (setf lis (cons val lis)).

pop(lis)
     Remove  (pop)  the first item from lis (a Lisp list). This is a macro that
     is equivalent to writing (setf lis (cdr lis)).  Note  that  the  remaining
     list  is returned, not the head of the list that has been popped. Retrieve
     the head of the  list  (i.e.  the  top  of  the  stack)  using  first  or,
     equivalently, car.

  The following macros are useful control constructs.

while(test, stmt1, stmt2, ...)
     A conventional ``while'' loop. If test is  true,  perform  the  statements
     (stmt1, stmt2, etc.) and repeat. If test is false, return. This expression
     evaluates to NIL unless the expression  (return  expr)  is  evaluated,  in
     which case the value of expr is returned.

when(test, action)
     A conventional ``if-then'' statement. If test is true, action is evaluated
     and  returned.  Otherwise,  NIL  is returned. (Use if or cond to implement
     ``if-then-else'' and more complex conditional forms.

  Sometimes it is important to load files relative to  the  current  file.  For
example,  the  lib/piano.lsp  library  loads  data  files  from  the  lib/piano
directory, but how can we find out the full path of lib? The solution is:

current-path()
     Returns the full path name of the file that is currently being loaded (see
     load). Returns NIL if no file is being loaded.

  Finally, there are some helpful math functions:

real-random(from, to)
     Returns  a  random FLONUM between from and to. (See also rrandom, which is
     equivalent to (real-random 0 1)).

power(x, y)
     Returns x raised to the y power.
13. Xmusic and Algorithmic Composition
  Several  Nyquist  libraries offer support for algorithmic composition. Xmusic
is a library for generating sequences and patterns of data. Included in  Xmusic
is  the  score-gen macro which helps to generate scores from patterns.  Another
important facility is the distributions.lsp library, containing many  different
random number generators.

13.1. Xmusic Basics
  Xmusic  is  inspired  by  and based on Common Music by Rick Taube. Currently,
Xmusic only implements patterns and  some  simple  support  for  scores  to  be
realized  as  sound  by  Nyquist.  In  contrast, Common Music supports MIDI and
various other synthesis languages and  includes  a  graphical  interface,  some
visualization  tools, and many other features. Common Music runs in Common Lisp
and Scheme, but not XLISP, which is the base language for Nyquist.

  Xmusic patterns are objects that generate  data  streams.  For  example,  the
cycle-class  of  objects  generate cyclical patterns such as "1 2 3 1 2 3 1 2 3
...", or "1 2 3 4 3 2 1 2 3 4 ...". Patterns  can  be  used  to  specify  pitch
sequences, rhythm, loudness, and other parameters.

  To  use  any of the Xmusic functions, you must manually load xm.lsp, that is,
type (load "xm") to Nyquist.  To use a pattern object,  you  first  create  the
pattern, e.g.

    (setf pitch-source (make-cycle (list c4 d4 e4 f4)))

After  creating the pattern, you can access it repeatedly with next to generate
data, e.g.

    (play (seqrep (i 13) (pluck (next pitch-source) 0.2)))

This will create a sequence of notes with the following pitches: c, d, e, f, c,
d,  e,  f,  c,  d, e, f, c. If you evaluate this again, the pitch sequence will
continue, starting on "d".

  It is very important not to confuse the  creation  of  a  sequence  with  its
access. Consider this example:

    (play (seqrep (i 13)
           (pluck (next (make-cycle (list c4 d4 e4 f4))) 0.2)))

This  looks  very  much like the previous example, but it only repeats notes on
middle-C. The reason is that every  time  pluck  is  evaluated,  make-cycle  is
called and creates a new pattern object. After the first item of the pattern is
extracted with next, the cycle is not  used  again,  and  no  other  items  are
generated.

  To  summarize  this  important point, there are two steps to using a pattern.
First, the pattern is created and stored in a variable using setf. Second,  the
pattern is accessed (multiple times) using next.

  Patterns  can  be  nested,  that  is, you can write patterns of patterns.  In
general, the next function does not return patterns. Instead, if the next  item
in  a pattern is a (nested) pattern, next recursively gets the next item of the
nested pattern.

  While you might expect that each call to next  would  advance  the  top-level
pattern  to  the  next  item,  and  descend  recursively  if  necessary  to the
inner-most nesting level, this is not how next works. Instead,  next  remembers
the  last  top-level  item, and if it was a pattern, next continues to generate
items from that same inner pattern until the end of the inner pattern's  period
is reached. The next paragraph explains the concept of the period.

  The  data  returned  by  a  pattern  object is structured into logical groups
called periods. You can get an entire period  (as  a  list)  by  calling  (next
pattern t). For example:

    (setf pitch-source (make-cycle (list c4 d4 e4 f4)))
    (next pitch-source t)

This prints the list (60 62 64 65), which is one period of the cycle.

  You  can  also  get  explicit markers that delineate periods by calling (send
pattern :next). In this case, the value returned is either the next item of the
pattern,  or  the  symbol  +eop+  if the end of a period has been reached. What
determines a period? This is up to the  specific  pattern  class,  so  see  the
documentation  for specifics. You can override the ``natural'' period using the
keyword :for, e.g.

    (setf pitch-source (make-cycle (list c4 d4 e4 f4) :for 3))
    (next pitch-source t)
    (next pitch-source t)

This prints the lists (60 62 64) (65 60 62). Notice  that  these  periods  just
restructure the stream of items into groups of 3.

  Nested  patterns  are  probably  easier  to  understand  by  example  than by
specification. Here is a simple nested pattern of cycles:

    (setf cycle-1 (make-cycle '(a b c)))
    (setf cycle-2 (make-cycle '(x y z)))
    (setf cycle-3 (make-cycle (list cycle-1 cycle-2)))
    (dotimes (i 9) (format t "~A " (next cycle-3)))

This will print "A B C X Y Z A B C". Notice that the inner-most cycles  cycle-1
and cycle-2 generate a period of items before the top-level cycle-3 advances to
the next pattern.

  Before describing  specific  pattern  classes,  there  are  several  optional
parameters that apply in the creating of any pattern object. These are:

:for                The  length  of  a  period.  This  overrides the default by
                    providing a numerical length. The value  of  this  optional
                    parameter  may  be  a  pattern that generates a sequence of
                    integers that  determine  the  length  of  each  successive
                    period.  A period length may not be negative, but it may be
                    zero.

:name               A pattern object may be given a name. This is useful if the
                    :trace option is used.

:trace              If  non-null,  this  optional  parameter causes information
                    about the pattern to  be  printed  each  time  an  item  is
                    generated from the pattern.

  The built-in pattern classes are described in the following section.

13.2. Pattern Classes



13.2.1. cycle
  The  cycle-class  iterates  repeatedly through a list of items.  For example,
two periods of (make-cycle '(a b c)) would be (A B C) (A B C).

make-cycle(items, [for: for,] [name: name,] [trace: trace])
     Make  a  cycle pattern that iterates over items. The default period length
     is the length of items. (See above  for  a  description  of  the  optional
     parameters.)  If  items  is a pattern, a period of the pattern becomes the
     list from which items are generated. The list is replaced every period  of
     the cycle.



13.2.2. line
  The  line-class is similar to the cycle class, but when it reaches the end of
the list of items, it simply repeats the last item in the list.   For  example,
two periods of (make-line '(a b c)) would be (A B C) (C C C).

make-line(items, [for: for,] [name: name,] [trace: trace])
     Make a line pattern that iterates over items. The default period length is
     the  length  of  items.  As  with make-cycle, items may be a pattern. (See
     above for a description of the optional parameters.)



13.2.3. random
  The random-class generates items at random from a list. The default selection
is  uniform  random with replacement, but items may be further specified with a
weight, a minimum repetition count, and a  maximum  repetition  count.  Weights
give  the  relative  probability  of  the selection of the item (with a default
weight of one). The minimum count  specifies  how  many  times  an  item,  once
selected  at  random, will be repeated. The maximum count specifies the maximum
number of times an item can be selected  in  a  row.    If  an  item  has  been
generated  n  times in succession, and the maximum is equal to n, then the item
is disqualified in the next random  selection.    Weights  (but  not  currently
minima  and  maxima)  can  be  patterns.  The  patterns  (thus the weights) are
recomputed every period.

make-random(items, [for: for,] [name: name,] [trace: trace])
     Make  a random pattern that selects from items. Any (or all) element(s) of
     items may be lists of the following form: (value  [:weight  weight]  [:min
     mincount]  [:max  maxcount],  where  value  is the item (or pattern) to be
     generated, weight is the relative  probability  of  selecting  this  item,
     mincount  is the minimum number of repetitions when this item is selected,
     and maxcount is the maximum number of repetitions allowed before selecting
     some  other  item.  The  default  period length is the length of items. If
     items is a pattern, a period from that pattern becomes the list from which
     random selections are made, and a new list is generated every period.



13.2.4. palindrome
  The palindrome-class repeatedly traverses a list forwards and then backwards.
For example, two periods of (make-palindrome '(a b c)) would be (A B C C  B  A)
(A  B  C C B A). The :elide keyword parameter controls whether the first and/or
last elements are repeated:

    (make-palindrome '(a b c) :elide nil)
         ;; generates A B C C B A A B C C B A ...

    (make-palindrome '(a b c) :elide t)
         ;; generates A B C B A B C B ...

    (make-palindrome '(a b c) :elide :first)
         ;; generates A B C C B A B C C B ...

    (make-palindrome '(a b c) :elide :last)
         ;; generates A B C B A A B C B A ...

make-palindrome(items,  [elide:  elide,]  [for:  for,]  [name:  name,]  [trace:
     trace])
     Generate  items  from  list   alternating   in-order   and   reverse-order
     sequencing. The keyword parameter elide can have the values :first, :last,
     t, or nil to control repetition of the first and last elements.  The elide
     parameter  can  also  be  a  pattern,  in which case it is evaluated every
     period. One period is one complete forward and backward traversal  of  the
     list.  If  items is a pattern, a period from that pattern becomes the list
     from which random selections are made, and a new list is  generated  every
     period.
13.2.5. heap
  The heap-class selects items in random order from a list without replacement,
which means that all items are generated once before any item is repeated.  For
example,  two  periods  of  (make-heap  '(a  b  c))  might  be (C A B) (B A C).
Normally, repetitions can occur even if all list elements  are  distinct.  This
happens  when  the last element of a period is chosen first in the next period.
To avoid repetitions, the :max keyword argument can  be  set  to  1.  The  :max
keyword  only  controls repetitions from the end of one period to the beginning
of the next.  If the list contains more than one copy of the same value, it may
be repeated within a period regardless of the value of :max.

make-heap(items, [for: for,] [max: max,] [name: name,] [trace: trace])
     Generate items randomly from list without replacement. If max  is  1,  the
     first  element of a new period will not be the same as the last element of
     the previous period, avoiding repetition. The default value of max  is  2,
     meaning  repetition  is allowed. The period length is the length of items.
     If items is a pattern, a period from that pattern becomes  the  list  from
     which  random  selections  are  made,  and  a  new list is generated every
     period.



13.2.6. copier
  The copier-class makes copies of periods from a sub-pattern.    For  example,
three  periods of (make-copier (make-cycle '(a b c) :for 1) :repeat 2 :merge t)
would be (A A) (B B) (C C). Note that entire periods (not individual items) are
repeated,  so  in this example the :for keyword was used to force periods to be
of length one so that each item is repeated by the :repeat count.

make-copier(sub-pattern, [repeat: repeat,] [merge: merge,] [for:  for,]  [name:
     name,] [trace: trace])
     Generate a period from sub-pattern and repeat it repeat times. If merge is
     false  (the default), each repetition of a period from sub-pattern results
     in a period by default. If merge  is  true  (non-null),  then  all  repeat
     repetitions of the period are merged into one result period by default. If
     the :for keyword is used, the same items are generated, but the items  are
     grouped  into  periods  determined  by  the  :for  parameter.  If the :for
     parameter is a pattern, it is evaluated every result  period.  The  repeat
     and  merge values may be patterns that return a repeat count and a boolean
     value, respectively.  If so, these patterns are  evaluated  initially  and
     after  each  repeat  copies  are  made  (independent  of  the :for keyword
     parameter, if any).  The repeat value returned by a pattern  can  also  be
     negative.  A  negative number indicates how many periods of sub-pattern to
     skip. After skipping these patterns,  new  repeat  and  merge  values  are
     generated.



13.2.7. accumulate
  The  accumulate-class  forms  the sum of numbers returned by another pattern.
For example, each period of (make-accumulate (make-cycle '(1 2 -3)))  is  (1  3
0).  The default output period length is the length of the input period.

make-accumulate(sub-pattern, [for: for,] [max: maximum,] [min: minimum,] [name:
     name,] [trace: trace])
     Keep a running sum of numbers generated by sub-pattern. The default period
     lengths match the period lengths from sub-pattern. If maximum  (a  pattern
     or  a  number)  is  specified,  and  the  running sum exceeds maximum, the
     running sum is reset to maximum. If minimum (a pattern  or  a  number)  is
     specified,  and  the  running  sum falls below minimum, the running sum is
     reset to minimum. If minimum is greater than maximum, the running sum will
     be set to one of the two values.



13.2.8. sum
  The  sum-class forms the sum of numbers, one from each of two other patterns.
For example, each period of (make-sum (make-cycle '(1 2 3)) (make-cycle  '(4  5
6)))  is  (5 7 9).  The default output period length is the length of the input
period of the first argument. Therefore, the first argument must be a  pattern,
but the second argument can be a pattern or a number.

make-sum(x, y, [for: for,] [name: name,] [trace: trace])
     Form sums of items (which must be numbers) from pattern x and  pattern  or
     number y.  The default period lengths match the period lengths from x.



13.2.9. product
  The  product-class  forms  the product of numbers, one from each of two other
patterns.  For example, each period of  (make-product  (make-cycle  '(1  2  3))
(make-cycle  '(4  5 6))) is (4 10 18).  The default output period length is the
length of the input period of the first argument. Therefore, the first argument
must be a pattern, but the second argument can be a pattern or a number.

make-product(x, y, [for: for,] [name: name,] [trace: trace])
     Form products of items (which must be numbers) from pattern x and  pattern
     or number y.  The default period lengths match the period lengths from x.



13.2.10. eval
  The  eval-class  evaluates  an  expression  to produce each output item.  The
default output period length is 1.

make-eval(expr, [for: for,] [name: name,] [trace: trace])
     Evaluate  expr  to  generate each item. If expr is a pattern, each item is
     generated by getting the next item from expr and evaluating it.



13.2.11. length
  The length-class  generates  periods  of  a  specified  length  from  another
pattern.  This is similar to using the :for keyword, but for many patterns, the
:for parameter alters the points at which other  patterns  are  generated.  For
example,  if  the palindrome pattern has an :elide pattern parameter, the value
will be computed every period. If there is also a :for parameter with  a  value
of  2,  then  :elide  will  be  recomputed  every  2 items. In contrast, if the
palindrome (without a :for parameter) is embedded in a length  pattern  with  a
lenght  of 2, then the periods will all be of length 2, but the items will come
from default periods of the palindrome, and therefore the :elide values will be
recomputed at the beginnings of default palindrome periods.

make-length(pattern, length-pattern, [name: name,] [trace: trace])
     Make a pattern of class length-class that regroups items  generated  by  a
     pattern  according  to pattern lengths given by length-pattern.  Note that
     length-pattern is not optional: There is no default pattern length and  no
     :for keyword.



13.2.12. window
  The window-class groups items from another pattern by using a sliding window.
If the skip value is 1, each output period is formed by dropping the first item
of  the previous perioda and appending the next item from the pattern. The skip
value and the output period length  can  change  every  period.  For  a  simple
example,  if  the  period  length  is  3 and the skip value is 1, and the input
pattern generates the sequence A, B, C, ..., then the output periods will be (A
B C), (B C D), (C D E), (D E F), ....

make-window(pattern,   length-pattern,   skip-pattern,  [name:  name,]  [trace:
     trace])
     Make  a  pattern  of class window-class that regroups items generated by a
     pattern according to pattern lengths given by length-pattern and where the
     period  advances  by the number of items given by skip-pattern.  Note that
     length-pattern is not optional: There is no default pattern length and  no
     :for keyword.



13.2.13. markov
  The  markov-class  generates  items  from  a  Markov  model.  A  Markov model
generates a sequence of states according to rules which specify possible future
states  given  the most recent states in the past. For example, states might be
pitches, and each pitch might lead to a choice of pitches for the  next  state.
In the markov-class, states can be either symbols or numbers, but not arbitrary
values or patterns. This makes it easier to specify rules.    However,  symbols
can  be  mapped to arbitrary values including pattern objects, and these become
the actual generated items.    By  default,  all  future  states  are  weighted
equally,  but weights may be associated with future states. A Markov model must
be initialized with a sequence of past states using the  :past  keyword.    The
most  common  form of Markov model is a "first order Markov model" in which the
future item depends only upon one past item. However, higher order models where
the  future items depend on two or more past items are possible. A "zero-order"
Markov model, which depends on no past states, is essentially equivalent to the
random  pattern.  As an example of a first-order Markov pattern, two periods of
(make-markov '((a -> b c) (b -> c) (c -> a)) :past '(a)) might be (C A C) (A  B
C).

make-markov(rules,  [past:  past,]  [produces:  produces,]  [for:  for,] [name:
     name,] [trace: trace])
     Generate  a  sequence  of items from a Markov process. The rules parameter
     has the form:  (prev1 prev2 ... prevn ->  next1  next2  ...  nextn)  where
     prev1 through prevn represent a sequence of most recent (past) states. The
     symbol * is treated specially: it matches any  previous  state.  If  prev1
     through  prevn (which may be just one state as in the example above) match
     the previously generated states, this rule applies. Note that  every  rule
     must  specify  the same number of previous states; this number is known as
     the order of the Markov model.  The first rule in rules  that  applies  is
     used  to  select the next state. If no rule applies, the next state is NIL
     (which is a valid state that can be used  in  rules).    Assuming  a  rule
     applies,  the  list  of possible next states is specified by next1 through
     nextn. Notice that these are alternative choices for the next state, not a
     sequence  of  future states, and each rule can have any number of choices.
     Each choice may be the state itself (a symbol or a number), or the  choice
     may  be  a  list  consisting  of the state and a weight. The weight may be
     given by a pattern, in which case the next item of the pattern is obtained
     every  time  the rule is applied. For example, this rules says that if the
     previous states were A and B, the next state can be A with a weight of 0.5
     or  C  with an implied weight of 1: (A B -> (A 0.5) C). The default length
     of the period is the length of rules. The past parameter must be provided.
     It is a list of states whose length matches the order of the Markov model.
     The keyword parameter produces may be used to map from  state  symbols  or
     numbers  to  other  values  or  patterns.  The  parameter  is  a  list  of
     alternating symbols and values. For example, to map A to 69 and B  to  71,
     use  (list 'a 69 'b 71). You can also map symbols to patterns, for example
     (list 'a (make-cycle '(57 69)) 'b (make-random '(59 71))). The  next  item
     of  the  pattern  is is generated each time the Markov model generates the
     corresponding state.  Finally, the produces keyword can  be  :eval,  which
     means  to  evaluate the Markov model state. This could be useful if states
     are Nyquist global variables such as C4, CS4, D4, ]..., which evaluate  to
     numerical values (60, 61, 62, ....

markov-create-rules(sequence, order, [generalize])
     Generate a set  of  rules  suitable  for  the  make-markov  function.  The
     sequence  is  a  ``typical'' sequence of states, and order is the order of
     the Markov model. It is often the case that a  sample  sequence  will  not
     have a transition from the last state to any other state, so the generated
     Markov model can reach a ``dead end'' where no rule  applies.  This  might
     lead to an infinite stream of NIL's. To avoid this, the optional parameter
     generalize can be set to t (true),  indicating  that  there  should  be  a
     fallback rule that matches any previous states and whose future states are
     weighted according  to  their  frequency  in  sequence.  For  example,  if
     sequence  contains 5 A's, 5 B's and 10 G's, the default rule will be (* ->
     (A 5) (B 5) (G 10)). This rule will be appended to the end so it will only
     apply if no other rule does.

13.3. Random Number Generators
  The distributions.lsp library implements random number generators that return
random values with various probability distributions. Without this library, you
can   generate   random  numbers  with  uniform  distributions.  In  a  uniform
distribution, all values are equally likely. To generate a  random  integer  in
some  range,  use random. To generate a real number (FLONUM) in some range, use
real-random (or rrandom if the range is 0-1). But there are  other  interesting
distributions.  For  example,  the Gaussian distribution is often used to model
real-world errors and fluctuations  where  values  are  clustered  around  some
central  value  and  large  deviations  are  more unlikely than small ones. See
Dennis Lorrain, "A Panoply of Stochastic 'Canons'," Computer Music Journal vol.
4, no. 1, 1980, pp. 53-81.

  In  most  of the random number generators described below, there are optional
parameters to indicate a maximum and/or minimum value. These  can  be  used  to
truncate  the  distribution.  For  example,  if  you  basically want a Gaussian
distribution, but you never want a value greater than 5, you can specify  5  as
the  maximum  value.    The  upper  and  lower bounds are implemented simply by
drawing a random number from the full distribution repeatedly  until  a  number
falling  into  the  desired  range  is  obtained.  Therefore,  if you select an
acceptable range that is unlikely, it may take Nyquist a long time to find each
acceptable  random number. The intended use of the upper and lower bounds is to
weed out values that are already fairly unlikely.

linear-dist(g)
     Return a FLONUM value from a linear distribution, where the probability of
     a value decreases linearly from zero to g which must be greater than zero.
     (See  Figure  7.)  The  linear  distribution  is useful for generating for
     generating time and pitch intervals.


















     Figure 7:  The Linear Distribution, g = 1.


exponential-dist(delta, [high])
     Return  a  FLONUM  value  from  an  exponential  distribution. The initial
     downward slope is steeper with larger  values  of  delta,  which  must  be
     greater  than  zero.  (See  Figure  8. The optional high parameter puts an
     artificial upper bound on the return value.  The exponential  distribution
     generates  values  greater  than  0,  and  can  be  used  to generate time
     intervals. Natural random intervals such as the time intervals between the
     release  of  atomic  particles  or  the  passing  of yellow volkswagons in
     traffic have exponential distributions. The  exponential  distribution  is
     memory-less:  knowing  that  a  random  number  from  this distribution is
     greater than some value (e.g. a note duration is at least 1 second)  tells
     you  nothing  new  about  how soon the note will end. This is a continuous
     distribution, but geometric-dist (described below) implements the discrete
     form.


















     Figure 8:  The Exponential Distribution, delta = 1.


gamma-dist(nu, [high])
     Return a FLONUM value from a Gamma distribution. The value is greater than
     zero,  has a mean of nu (a FIXNUM greater than zero), and a mode (peak) of
     around nu - 1.  The optional high parameter puts an artificial upper bound
     on the return value.


















     Figure 9:  The Gamma Distribution, nu = 4.


bilateral-exponential-dist(xmu, tau, [low,] [high])
     Returns a FLONUM value from a bilateral  exponential  distribution,  where
     xmu is the center of the double exponential and tau controls the spread of
     the distribution.  A  larger  tau  gives  a  wider  distribution  (greater
     variance),  and tau must be greater than zero. The low and high parameters
     give optional artificial bounds on the minimum and maximum output  values,
     respectively.   This distribution is similar to the exponential, except it
     is centered at 0  and  can  output  negative  values  as  well.  Like  the
     exponential,  it can be used to generate time intervals; however, it might
     be necessary to add a lower bound so as not to  compute  a  negative  time
     interval.


















     Figure 10:  The Bilateral Exponential Distribution.


cauchy-dist(tau, [low,] [high])
     Returns a FLONUM from the Cauchy  distribution,  a  symetric  distribution
     with  a  high  peak  at  zero  and  a width (variance) that increases with
     parameter tau,  which  must  be  greater  than  zero.  The  low  and  high
     parameters  give  optional  artificial  bounds  on the minimum and maximum
     output values, respectively.


















     Figure 11:  The Cauchy Distribution, tau = 1.


hyperbolic-cosine-dist( [low,] [high])
     Returns a FLONUM value from the hyperbolic cosine distribution, a symetric
     distribution with its peak at zero.  The  low  and  high  parameters  give
     optional  artificial  bounds  on  the  minimum  and maximum output values,
     respectively.

logistic-dist(alpha, beta, [low,] [high])
     Returns  a  FLONUM value from the logistic distribution, which is symetric
     about  the  mean.  The  alpha  parameter  primarily   affects   dispersion
     (variance),  with  larger  values  resulting  in values closer to the mean
     (less variance), and the beta parameter primarily influences the mean. The
     low and high parameters give optional artificial bounds on the minimum and
     maximum output values, respectively.

arc-sine-dist()
     Returns  a  FLONUM  value  from  the  arc sine distribution, which outputs
     values between 0 and 1. It is symetric about the mean of 1/2, but is  more
     likely to generate values closer to 0 and 1.

gaussian-dist(xmu, sigma, [low,] [high])
     Returns a FLONUM value from the Gaussian or Gauss-Laplace distribution,  a
     linear  function of the normal distribution. It is symetric about the mean
     of xmu, with a standard deviation of sigma, which  must  be  greater  than


















     Figure 12:  The Hyperbolic Cosine Distribution.



















     Figure 13:  The Logistic Distribution, alpha = 1, beta = 2.



















     Figure 14:  The Arc Sine Distribution.


     zero.  The  low and high parameters give optional artificial bounds on the
     minimum and maximum output values, respectively.


















     Figure 15:  The Gauss-Laplace (Gaussian) Distribution, xmu = 0, sigma
     = 1.


beta-dist(a, b)
     Returns a FLONUM value  from  the  Beta  distribution.  This  distribution
     outputs  values between 0 and 1, with outputs more likely to be close to 0
     or 1. The parameter a controls the height (probability) of the right  side
     of  the distribution (at 1) and b controls the height of the left side (at
     0). The distribution is symetric about 1/2 when a = b.


















     Figure 16:  The Beta Distribution, alpha = .5, beta = .25.


bernoulli-dist(px1, [x1,] [x2])
     Returns either x1 (default value is 1) with probability px1 or x2 (default
     value is 0) with probability 1 - px1. The value of px1 should be between 0
     and  1.  By  convention, a result of x1 is viewed as a success while x2 is
     viewed as a failure.
























     Figure 17:  The Bernoulli Distribution, px1 = .75.


(binomial-dist n p
     Returns  a  FIXNUM  value  from  the binomial distribution, where n is the
     number of Bernoulli trials run (a FIXNUM) and  p  is  the  probability  of
     success  in  the  Bernoulli  trial (a FLONUM from 0 to 1). The mean is the
     product of n and p.
























     Figure 18:  The Binomial Distribution, n = 5, p = .5.


geometric-dist(p)
     Returns  a  FIXNUM value from the geometric distribution, which is defined
     as the number of failures before a success  is  achieved  in  a  Bernoulli
     trial with probability of success p (a FLONUM from 0 to 1).

poisson-dist(delta)
     Returns a FIXNUM value from the Poisson distribution with a mean of  delta
     (a  FIXNUM). The Poisson distribution is often used to generate a sequence
     of time intervals, resulting in random but often pleasing rhythms.

13.4. Score Generation and Manipulation
  A common application of pattern  generators  is  to  specify  parameters  for
notes.  (It  should  be  understood  that  ``notes''  in this context means any
Nyquist behavior, whether it represents a conventional note, an abstract  sound
object,  or even some micro-sound event that is just a low-level component of a
hierarchical sound organization. Similarly, ``score'' should be taken to mean a
specification for a sequence of these ``notes.'')  The score-gen macro (defined
by loading xm.lsp) establishes a convention for  representing  scores  and  for
generating them using patterns.

  The  timed-seq  macro,  described  in  Section 7.4, already provides a way to
represent a ``score'' as a list of expressions.  The Xmusic representation goes
a  bit  further by specifying that all notes are specified by an alternation of
keywords  and  values,  where  some  keywords  have   specific   meanings   and
























     Figure 19:  The Geometric Distribution, p = .4.

























     Figure 20:  The Poisson Distribution, delta = 3.


interpretations.

  The basic idea of score-gen is you provide a template for notes in a score as
a set of keywords and values. For example,

    (setf pitch-pattern (make-cycle (list c4 d4 e4 f4)))
    (score-gen :dur 0.4 :name 'my-sound
             :pitch (next pitch-pattern) :score-len 9)

generates a score of 9 notes as follows:

    ((0 0 (SCORE-BEGIN-END 0 3.6))
     (0 0.4 (MY-SOUND :PITCH 60))
     (0.4 0.4 (MY-SOUND :PITCH 62))
     (0.8 0.4 (MY-SOUND :PITCH 64))
     (1.2 0.4 (MY-SOUND :PITCH 65))
     (1.6 0.4 (MY-SOUND :PITCH 60))
     (2 0.4 (MY-SOUND :PITCH 62))
     (2.4 0.4 (MY-SOUND :PITCH 64))
     (2.8 0.4 (MY-SOUND :PITCH 65))
     (3.2 0.4 (MY-SOUND :PITCH 60)))

The use of keywords like :PITCH helps to  make  scores  readable  and  easy  to
process  without specific knowledge of about the functions called in the score.
For example, one could write a transpose operation to transform all the  :pitch
parameters  in a score without having to know that pitch is the first parameter
of pluck and the second parameter of piano-note. Keyword  parameters  are  also
used  to  give  flexibility  to  note  specification with score-gen. Since this
approach requires the use of keywords, the next section is a brief  explanation
of how to define functions that use keyword parameters.



13.4.1. Keyword Parameters
  Keyword  parameters  are  parameters whose presence is indicated by a special
symbol, called a keyword, followed by the actual parameter. Keyword  parameters
may have default values that are used if no actual parameter is provided by the
caller of the function.

  To specify that a parameter is a keyword parameter, use &key to specify  that
the  following  parameters  are  keyword  parameters.  For  example,  here is a
function that accepts keyword parameters and invokes the pluck function:

    (defun k-pluck (&key pitch dur)
      (pluck pitch dur))

Now, we can call k-pluck with keyword parameters. The keywords are  simply  the
formal  parameter  names  with  a prepended colon character (:pitch and :dur in
this example), so a function call would look like:

    (pluck :key c3 :dur 3)

Usually, it is best to give keyword parameters useful default values. That way,
if  a  parameter such as :dur is missing, a reasonable default value (1) can be
used automatically. If no default value is given, the NIL will be used.  It  is
never  an  error to omit a keyword parameter, but the called function can check
to see if a keyword  parameter  was  supplied  or  not.    Default  values  are
specified by placing the parameter and the default value in parentheses:

    (defun k-pluck (&key (pitch 60) (dur 1))
      (pluck pitch dur))

Now,  we  can  call (k-pluck :pitch c3) with no duration, (k-pluck :dur 3) with
only a duration, or even (k-pluck) with no parameters.

  There is additional syntax to specify an alternate symbol to be used  as  the
keyword  and to allow the called function to determine whether or not a keyword
parameter was supplied, but these  features  are  little-used.  See  the  XLISP
manual for details.



13.4.2. Using score-gen
  The  score-gen  macro  computes  a  score  based on keyword parameters.  Some
keywords have a special meaning, while others are not  interpreted  but  merely
placed  in  the  score.  The resulting score can be synthesized using timed-seq
(see Section 7.4).

  The form of a call to score-gen is simply (score-gen :k1 e1  :k2  e2  ...  ),
where the k's are keywords and the e's are expressions. A score is generated by
evaluating the expressions once for  each  note  and  constructing  a  list  of
keyword-value  pairs.  A  number  of keywords have special interpretations. The
rules for interpreting these parameters will be explained through a set of "How
do I ..."  questions:

  How  many notes will be generated? The keyword parameter :score-len specifies
an upper bound on the number of notes.  The  keyword  :score-dur  specifies  an
upper  bound  on  the  starting time of the last note in the score. (To be more
precise, the :score-dur bound is reached when the default starting time of  the
next  note is greater than or equal to the :score-dur value. This definition is
necessary because note times are not strictly increasing.) When either bound is
reached,  score  generation  ends. At least one of these two parameters must be
specified or an error is raised. These keyword parameters  are  evaluated  just
once and are not copied into the parameter lists of generated notes.

  What  is  the duration of generated notes? The keyword :dur defaults to 1 and
specifies the nominal duration in seconds. Since the  generated  note  list  is
compatible  with  timed-seq, the starting time and duration (to be precise, the
stretch factor) are not passed  as  parameters  to  the  notes.  Instead,  they
control the Nyquist environment in which the note will be evaluated.

  What is the start time of a note? The default start time of the first note is
zero. Given a note, the default start time of the next note is the  start  time
plus  the  inter-onset  time,  which is given by the :ioi parameter. If no :ioi
parameter is specified, the inter-onset time defaults to the duration, given by
:dur.  In  all cases, the default start time of a note can be overridden by the
keyword parameter :time.

  When does the score begin and end? The behavior SCORE-BEGIN-END contains  the
beginning and ending of the score (these are used for score manipulations, e.g.
when scores are merged, their begin times can be aligned.)  When  timed-seq  is
used  to  synthesize  a score, the SCORE-BEGIN-END marker is not evaluated. The
score-gen macro inserts a ``note'' of the form (0 0 (SCORE-BEGIN-END begin-time
end-time))  at  the  time  given  by  the  :begin  keyword, with begin-time and
end-time determined by the :begin and :end keyword parameters, respectively. If
the  :begin  keyword  is  not  provided,  the score begins at zero. If the :end
keyword is not provided, the score ends at the default start time of what would
be the next note after the last note in the score (as described in the previous
paragraph). Note: if :time is used to compute note starting  times,  and  these
times  are not increasing, it is strongly advised to use :end to specify an end
time for the score, because the default end time may be anywhere in the  middle
of the generated sequence.

  What function is called to synthesize the note? The :name parameter names the
function. Like other parameters, the value can  be  any  expression,  including
something like (next fn-name-pattern), allowing function names to be recomputed
for each note. The default value is note.

  Can I make parameters depend upon the starting time or the  duration  of  the
note?  Parameter  expressions  can use the variable sg:time to access the start
time of the note, sg:ioi to access the inter-onset time, and sg:dur  to  access
the duration (stretch factor) of the note. Also, sg:count counts how many notes
have been computed so far, starting at 0. The order of computation is:  sg:time
first,  then sg:ioi and sg:dur, so for example, an expression to compute sg:dur
can depend on sg:ioi.

  Can  parameters  depend  on  each  other?  The  keyword  :pre  introduces  an
expression that is evaluated before each note, and :post provides an expression
to be evaluated after each note.  The :pre expression can assign  one  or  more
global variables which are then used in one or more expressions for parameters.

  How  do  I  debug  score-gen expressions? You can set the :trace parameter to
true (t) to enable a print statement for each generated note.

  How can I save scores generated by score-gen that  I  like?  If  the  keyword
parameter  :save is set to a symbol, the global variable named by the symbol is
set to the value of the generated sequence. Of course, the  value  returned  by
score-gen is just an ordinary list that can be saved like any other value.

  In summary, the following keywords have special interpretations in score-gen:
:begin, :end, :time, :dur, :name, :ioi, :trace, :save, :score-len,  :score-dur,
:pre,  :post.   All other keyword parameters are expressions that are evaluated
once for each note and become the parameters of the notes.



13.4.3. Score Manipulation
  Nyquist encourages the representation of music  as  executable  programs,  or
behaviors,  and  there  are  various  ways  to modify behaviors, including time
stretching, transposition, etc. An alternative to composing executable programs
is  to  manipulate scores as editable data. Each approach has its strengths and
weaknesses. This section describes  functions  intended  to  manipulate  Xmusic
scores as generated by, or at least in the form generated by, score-gen. Recall
that this means scores are lists of  events  (e.g.  notes),  where  events  are
three-element lists of the form (time duration expression, and where expression
is a standard lisp function call where all parameters are  keyword  parameters.
In  addition, the first ``note'' may be the special SCORE-BEGIN-END expression.
If this is missing, the score begins at zero and ends at the end  of  the  last
note.

  For convenience, a set of functions is offered to access properties of events
(or notes) in scores. Although lisp functions such as car, cadr, and caddr  can
be  used, code is more readable when more mnemonic functions are used to access
events.

event-time(event)
     Retrieve the time field from an event.

event-set-time(event, time)
     Construct a new event where the time of event is replaced by time.

event-dur(event)
     Retrieve the duration (i.e. the stretch factor) field from an event.

event-set-dur(event, dur)
     Construct a new event where the duration (or stretch factor) of  event  is
     replaced by dur.

event-expression(event)
     Retrieve the expression field from an event.

event-set-expression(event, dur)
     Construct  a  new  event  where  the  expression  of  event is replaced by
     expression.

event-end(event)
     Retrieve the end time of event, its time plus its duration.

expr-has-attr(expression, attribute)
     Test whether a score event expression has the given attribute.

expr-get-attr(expression, attribute, [default])
     Get  the  value  of  the given attribute from a score event expression. If
     attribute is not present, return default if specified, and otherwise nil.

expr-set-attr(expr, attribute, value)
     Construct a new expression identical to expr except that the attribute has
     value.

event-has-attr(event, attribute)
     Test whether a given score event's expression has the given attribute.

event-get-attr(event, attribute, [default])
     Get the value of the given attribute from a score event's  expression.  If
     attribute is not present, return default if specified, and otherwise nil.

event-set-attr(event, attribute, value)
     Construct a new event identical to event except  that  the  attribute  has
     value.

  Functions  are  provided  to shift the starting times of notes, stretch times
and durations, stretch only durations, add an offset to  a  keyword  parameter,
scale a keyword parameter, and other manipulations. Functions are also provided
to extract ranges of notes, notes that match criteria, and to  combine  scores.
Most  of  these  functions  (listed  below  in  detail)  share a set of keyword
parameters that optionally  limit  the  range  over  which  the  transformation
operates.  The  :from-index  and  :to-index parameters specify the index of the
first note and the index of the last note to be changed. If these  numbers  are
negative,  they are offsets from the end of the score, e.g. -1 denotes the last
note of the score. The :from-time and :to-time indicate  a  range  of  starting
times of notes that will be affected by the manipulation. Only notes whose time
is greater than or equal to the from-time and strictly less  than  the  to-time
are  modified.  If  both  index  and time ranges are specified, only notes that
satisfy both constraints are selected.

score-sorted(score)
     Test if score is sorted.

score-sort(score, [copy-flag])
     Sort the notes in a score into start-time order. If copy-flag is nil, this
     is a destructive operation which should only be performed if the top-level
     score list is a fresh copy that is not shared by any other variables. (The
     copy-flag  is  intended  for internal system use only.)  For the following
     operations, it is assumed that  scores  are  sorted,  and  all  operations
     return a sorted score.

score-shift(score,  offset,  [from-index:  i,]  [to-index:  j,] [from-time: x,]
     [to-time: y])
     Add  a constant offset to the starting time of a set of notes in score. By
     default, all notes are modified, but the range of  notes  can  be  limited
     with  the  keyword parameters. The begin time of the score is not changed,
     but the end time is increased by  offset.    The  original  score  is  not
     modified, and a new score is returned.

score-stretch(score,  factor,  [dur: dur-flag,] [time: time-flag,] [from-index:
     i,] [to-index: j,] [from-time: x,] [to-time: y])
     Stretch  note  times  and  durations  by  factor.  The default dur-flag is
     non-null, but if dur-flag is null, the original durations are retained and
     only  times  are  stretched. Similarly, the default time-flag is non-null,
     but if time-flag is  null,  the  original  times  are  retained  and  only
     durations  are  stretched.  If  both  dur-flag and time-flag are null, the
     score is not changed. If a range of notes is specified, times  are  scaled
     within  that  range,  and  notes  after  the range are shifted so that the
     stretched region does not create a  "hole"  or  overlap  with  notes  that
     follow.  If  the  range  begins  or  ends  with a time (via :from-time and
     :to-time), time stretching takes place over the  indicated  time  interval
     independent of whether any notes are present or where they start. In other
     words, the ``rests'' are stretched along with the  notes.    The  original
     score is not modified, and a new score is returned.

score-transpose(score,   keyword,   amount,  [from-index:  i,]  [to-index:  j,]
     [from-time: x,] [to-time: y])
     For  each  note  in  the  score  and in any indicated range, if there is a
     keyword parameter matching keyword and the parameter value  is  a  number,
     increment  the parameter value by amount. For example, to tranpose up by a
     whole step, write (score-transpose 2 :pitch score). The original score  is
     not modified, and a new score is returned.

score-scale(score, keyword, amount, [from-index: i,] [to-index: j,] [from-time:
     x,] [to-time: y])
     For  each  note  in  the  score  and in any indicated range, if there is a
     keyword parameter matching keyword and the parameter value  is  a  number,
     multiply  the  parameter  value  by  amount.  The  original  score  is not
     modified, and a new score is returned.

score-sustain(score, factor, [from-index: i,] [to-index:  j,]  [from-time:  x,]
     [to-time: y])
     For each note in the score  and  in  any  indicated  range,  multiply  the
     duration  (stretch factor) by amount. This can be used to make notes sound
     more legato or staccato, and does not change  their  starting  times.  The
     original score is not modified, and a new score is returned.

score-voice(score,  replacement-list,  [from-index:  i,]  [to-index: j,] [from-
     time: x,] [to-time: y])
     For  each  note  in  the  score  and  in  any indicated range, replace the
     behavior (function) name using replacement-list,  which  has  the  format:
     ((old1  new1)  (old2  new2)  ...), where oldi indicates a current behavior
     name and newi is the replacement. If oldi is *, it matches anything.   For
     example,  to  replace  my-note-1  by  trombone  and my-note-2 by horn, use
     (score-voice score '((my-note-1 trombone) (my-note-2 horn))).  To  replace
     all  instruments  with  piano,  use (score-voice score '((* piano))).  The
     original score is not modified, and a new score is returned.

score-merge(score1, score2, ...)
     Create  a  new score containing all the notes of the parameters, which are
     all scores. The resulting notes retain their original times and durations.
     The  merged  score  begin  time  is  the minimum of the begin times of the
     parameters and the merged score end time is the maximum of the  end  times
     of  the  parameters. The original scores are not modified, and a new score
     is returned.

score-append(score1, score2, ...)
     Create  a  new score containing all the notes of the parameters, which are
     all scores. The begin time of the first score is unaltered. The begin time
     of  each  other  score  is  aligned to the end time of the previous score;
     thus, scores are ``spliced'' in sequence.  The  original  scores  are  not
     modified, and a new score is returned.

score-select(score,  predicate, [from-index: i,] [to-index: j,] [from-time: x,]
     [to-time: y,] [reject: flag])
     Select  (or  reject) notes to form a new score. Notes are selected if they
     fall into the given ranges of index and time and they satisfy predicate, a
     function  of three parameters that is applied to the start time, duration,
     and the expression  of  the  note.  Alternatively,  predicate  may  be  t,
     indicating that all notes in range are to be selected.  The selected notes
     along with the existing score begin and end markers, are combined to  form
     a  new  score.  Alternatively,  if  the :reject parameter is non-null, the
     notes not selected form the new score (in other words the  selected  notes
     are  rejected or removed to form the new score). The original score is not
     modified, and a new score is returned.

score-set-begin(score, time)
     The begin time from the score's SCORE-BEGIN-END marker is set to time. The
     original score is not modified, and a new score is returned.

score-get-begin(score)
     Return the begin time of the score.

score-set-end(score, time)
     The end time from the score's SCORE-BEGIN-END marker is set to  time.  The
     original score is not modified, and a new score is returned.

score-get-end(score)
     Return the end time of the score.

score-must-have-begin-end(score)
     If  score  does  not  have  a begin and end time, construct a score with a
     SCORE-BEGIN-END expression and return it. If score already has a begin and
     end time, just return the score. The orignal score is not modified.

score-filter-length(score, cutoff)
     Remove notes that extend beyond  the  cutoff  time.  This  is  similar  to
     score-select,  but  the here, events are removed when their nominal ending
     time (start time plus duration) exceeds the cutoff, whereas  the  :to-time
     parameter is compared to the note's start time.  The original score is not
     modified, and a new score is returned.

score-repeat(score, n)
     Make  a  sequence  of n copies of score. Each copy is shifted to that it's
     begin time  aligns  with  the  end  time  of  the  previous  copy,  as  in
     score-append.    The  original  score  is not modified, and a new score is
     returned.

score-stretch-to-length(score, length)
     Stretch  the  score so that the end time of the score is the score's begin
     time plus length.  The original score is not modified, and a new score  is
     returned.

score-filter-overlap(score)
     Remove overlapping notes (based on the  note  start  time  and  duration),
     giving  priority  to  the  positional order within the note list (which is
     also time order).  The original score is not modified, and a new score  is
     returned.

score-print(score)
     Print a score with one note per line. Returns nil.

score-play(score)
     Play  score  using  timed-seq to convert the score to a sound, and play to
     play the sound.

score-adjacent-events(score,  function,   [from-index:   i,]   [to-index:   j,]
     [from-time: x,] [to-time: y])
     Call (function A B C), where A, B, and C  are  consecutive  notes  in  the
     score.  The result replaces B. If the result is nil, B is deleted, and the
     next call will be (function A C D), etc. The first call  is  to  (function
     nil  A B) and the last is to (function Y Z nil). If there is just one note
     in the score, (function nil A nil) is called. Function calls are not  made
     if the note is outside of the indicated range.  This function allows notes
     and their parameters to be adjusted according to their immediate  context.
     The original score is not modified, and a new score is returned.

score-apply(score,  function,  [from-index:  i,] [to-index: j,] [from-time: x,]
     [to-time: y])
     Replace  each  note  in  the  score  with the result of (function time dur
     expression), where time, dur, and expression are the time,  duration,  and
     expression  of the note.  If a range is indicated, only notes in the range
     are replaced.  The original score is not modified,  and  a  new  score  is
     returned.

score-indexof(score,  function, [from-index: i,] [to-index: j,] [from-time: x,]
     [to-time: y])
     Return  the index (position) of the first score event (in range) for which
     applying function using (function time dur expression) returns true.

score-last-indexof(score, function, [from-index: i,] [to-index: j,] [from-time:
     x,] [to-time: y])
     Return the index (position) of the last score event (in range)  for  which
     applying function using (function time dur expression) returns true.

score-randomize-start(score,  amt,  [from-index: i,] [to-index: j,] [from-time:
     x,] [to-time: y])
     Alter the start times of notes by a random amount up to plus or minus amt.
     The original score is not modified, and a new score is returned.



13.4.4. Xmusic and Standard MIDI Files
  Nyquist has a general facility to read and write MIDI files.   You  can  even
translate  to and from a text representation, as described in Chapter 10. It is
also useful sometimes to read notes from Standard MIDI Files into Xmusic scores
and  vice versa. At present, Xmusic only translates notes, ignoring the various
controls, program changes, pitch bends, and other messages.

  MIDI notes are translated to Xmusic score events as follows:

    (time dur (NOTE :chan channel :pitch keynum :vel velocity)),

where channel, keynum,  and  velocity  come  directly  from  the  MIDI  message
(channels  are  numbered starting from zero).  Note also that note-off messages
are implied by the stretch factor dur which is duration in seconds.

score-read-smf(filename)
     Read a standard MIDI file from filename. Return an Xmusic score, or nil if
     the file could not be opened. The start time is zero, and the end time  is
     the  maximum end time of all notes. A very limited interface is offered to
     extract MIDI program numbers from the file: The global variable *rslt*  is
     set  to a list of MIDI program numbers for each channel. E.g. if *rslt* is
     (0 20 77), then program for channel 0 is 0, for channel 1 is 20,  and  for
     channel  2  is  77.  Program changes were not found on other channels. The
     default program number is 0, so in this example, it is not  known  whether
     the  program  0  on  channel 0 is the result of a real MIDI program change
     command or just a default value.  If more than one program  change  exists
     on  a  channel,  the last program number is recorded and returned, so this
     information will only be completely  correct  when  the  MIDI  file  sends
     single  program  change  per  channel  before  any notes are played. This,
     however, is a fairly common practice.  Note  that  the  list  returned  as
     *rslt* can be passed to score-write-smf, described below.

score-write-smf(score, filename, [programs])
     Write a standard MIDI file to  filename  with  notes  in  score.  In  this
     function,  every event in the score with a :pitch attribute, regardless of
     the ``instrument'' (or function name), generates a MIDI  note,  using  the
     :chan  attribute  for  the  channel (default 0) and the :vel attribute for
     velocity  (default  100).  There  is   no   facility   (in   the   current
     implementation)   to   issue  control  changes,  but  to  allow  different
     instruments, MIDI programs may be set in two  ways.  The  simplest  is  to
     associate  programs  with  channels using the optional programs parameter,
     which is simply a list of up to 16  MIDI  program  numbers.  Corresponding
     program  change  commands  are added to the beginning of the MIDI file. If
     programs has less than 16 elements, program change commands are only  sent
     on  the  first n channels. The second way to issue MIDI program changes is
     to add a :program keyword parameter to a note in the score. Typically, the
     note  will  have a :pitch of nil so that no actual MIDI note-on message is
     generated. If program changes and notes  have  the  same  starting  times,
     their relative playback order is undefined, and the note may be cut off by
     an immediately following program change. Therefore, program changes should
     occur  slightly, e.g. 1 ms, before any notes. Program numbers and channels
     are numbered starting at zero, matching the internal MIDI  representation.
     This may be one less than displayed on MIDI hardware, sequencers, etc.



13.4.5. Workspaces
  When  working  with  scores,  you may find it necessary to save them in files
between work sessions. This is not an issue with  functions  because  they  are
normally  edited in files and loaded from them. In contrast, scores are created
as Lisp data, and unless you take care to save them,  they  will  be  destroyed
when you exit the Nyquist program.

  A  simple mechanism called a workspace has been created to manage scores (and
any other Lisp data, for that matter).  A workspace  is  just  a  set  of  lisp
global  variables.  These  variables are stored in the file workspace.lsp.  For
simplicity, there is only  one  workspace,  and  no  backups  or  versions  are
maintained,  but  the user is free to make backups and copies of workspace.lsp.
To help remember what each variable is for, you can also associate and retrieve
a text string with each variable.  The following functions manage workspaces.

  In  addition,  when  a workspace is loaded, you can request that functions be
called. For example, the workspace might  store  descriptions  of  a  graphical
interface.  When the workspace is loaded, a function might run to convert saved
data into a graphical interface. (This is how sliders are saved by the IDE.)

add-to-workspace(symbol)
     Adds  a  global variable to the workspace. The symbol should be a (quoted)
     symbol.

save-workspace()
     All  global  variables in the workspace are saved to workspace.lsp (in the
     current directory), overwriting the previous file.

describe(symbol, [description])
     If  description, a text string, is present, associate description with the
     variable named by the symbol. If symbol is not already in  the  workspace,
     it  is  added. If description is omitted, the function returns the current
     description (from a previous call) for symbol.

add-action-to-workspace(symbol)
     Requests that the function named by symbol be called when the workspace is
     loaded (if the function is defined).

  To restore a workspace, use (load "workspace"). This restores the  values  of
the  workspace  variables  to  the values they had when save-workspace was last
called. It also restores the documentation strings, if set, by describe. If you
load  two  or  more  workspace.lsp  files,  the variables will be merged into a
single workspace. The current set of workspace variables are saved in the  list
*workspace*.  To  clear  the  workspace,  set *workspace* to nil. This does not
delete  any  variables,  but  means  that  no  variables  will  be   saved   by
save-workspace until variables are added again.

  Functions  to  be called are saved in the list *workspace-actions*.  to clear
the functions, set *workspace-actions* to nil.  Restore functions to  the  list
with add-action-to-workspace.



13.4.6. Utility Functions
  This  chapter  concludes  with details of various utility functions for score
manipulation.

patternp(expression)
     Test if expression is an Xmusic pattern.

params-transpose(params, keyword, amount)
     Add a  transposition  amount  to  a  score  event  parameter.  The  params
     parameter  is  a  list  of keyword/value pairs (not preceded by a function
     name).  The keyword is the keyword of the value to be altered, and  amount
     is a number to be added to the value. If no matching keyword is present in
     params, then params is  returned.  Otherwise,  a  new  parameter  list  is
     constructed and returned. The original params is not changed.

params-scale(params, keyword, amount)
     Scale  a  score  event  parameter   by   some   factor.   This   is   like
     params-transpose,  only using multiplication. The params list is a list of
     keyword/value pairs, keyword is the parameter keyword, and amount  is  the
     scale factor.

interpolate(x, x1, y1, x2, y2)
     Linearly interpolate (or extrapolate) between points (x1, y1) and (x2, y2)
     to compute the y value corresponding to x.

intersection(a, b)
     Compute the set intersection of lists a and b.

union(a, b)
     Compute the set union of lists a and b.

set-difference(a, b)
     Compute the set of all elements that are in a but not in b.

subsetp(a, b)\
     Returns  true  iff  a  is  a  subset of b, that is, each element of a is a
     member of b.
14. Nyquist Libraries
  Nyquist is always  growing  with  new  functions.  Functions  that  are  most
fundamental  are  added to the core language. These functions are automatically
loaded when you start  Nyquist,  and  they  are  documented  in  the  preceding
chapters.  Other  functions seem less central and are implemented as lisp files
that you can load. These are called library functions, and they  are  described
here.

  To  use  a  library  function,  you  must  first load the library, e.g. (load
"pianosyn") loads the piano synthesis library. The libraries are all located in
the  lib  directory,  and  you  should therefore include this directory on your
XLISPPATH variable. (See Section 1.) Each library is documented in one  of  the
following  sections.  When  you  load the library described by the section, all
functions documented in that section become available.

14.1. Piano Synthesizer
  The piano synthesizer (library  name  is  pianosyn.lsp)  generates  realistic
piano  tones  using a multiple wavetable implementation by Zheng (Geoffrey) Hua
and Jim  Beauchamp,  University  of  Illinois.  Please  see  the  notice  about
acknowledgements  that  prints when you load the file. Further informations and
example code can be  found  in  demos/piano.htm.    There  are  several  useful
functions in this library:

piano-note(duration, step, dynamic)
     Synthesizes a piano tone. Duration is the duration to  the  point  of  key
     release,  after  which  there  is a rapid decay. Step is the pitch in half
     steps, and dynamic is approximately equivalent  to  a  MIDI  key  velocity
     parameter.  Use  a  value near 100 for a loud sound and near 10 for a soft
     sound.

piano-note-2(step, dynamic)
     Similar to piano-note except the duration is nominally 1.0.

piano-midi(midi-file-name)
     Use the piano synthesizer to play a MIDI file. The file name (a string) is
     given by midi-file-name.

piano-midi2file(midi-file-name, sound-file-name)
     Use the piano synthesizer to play a MIDI file. The MIDI file is  given  by
     midi-file-name  and  the  (monophonic) result is written to the file named
     sound-file-name.

14.2. Dymanics Compression
  To use these functions, load the file compress.lsp. This library implements a
compressor  originally intended for noisy speech audio, but usable in a variety
of situations.  There are actually two compressors that can be used in  series.
The  first, compress, is a fairly standard one: it detects signal level with an
RMS detector and uses table-lookup to determine how much gain to place  on  the
original  signal  at  that  point.  One  bit of cleverness here is that the RMS
envelope is ``followed'' or enveloped using snd-follow, which  does  look-ahead
to anticipate peaks before they happen.

  The other interesting feature is compress-map, which builds a map in terms of
compression and expansion. For speech, the recommended procedure is  to  figure
out the noise floor on the signal you are compressing (for example, look at the
signal where the speaker is not talking).  Use a compression  map  that  leaves
the  noise  alone and boosts signals that are well above the noise floor. Alas,
the  compress-map  function  is  not  written   in   these   terms,   so   some
head-scratching is involved, but the results are quite good.

  The second compressor is called agc, and it implements automatic gain control
that keeps peaks at or below 1.0.  By  combining  compress  and  agc,  you  can
process  poorly  recorded  speech for playback on low-quality speakers in noisy
environments. The  compress  function  modulates  the  short-term  gain  to  to
minimize the total dynamic range, keeping the speech at a generally loud level,
and the agc function rides the long-term gain to set the overall level  without
clipping.

compress-map(compress-ratio,  compress-threshold,  expand-ratio,  expand-ratio,
     [limit: limit,] [transition:  transition])
     Construct  a map for the compress function. The map consists of two parts:
     a compression part and an expansion part.  The intended use is to compress
     everything  above  compress-threshold  by  compress-ratio, and to downward
     expand everything below expand-ratio by expand-ratio.  Thresholds  are  in
     dB  and  ratios are dB-per-dB.  0dB corresponds to a peak amplitude of 1.0
     or rms amplitude of 0.7 If the  input  goes  above  0dB,  the  output  can
     optionally  be limited by setting :limit (a keyword parameter) to T.  This
     effectively changes the compression ratio to infinity at 0dB.   If  :limit
     is  nil (the default), then the compression-ratio continues to apply above
     0dB.

Another keyword parameter, :transition, sets the amount  below  the  thresholds
     (in  dB)  that  a smooth transition starts. The default is 0, meaning that
     there is no smooth  transition.  The  smooth  transition  is  a  2nd-order
     polynomial  that matches the slopes of the straight-line compression curve
     and interpolates between them.

It is assumed that expand-threshold <= compress-threshold  <=  0  The  gain  is
     unity  at  0dB so if compression-ratio > 1, then gain will be greater than
     unity below 0dB.

The result returned by this function is a sound for use in the shape  function.
     The  sound  maps  input  dB to gain. Time 1.0 corresponds to 0dB, time 0.0
     corresponds to -100 dB, and time 2.0 corresponds to +100dB, so this  is  a
     100hz ``sample rate'' sound. The sound gives gain in dB.

db-average(input)
     Compute the average amplitude of input in dB.

compress(input, map, rise-time, fall-time, [lookahead])
     Compress  input  using  map,  a  compression  curve  probably generated by
     compress-map (see above). Adjustments in gain have the given rise-time and
     fall-time.  Lookahead  tells  how  far ahead to look at the signal, and is
     rise-time by default.

agc(input, range, rise-time, fall-time, [lookahead])
     An  automatic  gain  control  applied  to input. The maximum gain in dB is
     range. Peaks are attenuated to 1.0, and gain is controlled with the  given
     rise-time and fall-time. The look-ahead time default is rise-time.

14.3. Clipping Softener
  This  library,  in  soften.lsp,  was written to improve the quality of poorly
recorded speech. In recordings of speech, extreme clipping generates harsh high
frequency  noise.  This  can  sound particulary bad on small speakers that will
emphasize high  frequencies.  This  problem  can  be  ameliorated  by  low-pass
filtering  regions  where  clipping  occurs.  The  effect  is to dull the harsh
clipping. Intelligibility is not affected by much, and the result can  be  much
more  pleasant  on  the  ears. Clipping is detected simply by looking for large
signal values. Assuming 8-bit recording, this level is set to 126/127.

  The function works by cross-fading between the normal signal and  a  filtered
signal as opposed to changing filter coefficients.

soften-clipping(snd, cutoff)
     Filter the loud regions of a signal  where  clipping  is  likely  to  have
     generated  additional high frequencies. The input signal is snd and cutoff
     is the filter cutoff frequency (4 kHz is recommended for speech).

14.4. Graphical Equalizer
  There's nothing really ``graphical'' about this  library  (grapheq.lsp),  but
this  is  a  common  term  for  multi-band equalizers. This implementation uses
Nyquist's  eq-band  function  to  split  the  incoming  signal  into  different
frequency  bands.  Bands  are spaced geometrically, e.g. each band could be one
octave,  meaning  that  each  successive  band  has  twice  the  bandwidth.  An
interesting  possibility  is  using  computed  control  functions  to  make the
equalization change over time.

nband-range(input, gains, lowf, highf)
     A  graphical  equalizer  applied to input (a SOUND). The gain controls and
     number of bands is given by gains, an ARRAY of SOUNDs (in other  words,  a
     Nyquist  multichannel  SOUND). Any sound in the array may be replaced by a
     FLONUM. The  bands  are  geometrically  equally  spaced  from  the  lowest
     frequency lowf to the highest frequency highf (both are FLONUMs).

nband(input, gains)
     A graphical equalizer, identical to nband-range with  a  range  of  20  to
     20,000 Hz.

14.5. Sound Reversal
  The reverse.lsp library implements functions to play sounds in reverse.

s-reverse(snd)
     Reverses snd (a SOUND). Sound must be shorter than  *max-reverse-samples*,
     which  is  currently initialized to 25 million samples. Reversal allocates
     about 4 bytes per sample. This function uses XLISP  in  the  inner  sample
     loop,  so  do not be surprised if it calls the garbage collector a lot and
     runs slowly. The result starts at the starting time given by  the  current
     environment  (not  necessarily  the  starting  time  of  snd).  If snd has
     multiple channels, a multiple channel, reversed sound is returned.

s-read-reverse(filename,  [time-offset:  offset,]  [srate:  sr,]  [dur:   dur,]
     [nchans: chans,] [format: format,] [mode: mode,] [bits: n,] [swap: flag])
     This function is identical to  s-read  (see  7.5),  except  it  reads  the
     indicated samples in reverse. Like s-reverse (see above), it uses XLISP in
     the inner loop, so it is slow.  Unlike s-reverse,  s-read-reverse  uses  a
     fixed  amount  of  memory  that  is  independent  of  how many samples are
     computed. Multiple channels are handled.

14.6. Time Delay Functions
  The time-delay-fns.lsp library implements chorus, phaser, and flange effects.

phaser(snd)
     A  phaser  effect  applied  to snd (a SOUND). There are no parameters, but
     feel free to modify the source code of this one-liner.

flange(snd)
     A flange effect applied to snd. To vary the rate and other parameters, see
     the source code.

stereo-chorus(snd)
     A  chorus  effect  applied  to  snd, a SOUND (monophonic). The output is a
     stereo sound. All parameters are built-in, but see the simple source  code
     to make modifications.

chorus(snd, maxdepth, depth, rate, saturation)
     A chorus effect applied to snd. All parameters may be arrays as usual. The
     maxdepth is a FLONUM giving twice the maximum value of depth, which may be
     a FLONUM or a SOUND.  The  chorus  is  implemented  as  a  variable  delay
     modulated  by  a  sinusoid  running at rate Hz (a FLONUM). The sinusoid is
     scaled by depth and offset by maxdepth/2. The delayed signal is mixed with
     the  original,  and  saturation  gives  the fraction of the delayed signal
     (from 0 to 1) in the mix. A  reasonable  choice  of  parameter  values  is
     maxdepth = 0.05, depth = 0.025, rate = 0.5, and saturation = 0.5.

14.7. Multiple Band Effects
  The bandfx.lsp library implements several effects based on multiple frequency
bands. The idea is to separate a signal into different frequency bands, apply a
slightly  different  effect  to  each  band,  and  sum  the effected bands back
together to form the result. This file includes its own set of examples.  After
loading the file, try (f2), (f3), (f4), and (f5) to hear them.

  There is much room for expansion and experimentation with this library. Other
effects might include distortion in  certain  bands  (for  example,  there  are
commercial  effects that add distortion to low frequencies to enhance the sound
of  the  bass),  separating  bands  into  different  channels  for  stereo   or
multi-channel   effects,  adding  frequency-dependent  reverb,  and  performing
dynamic compression, limiting, or noise gate functions on each band. There  are
also  opportunities  for  cross-synthesis: using the content of bands extracted
from one signal to modify the bands of another. The simplest of these would  be
to  apply  amplitude  envelopes  of  one  sound  to  another. Please contact us
(dannenberg@cs.cmu.edu) if you are interested in working on this library.

apply-banded-delay( s, lowp, highp, num-bands, lowd, highd, fb, wet)
     Separates  input  SOUND s into FIXNUM num-bands bands from a low frequency
     of lowp to a high frequency of  highp  (these  are  FLONUMS  that  specify
     steps, not Hz), and applies a delay to each band. The delay for the lowest
     band is given by the FLONUM lowd  (in  seconds)  and  the  delay  for  the
     highest  band is given by the FLONUM highd. The delays for other bands are
     linearly interpolated between these values. Each delay has  feedback  gain
     controlled  by  FLONUM fb. The delayed bands are scaled by FLONUM wet, and
     the original sound is scaled by 1 -  wet.  All  are  summed  to  form  the
     result, a SOUND.

apply-banded-bass-boost(s, lowp, highp, num-bands, num-boost, gain)
     Applies a boost to low frequencies. Separates input SOUND  s  into  FIXNUM
     num-bands  bands from a low frequency of lowp to a high frequency of highp
     (these are FLONUMS that specify steps, not  Hz),  and  scales  the  lowest
     num-boost (a FIXNUM) bands by gain, a FLONUM. The bands are summed to form
     the result, a SOUND.

apply-banded-treble-boost(s, lowp, highp, num-bands, num-boost, gain)
     Applies  a  boost to high frequencies. Separates input SOUND s into FIXNUM
     num-bands bands from a low frequency of lowp to a high frequency of  highp
     (these  are  FLONUMS  that  specify steps, not Hz), and scales the highest
     num-boost (a FIXNUM) bands by gain, a FLONUM. The bands are summed to form
     the result, a SOUND.

14.8. Granular Synthesis
  Some  granular  synthesis  functions  are implemented in the gran.lsp library
file. There are many  variations  and  control  schemes  one  could  adopt  for
granular  synthesis,  so it is impossible to create a single universal granular
synthesis function. One of the advantages of  Nyquist  is  the  integration  of
control  and  synthesis  functions, and users are encouraged to build their own
granular synthesis functions  incorporating  their  own  control  schemes.  The
gran.lsp  file  includes  many comments and is intended to be a useful starting
point.

sf-granulate(sf-granulate,  filename,  grain-dur,  grain-dev,   ioi,   ioi-dev,
     pitch-dev, [file-start,] [file-end])
     Granular synthesis using a sound file named filename  as  the  source  for
     grains.  Each  grain  duration is the sum of grain-dur and a random number
     from 0 to grain-dev. The inter-onset interval  between  successive  grains
     (which  may  overlap)  is  the  sum  of  ioi and a random number from 0 to
     ioi-dev. Grains are resampled at a  rate  between  1  and  pitch-dev.  The
     duration  of  the result sound is determined by the stretch factor (not by
     the sound file), and grains are selected from  the  file  by  more-or-less
     stepping  through  the  file uniformly (the step size depends on the total
     number of grains needed for the output.) The optional  parameters  give  a
     starting  point  and  ending point (in seconds) from which to take samples
     from the file. To achieve a rich granular synthesis effect, it is often  a
     good  idea  to  sum four or more copies of sf-granulate together. (See the
     gran-test function in gran.lsp.)

14.9. MIDI Utilities
  The midishow.lsp library has functions that can print the  contents  fo  MIDI
files. This intended as a debugging aid.

midi-show-file(file-name)
     Print the contents of a MIDI file to the console.

midi-show(the-seq, [out-file])
     Print  the  contents  of  the sequence the-seq to the file out-file (whose
     default value is the console.)

14.10. Reverberation
  The reverb.lsp library implements artificial reverberation.

reverb(snd, time)
     Artificial reverberation applied to snd with a decay time of time.

14.11. DTMF Encoding
  The  dtmf.lsp  library  implements  DTMF encoding. DTMF is the ``touch tone''
code used by telephones.

dtmf-tone(key, len, space)
     Generate a single DTMF tone. The key parameter is either a digit (a FIXNUM
     from 0 through 9) or the atom STAR or POUND. The duration of the  done  is
     given  by  len  (a FLONUM) and the tone is followed by silence of duration
     space (a FLONUM).

speed-dial(thelist)
     Generates  a  sequence  of DTMF tones using the keys in thelist (a LIST of
     keys as described above under dtmf-tone). The duration of each tone is 0.2
     seconds,  and the space between tones is 0.1 second. Use stretch to change
     the ``dialing'' speed.

14.12. Dolby Surround(R), Stereo and Spatialization Effects
  The spatial.lsp library implements various functions for stereo  manipulation
and  spatialization.  It  also  includes  some  functions  for  Dolby Pro-Logic
panning, which encodes left, right, center, and surround channels into  stereo.
The  stereo  signal  can  then  be  played  through  a Dolby decoder to drive a
surround speaker array. This library has a somewhat simplified encoder, so  you
should  certainly  test  the  output.  Consider  using  a  high-end encoder for
critical work. There are a number of functions in spatial.lsp for testing.  See
the source code for comments about these.

stereoize(snd)
     Convert a mono sound, snd, to stereo. Four bands of equalization and  some
     delay are used to create a stereo effect.

widen(snd, amt)
     Artificially widen the stereo field  in  snd,  a  two-channel  sound.  The
     amount  of  widening  is  amt, which varies from 0 (snd is unchanged) to 1
     (maximum widening).  The amt can be a SOUND or a number.

span(snd, amt)
     Pan  the  virtual  center  channel of a stereo sound, snd, by amt, where 0
     pans all the way to the left, while 1 pans all the way to the  right.  The
     amt can be a SOUND or a number.

swapchannels(snd)
     Swap left and right channels in snd, a stereo sound.

prologic(l, c, r, s)
     Encode  four  monaural  SOUNDs  representing the front-left, front-center,
     front-right, and rear channels, respectively.    The  return  value  is  a
     stereo sound, which is a Dolby-encoded mix of the four input sounds.

pl-left(snd)
     Produce a Dolby-encoded (stereo) signal with snd, a SOUND, encoded as  the
     front left channel.

pl-center(snd)
     Produce a Dolby-encoded (stereo) signal with snd, a SOUND, encoded as  the
     front center channel.

pl-right(snd)
     Produce a Dolby-encoded (stereo) signal with snd, a SOUND, encoded as  the
     front right channel.

pl-rear(snd)
     Produce a Dolby-encoded (stereo) signal with snd, a SOUND, encoded as  the
     rear, or surround, channel.

pl-pan2d(snd, x, y)
     Comparable to Nyquist's existing pan function, pl-pan2d provides not  only
     left-to-right  panning,  but  front-to-back  panning as well. The function
     accepts three parameters: snd is the (monophonic)  input  SOUND,  x  is  a
     left-to-right  position, and y is a front-to-back position.  Both position
     parameters may be numbers or SOUNDs. An x value of 0  means  left,  and  1
     means  right.  Intermediate  values  map  linearly between these extremes.
     Similarly, a y value of 0 causes the sound to play  entirely  through  the
     front  speakers(s),  while  1 causes it to play entirely through the rear.
     Intermediate values map linearly.  Note that, although there  are  usually
     two  rear  speakers in Pro-Logic systems, they are both driven by the same
     signal. Therefore any sound that is panned totally to  the  rear  will  be
     played  over both rear speakers. For example, it is not possible to play a
     sound exclusively through the rear left speaker.

pl-position(snd, x, y, config)
     The  position  function builds upon speaker panning to allow more abstract
     placement of sounds. Like pl-pan2d, it accepts a (monaural) input sound as
     well  as left-to-right (x) and front-to-back (y) coordinates, which may be
     FLONUMs or SOUNDs. A fourth parameter config specifies the  distance  from
     listeners  to the speakers (in meters). Current settings assume this to be
     constant for all speakers, but this assumption can be changed easily  (see
     comments  in  the  code  for  more  detail).   There are several important
     differences between pl-position and pl-pan2d. First,  pl-position  uses  a
     Cartesian coordinate system that allows x and y coordinates outside of the
     range (0, 1). This model  assumes  a  listener  position  of  (0,0).  Each
     speaker  has  a  predefined  position as well. The input sound's position,
     relative to the listener, is given by the vector (x,y).

pl-doppler(snd, r)
     Pitch-shift  moving  sounds  according to the equation: fr = f0((c+vr)/c),
     where fr is the output frequency, f0 is the emitted (source) frequency,  c
     is  the  speed of sound (assumed to be 344.31 m/s), and vr is the speed at
     which the emitter approaches the receiver. (vr is the first derivative  of
     parameter r, the distance from the listener in meters.

14.13. Drum Machine
  The  drum  machine software in demos/plight deserves further explanation.  to
use the software, load the code by evaluating:

    (load "../demos/plight/drum.lsp")
    (load-props-file (strcat *plight-drum-path* "beats.props"))
    (create-drum-patches)
    (create-patterns)

  Drum sounds and patterns are specified in the beats.props file  (or  whatever
name   you   give   to  load-props-file).  This  file  contains  two  types  of
specifications. First, there are sound file specifications.   Sound  files  are
located by a line of the form:

    sound-directory = kit/

This  gives  the  name of the sound file directory, relative to the beats.props
file. Then, for each sound file, there should be a line of the form:

    track.2.5 = big-tom-5.wav
This says that on track 2, a velocity value of 5 means to play the  sound  file
big-tom-5.wav.   (Tracks  and  velocity  values  are  described  below.)    The
beats.props  file  contains  specifications  for  all  the   sound   files   in
demos/plight/kit  using  8  tracks.  If  you make your own specifications file,
tracks should be numbered consecutively from 1, and velocities should be in the
range of 1 to 9.

  The second set of specifications is of beat patterns. A beat pattern is given
by a line in the following form:

    beats.5 = 2--32--43-4-5---

The number after beats is just a pattern number. Each pattern is given a unique
number. After the equal sign, the digits and dashes are velocity values where a
dash means ``no sound.'' Beat patterns should be numbered consecutively from 1.

  Once data is loaded, there are several functions to access drum patterns  and
create  drum sounds (described below). The demos/plight/drums.lsp file contains
an example function plight-drum-example to play some drums.  There is also  the
file  demos/plight/beats.props  to  serve as an example of how to specify sound
files and beat patterns.

drum(tracknum, patternnum, bpm)
     Create  a  sound by playing drums sounds associated with track tracknum (a
     FIXNUM) using pattern patternnum. The tempo is given by bpm in  beats  per
     minute.  Normally patterns are a sequence of sixteenth notes, so the tempo
     is in sixteenth notes per minute. For example, if patternnum is  10,  then
     use  the  pattern  specified  for beats.10. If the third character of this
     pattern is 3 and tracknum is 5, then on the third beat, play the soundfile
     assigned to track.5.3. This function returns a SOUND.

drum-loop(snd, duration, numtimes)
     Repeat the sound given by snd numtimes times. The repetitions occur  at  a
     time offset of duration, regardless of the actual duration of snd. A SOUND
     is returned.

length-of-beat(bpm)
     Given  a  tempo  of  bpm, return the duration of the beat in seconds. Note
     that this software has no real notion of beat.  A  ``beat''  is  just  the
     duration  of  each  character  in  the beat pattern strings. This function
     returns a FLONUM.

14.14. Minimoog-inspired Synthesis
  The moog.lsp library gives  the  Nyquist  user  easy  access  to  ``classic''
synthesizer  sounds  through  an emulation of the Minimoog Synthesizer.  Unlike
modular Moogs that were very large, the Minimoog was the first  successful  and
commonly  used portable synthesizer. The trademark filter attack was unique and
easily recognizable. The goal of this Nyquist instrument is not only to provide
the  user  with  default  sounds,  but  also  to  give control over many of the
``knobs'' found on the Minimoog. In this implementation, these  parameters  are
controlled  using  keywords. The input to the moog instrument is a user-defined
sequence of notes, durations, and articulations that simulate notes played on a
keyboard.  These  are  translated  into  control  voltages  that drive multiple
oscillators, similar to the Voltage Controlled Oscillator or VCO found  in  the
original analog Moog.

  The  basic  functionality of the Minimoog has been implemented, including the
often-used "glide". The glide feature essentially low-pass filters the  control
voltage  sequence  in  order  to  create  sweeps between notes.  Figure 21 is a
simplified schematic of the data flow in the Moog.  The control lines have been
omitted.


















     Figure 21:  System diagram for Minimoog emulator.


  The  most  recognizable  feature  of  the  Minimoog is its resonant filter, a
Four-Pole Ladder Filter invented by Robert Moog. It is simply implemented in  a
circuit with four transistors and provides an outstanding 24 dB/octave rolloff.
It is modeled here using the built-in Nyquist resonant filter.  One of the Moog
filter  features  is a constant Q, or center frequency to bandwidth ratio. This
is implemented and the user can control the Q.

  The user can control many parameters using keywords.  Their  default  values,
acceptable ranges, and descriptions are shown below. The defaults were obtained
by experimenting with the official Minimoog software synthesizer by Arturia.



14.14.1. Oscillator Parameters
  range-osc1 (2)
range-osc2 (1)
range-osc3 (3)
These  parameters  control  the  octave  of  each  oscillator.  A  value  of  1
corresponds  to  the  octave  indicated  by the input note. A value of 3 is two
octaves above the fundamental. The allowable range is 1 to 7.

  detun2 (-.035861)
detun3 (.0768)
Detuning of two oscillators adds depth to the sound. A value of  1  corresponds
to  an  increase  of  a single semitone and a -1 corresponds to a decrease in a
semitone. The range is -1 to 1.

  shape-osc1 (*saw-table*)
shape-osc2 (*saw-table*)
shape-osc3 (*saw-table*)
Oscilators can use any wave shape. The default sawtooth waveform is a  built-in
Nyquist variable. Other waveforms can be defined by the user.

  volume-osc1 (1)
volume-osc2 (1)
volume-osc3 (1)
These  parameters  control the relative volume of each oscillator. The range is
any FLONUM greater than or equal to zero.



14.14.2. Noise Parameters
  noiselevel (.05)
This parameter controls the relative volume of the noise source. The  range  is
any FLONUM greater than or equal to zero.



14.14.3. Filter Parameters
  filter-cutoff (768)
The  cutoff frequency of the filter in given in Hz. The range is zero to 20,000
Hz.

  Q (2)
Q is the ratio of center frequency to bandwidth. It is held constant by  making
the  bandwidth  a  function  of frequency. The range is any FLONUM greater than
zero.

  contour (.65)
Contour controls the range of the transient frequency sweep from a high to  low
cutoff  frequency  when a note is played. The high frequency is proportional to
contour. A contour of 0 removes this sweep. The range is 0 to 1.

  filter-attack (.0001)
Filter attack controls the attack time of the filter, i.e. the  time  to  reach
the high cutoff frequency. The range is any FLONUM greater than zero (seconds).

  filter-decay (.5)
Filter  decay controls the decay time of the filter, i.e. the time of the sweep
from the high to low cutoff frequency. The range is  any  FLONUM  greater  than
zero (seconds).

  filter-sustain (.8)
Filter  sustain controls the percentage of the filter cutoff frequency that the
filter settles on following the sweep. The range is 0 to 1.



14.14.4. Amplitude Parameters
  amp-attack (.01)
This parameter controls the amplitude envelope attack time, i.e.  the  time  to
reach maximum amplitude. The range is any FLONUM greater than zero (seconds).

  amp-decay (1)
This  parameter  controls  the  amplitude  envelope  decay  time, i.e. the time
between the maximum and sustain volumes. The range is any FLONUM  greater  than
zero (seconds).

  amp-sustain (1)
This  parameter  controls  the amplitude envelope sustain volume, a fraction of
the maximum. The range is 0 to 1.

  amp-release (0)
This parameter controls the amplitude envelope release time, i.e. the  time  it
takes  between  the  sustain  volume  and  0  once the note ends.  The duration
controls the overall length of the sound.  The  range  of  amp-release  is  any
FLONUM greater than zero (seconds).



14.14.5. Other Parameters
  glide (0)
Glide  controls  the  low-pass  filter on the control voltages. This models the
glide knob on a  Minimoog.  A  higher  value  corresponds  to  a  lower  cutoff
frequency and hence a longer "glide" between notes. A value of 0 corresponds to
no glide. The range is zero to 10.



14.14.6. Input Format
  A single note or a series of notes can be input to  the  Moog  instrument  by
defining a list with the following format:

    (list (list frequency duration articulation) ... )

where  frequency is a FLONUM in steps, duration is the duration of each note in
seconds (regardless of the release time of the amplifier), and articulation  is
a  percentage  of  the  duration  that a sound will be played, representing the
amount of time that a key is pressed. The filter and  amplitude  envelopes  are
only  triggered  if a note is played when the articulation of the previous note
is less than 1, or a key is not down at the same time. This Moog instrument  is
a  monophonic  instrument,  so  only  one note can sound at a time. The release
section of the amplifier is triggered when the articulation is less than  1  at
the time (duration * articulation).



14.14.7. Sample Code/Sounds
  Sound 1 (default parameters):

    (setf s '((24 .5 .99)(26 .5 .99)(28 .5 .99)(29 .5 .99)(31 2 1)))
    (play (moog s))


  Sound 2 (articulation, with amplitude release):

    (setf s '((24 .5 .5)(26 .5 1)(28 .5 .25)(29 .5 1)(31 1 .8)))
    (play (moog s :amp-release .2))


  Sound 3 (glide):

    (setf s '((24 .5 .5)(38 .5 1)(40 .5 .25)
              (53 .5 1)(55 2 1)(31 2 .8)(36 2 .8)))
    (play (moog s :amp-release .2 :glide .5))


  Sound  4  (keyword  parameters): Filter attack and decay are purposely longer
than notes being played with articulation equal to 1.

    (setf s '((20 .5 1)(27 .5 1)(26 .5 1)(21 .5 1)
              (20 .5 1)(27 .5 1)(26 .5 1)(21 .5 1)))
    (play (moog s :shape-osc1 *tri-table* :shape-osc2 *tri-table*
                  :filter-attack 2 :filter-decay 2
                  :filter-cutoff 300 :contour .8 :glide .2 :Q 8))


  Sound 5: This example illustrates the ability  to  completely  define  a  new
synthesizer  with  different parameters creating a drastically different sound.
Sine waves are used for wavetables. There is a high value for glide.

    (defun my-moog (freq) (moog freq
      :range-osc1 3 :range-osc2 2 :range-osc3 4
      :detun2 -.043155 :detun3 .015016
      :noiselevel 0
      :filter-cutoff 400 :Q .1 :contour .0000001
      :filter-attack 0 :filter-decay .01 :filter-sustain 1
      :shape-osc1 *sine-table* :shape-osc2 *sine-table*
      :shape-osc3 *sine-table* :volume-osc1 1 :volume-osc2 1
      :volume-osc3 .1 :amp-attack .1 :amp-decay 0
      :amp-sustain 1 :amp-release .3 :glide 2))

    (setf s '((80 .4 .75)(28 .2 1)(70 .5 1)(38 1 .5)))
    (play (my-moog s))


  Sound 6: This example has another variation on the default parameters.

    (setf s '((24 .5 .99)(26 .5 .99)(28 .5 .99)(29 .5 .99)(31 2 1)))
    (play (moog s :shape-osc1 *tri-table* :shape-osc2 *tri-table*
                  :filter-attack .5 :contour .5))
I. Extending Nyquist
  WARNING:  Nyquist sound functions look almost like a human wrote  them;  they
even  have  a  fair  number  of  comments  for human readers.  Don't be fooled:
virtually all Nyquist functions are written by a special translator.    If  you
try to write a new function by hand, you will probably not succeed, and even if
you do, you will waste a great deal of time.  (End of Warning.)

I.1. Translating Descriptions to C Code
  The translator code used to extend Nyquist resides in the  trnsrc  directory.
This  directory  also  contains  a  special  init.lsp, so if you start XLisp or
Nyquist in this directory, it will automatically read init.lsp, which  in  turn
will load the translator code (which resides in several files).

  Also  in  the  trnsrc directory are a number of .alg files, which contain the
source code for the translator (more on these will follow),  and  a  number  of
corresponding .h and .c files.

  To  translate  a  .alg file to .c and .h files, you start XLisp or Nyquist in
the trnsrc directory and type

    (translate "prod")

where "prod" should really be replaced by the filename (without a  suffix)  you
want  to translate.  Be sure you have a saved, working copy of Nyquist or Xlisp
before you recompile!

  Note: On the Macintosh, just run Nyquist out of  the  runtime  directory  and
then  use  the  Load  menu  command to load init.lsp from the trnsrc directory.
This will load the translation code and change Nyquist's current  directory  to
trnsrc so that commands like (translate "prod") will work.

I.2. Rebuilding Nyquist
  After  generating prod.c and prod.h, you need to recompile Nyquist.  For Unix
systems, you will want to generate a new Makefile.   Modify  transfiles.lsp  in
your  main  Nyquist  directory,  run  Xlisp  or  Nyquist and load makefile.lsp.
Follow the instructions to set your machine type, etc., and  execute  (makesrc)
and (makefile).

I.3. Accessing the New Function
  The  new  Lisp  function  will  generally  be  named with a snd- prefix, e.g.
snd-prod.  You can test this by  running  Nyquist.    Debugging  is  usually  a
combination  of  calling  the  code  from  within  the interpreter, reading the
generated code when things go wrong, and using a C debugger to step through the
inner  loop  of  the  generated code.  An approach I like is to set the default
sample rate to 10 hertz.  Then, a one-second sound has only 10  samples,  which
are easy to print and study on a text console.

  For  some functions, you must write some Lisp code to impose ordinary Nyquist
behaviors such as stretching and time shifting.  A good  approach  is  to  find
some  structurally similar functions and see how they are implemented.  Most of
the Lisp code for Nyquist is in nyquist.lsp.

  Finally, do not forget to write up some documentation.   Also,  contributions
are  welcome.    Send your .alg file, documentation, Lisp support functions for
nyquist.lsp, and examples or test programs to rbd@cs.cmu.edu.   I  will  either
put them in the next release or make them available at a public ftp site.

I.4. Why Translation?
  Many  of  the  Nyquist  signal processing operations are similar in form, but
they differ in details. This code is complicated by many factors: Nyquist  uses
lazy  evaluation,  so  the  operator  must  check to see that input samples are
available before trying to access them.  Nyquist  signals  can  have  different
sample  rates, different block sizes, different block boundaries, and different
start times, all of which must be taken into account.  The number  of  software
tests  is enormous. (This may sound like a lot of overhead, but the overhead is
amortized over many iterations of the inner loop.  Of  course  setting  up  the
inner loop to run efficiently is one more programming task.)

  The main idea behind the translation is that all of the checks and setup code
are similar and relatively easy to generate  automatically.  Programmers  often
use  macros for this sort of task, but the C macro processor is too limited for
the complex translation required here. To tell the translator how  to  generate
code, you write .alg files, which provide many details about the operation in a
declarative style.  For example, the code generator can make some optimizations
if  you  declare  that two input signals are commutative (they can be exchanged
with one another). The main part of the .alg file is the inner  loop  which  is
the heart of the signal processing code.

I.5. Writing a .alg File
  To  give you some idea how functions are specified, here is the specification
for snd-prod, which generates over 250 lines of C code:

    (PROD-ALG
      (NAME "prod")
      (ARGUMENTS ("sound_type" "s1") ("sound_type" "s2"))
      (START (MAX s1 s2))
      (COMMUTATIVE (s1 s2))
      (INNER-LOOP "output = s1 * s2")
      (LINEAR s1 s2)
      (TERMINATE (MIN s1 s2))
      (LOGICAL-STOP (MIN s1 s2))
    )

A .alg file is always of the form:

    (name
      (attribute value)
      (attribute value)
      ...
    )

There should be just one of these algorithms descriptions per file.   The  name
field is arbitrary: it is a Lisp symbol whose property list is used to save the
following attribute/value pairs.  There are many  attributes  described  below.
For more examples, see the .alg files in the trnsrc directory.

  Understanding  what  the  attributes  do  is  not  easy,  so  here  are three
recommendations for implementors.  First,  if  there  is  an  existing  Nyquist
operator  that is structurally similar to something you want to implement, make
a copy of the corresponding .alg file and work from there. In some  cases,  you
can merely rename the parameters and substitute a new inner loop.  Second, read
the generated code, especially the generated inner loop.  It may not  all  make
sense,  but sometimes you can spot obvious errors and work your way back to the
error in the .alg file.  Third, if you know where something bad  is  generated,
see if you can find where the code is generated.  (The code generator files are
listed in init.lsp.)  This code is poorly written and poorly documented, but in
some cases it is fairly straightforward to determine what attribute in the .alg
file is responsible for the erroneous output.

I.6. Attributes
  Here are the attributes used for code generation. Attributes and  values  may
be specified in any order.

(NAME "string") specifies a base name for many identifiers.  In particular, the
                generated filenames will be  string.c  and  string.h,  and  the
                XLisp function generated will be snd-string.

(ARGUMENTS arglist)
                describes the arguments to be passed from  XLisp.  Arglist  has
                the  form: (type1 name1) (type2 name2) ..., where type and name
                are strings in double quotes, e.g. ("sound_type" "s") specifies
                a SOUND parameter named s.  Note that arglist is not surrounded
                by parentheses.  As seen in this example, the  type  names  and
                parameter  names  are  C  identifiers. Since the parameters are
                passed in from XLisp, they must be  chosen  from  a  restricted
                set.      Valid  type  names  are:  "sound_type",  "rate_type",
                "double", "long", "string", and "LVAL".

(STATE statelist)
                describes  additional  state  (variables) needed to perform the
                computation.   A  statelist  is  similar  to  an  arglist  (see
                ARGUMENTS  above), and has the form: (type1 name1 init1 [TEMP])
                (type2 name2 init2 [TEMP]) ....  The types and names are as  in
                arglist,  and  the  "inits"  are  double-quoted initial values.
                Initial values may be any C expression.  State  is  initialized
                in  the  order implied by statelist when the operation is first
                called from XLisp.  If TEMP is omitted the state  is  preserved
                in   a   structure   until  the  sound  computation  completes.
                Otherwise,  the   state   variable   only   exists   at   state
                initialization time.

(INNER-LOOP innerloop-code)
                describes the inner loop, written as C code. The innerloop-code
                is  in  double  quotes, and may extend over multiple lines.  To
                make  generated  code  extra-beautiful,  prefix  each  line  of
                innerloop-code  with 12 spaces.  Temporary variables should not
                be  declared  at  the  beginning  of  innerloop-code.  Use  the
                INNER-LOOP-LOCALS  attribute  instead.   Within innerloop-code,
                each ARGUMENT of type sound_type must be referenced exactly one
                time.  If  you need to use a signal value twice, assign it once
                to a temporary and use the temporary twice.    The  inner  loop
                must  also  assign one time to the psuedo-variable output.  The
                model here is that the name of a  sound  argument  denotes  the
                value  of the corresponding signal at the current output sample
                time.  The inner loop code will be called once for each  output
                sample.    In practice, the code generator will substitute some
                expression  for  each  signal  name.  For   example,   prod.alg
                specifies

                    (INNER-LOOP "output = s1 * s2")

                (s1 and s2 are ARGUMENTS.)  This expands to the following inner
                loop in prod.c:

                    *out_ptr_reg++ = *s1_ptr_reg++ * *s2_ptr_reg++;

                In cases where arguments have different  sample  rates,  sample
                interpolation  is  in-lined,  and  the expressions can get very
                complex. The translator is currently very  simple-minded  about
                substituting  access  code in the place of parameter names, and
                this is a frequent source of bugs.  Simple string  substitution
                is  performed,  so  you  must not use a parameter or state name
                that is a substring of another.   For  example,  if  two  sound
                parameters were named s and s2, the translator might substitute
                for ``s'' in two places rather  than  one.    If  this  problem
                occurs,  you  will  almost  certainly  get  a C compiler syntax
                error.  The fix is to use ``more unique'' parameter  and  state
                variable names.

(INNER-LOOP-LOCALS "innerloop-code")
                The innerloop-code contains C declarations of  local  variables
                set and referenced in the inner loop.

(SAMPLE-RATE "expr")
                specifies the output sample rate; expr can be any C expression,
                including  a  parameter  from  the ARGUMENTS list. You can also
                write (SAMPLE-RATE (MAX name1 name2  ...))    where  names  are
                unquoted names of arguments.

(SUPPORT-HEADER "c-code")
                specifies arbitrary C code to be inserted in the  generated  .h
                file.   The   code   typically   contains  auxiliarly  function
                declarations and definitions of constants.

(SUPPORT-FUNCTIONS "c-code")
                specifies  arbitrary  C code to be inserted in the generated .c
                file. The code  typically  contains  auxiliarly  functions  and
                definitions of constants.

(FINALIZATION "c-code")
                specifies code  to  execute  when  the  sound  has  been  fully
                computed  and the state variables are about to be decallocated.
                This is the place to deallocate buffer memory, etc.

(CONSTANT "name1" "name2" ...)
                specifies state variables that do not change value in the inner
                loop.  The values of state variables are loaded into  registers
                before  entering  the  inner  loop  so that access will be fast
                within the loop.  On exiting the inner loop, the final register
                values  are  preserved in a ``suspension'' structure.  If state
                values  do  not  change  in  the  inner  loop,  this   CONSTANT
                declaration   can  eliminate  the  overhead  of  storing  these
                registers.

(START spec)    specifies when the output sound should start (a sound  is  zero
                and  no processing is done before the start time). The spec can
                take several forms: (MIN name1 name2 ...) means the start  time
                is  the  minimum  of  the  start  times of input signals name1,
                name2, ....  Note that these names are not quoted.

(TERMINATE spec)
                specifies  when  the  output  sound terminates (a sound is zero
                after this termination time and no more samples are  computed).
                The  spec  can  take several forms: (MIN name1 name2 ...) means
                the terminate time is the minimum of  the  terminate  times  of
                input  arguments  name1, name2, ....  Note that these names are
                not quoted.  To terminate at the time of a single argument  s1,
                specify  (MIN s1).  To terminate after a specific duration, use
                (AFTER "c-expr"), where c-expr is a C variable  or  expression.
                To terminate at a particular time, use (AT "c-expr").  spec may
                also be COMPUTED, which means to use the maximum sample rate of
                any input signal.

(LOGICAL-STOP spec)
                specifies the logical stop time of the output sound.  This spec
                is  just  like  the  one  for  TERMINATE.    If no LOGICAL-STOP
                attribute is present, the logical stop will coincide  with  the
                terminate time.

(ALWAYS-SCALE name1 name2 ...)
                says that the named sound  arguments  (not  in  quotes)  should
                always  be  multiplied by a scale factor.  This is a space-time
                tradeoff. When Nyquist sounds are scaled, the scale  factor  is
                merely  stored in a structure.  It is the responsibility of the
                user of the samples to actually scale them  (unless  the  scale
                factor  is  exactly 1.0).  The default is to generate code with
                and without scaling and to select the appropriate code  at  run
                                                                              N
                time.    If  there  are  N signal inputs, this will generate 2 
                versions of the code.  To avoid this code  explosion,  use  the
                ALWAYS-SCALE attribute.

(INLINE-INTERPOLATION T)
                specifies that sample rate interpolation  should  be  performed
                in-line  in  the inner loop. There are two forms of sample rate
                interpolation.  One is intended for use when the rate change is
                large  and  many points will be interpolated.  This form uses a
                divide instruction and some setup at the low sample  rate,  but
                the  inner  loop  overhead  is  just  an  add.  The other form,
                intended  for  less  drastic  sample  rate  changes,   performs
                interpolation  with 2 multiplies and several adds per sample at
                the high sample rate.  Nyquist generates  various  inner  loops
                and   selects   the   appropriate   one   at   run-time.     If
                INLINE-INTERPOLATION  is  not  set,  then  much  less  code  is
                generated  and  interpolation  is  performed  as  necessary  by
                instantiating a separate signal processing operation.

(STEP-FUNCTION name1 name2 ...)
                Normally  all argument signals are linearly interpolated to the
                output sample rate.  The linear interpolation can be turned off
                with  this  attribute.  This  is  used, for example, in Nyquist
                variable filters so that filter coefficients  are  computed  at
                low  sample  rates.   In fact, this attribute was added for the
                special case of filters.

(DEPENDS spec1 spec2 ...)
                Specifies  dependencies.  This attribute was also introduced to
                handle the case of filter  coefficients  (but  may  have  other
                applications.)  Use it when a state variable is a function of a
                potentially low-sample-rate input where the  input  is  in  the
                STEP-FUNCTION list.  Consider a filter coefficient that depends
                upon an input signal such as bandwidth.  In this case, you want
                to  compute  the  filter coefficient only when the input signal
                changes rather than every output sample, since output may occur
                at a much higher sample rate.  A spec is of the form

                    ("name" "arg" "expr" [TEMP "type"])

                which  is  interpreted  as follows: name depends upon arg; when
                arg changes, recompute expr and assign it  to  name.  The  name
                must be declared as a STATE variable unless TEMP is present, in
                which case name is not preserved and is used  only  to  compute
                other state.  Variables are updated in the order of the DEPENDS
                list.

(FORCE-INTO-REGISTER name1 name2 ...)
                causes  name1,  name2,  ...  to be loaded into registers before
                entering the inner loop.  If the inner loop references a  state
                variable  or  argument,  this  happens  automatically. Use this
                attribute only if references  are  ``hidden''  in  a  #define'd
                macro or referenced in a DEPENDS specification.

(NOT-REGISTER name1 name2 ...)
                specifies state and arguments that should not  be  loaded  into
                registers  before entering an inner loop.  This is sometimes an
                optimization for infrequently accessed state.

(NOT-IN-INNER-LOOP "name1" "name2" ...)
                says  that  certain  arguments  are not used in the inner loop.
                Nyquist assumes all arguments are used in the  inner  loop,  so
                specify  them here if not.  For example, tables are passed into
                functions  as  sounds,  but   these   sounds   are   not   read
                sample-by-sample  in  the  inner loop, so they should be listed
                here.

(MAINTAIN ("name1" "expr1") ("name2" "expr2") ...  )
                Sometimes  the IBM XLC compiler generates better loop code if a
                variable referenced in the loop is not  referenced  outside  of
                the  loop  after  the  loop exit.  Technically, optimization is
                better when variables are dead upon loop exit. Sometimes, there
                is  an  efficient  way  to  compute  the final value of a state
                variable without actually referencing it,  in  which  case  the
                variable  and the computation method are given as a pair in the
                MAINTAIN attribute.  This suppresses a store of  the  value  of
                the named variable, making it a dead variable.  Where the store
                would have been, the expression is computed and assigned to the
                named  variable.    See  partial.alg  for  an  example.    This
                optimization is never necessary and is only for fine-tuning.

(LINEAR name1 name2 ...)
                specifies that named arguments (without quotes) are linear with
                respect to the output.  What this really means is  that  it  is
                numerically  OK  to  eliminate  a  scale  factor from the named
                argument and store it in the output sound descriptor,  avoiding
                a  potential  multiply  in  this inner loop.  For example, both
                arguments to snd-prod (signal multiplication)  are  ``linear.''
                The inner loop has a single multiplication operator to multiply
                samples vs. a potential 3 multiplies if each sample  were  also
                scaled.    To  handle  scale  factors on the input signals, the
                scale factors are  automatically  multiplied  and  the  product
                becomes  the  scale  factor  of  the  resulting  output.  (This
                effectively ``passes the buck'' to some other, or perhaps  more
                than  one,  signal  processing  function,  which  is not always
                optimal. On the other hand, it works great if  you  multiply  a
                number  of  scaled  signals together: all the scale factors are
                ultimately handled with a single multiply.)

(INTERNAL-SCALING name1 name2 ...)
                indicates  that  scaling is handled in code that is hidden from
                the code generator for  name1,  name2,  ...,  which  are  sound
                arguments.  Although  it is the responsibility of the reader of
                samples to apply any given scale factor, sometimes scaling  can
                be had for free.  For example, the snd-recip operation computes
                the reciprocal of the input samples by  peforming  a  division.
                The simple approach would be to specify an inner loop of output
                = 1.0/s1, where s1 is the input.    With  scaling,  this  would
                generate an inner loop something like this:

                    *output++ = 1.0 / (s1_scale_factor * *s1++);

                but a much better approach would be the following:

                    *output++ = my_scale_factor / *s1++

                where  my_scale_factor  is  initialized  to  1.0  /  s1->scale.
                Working backward from the desired inner loop to the .alg  inner
                loop specification, a first attempt might be to specify:

                    (INNER-LOOP "output = my_scale_factor / s1")

                but this will generate the following:

                    *output++=my_scale_factor/(s1_scale_factor * *s1++);

                Since  the code generator does not know that scaling is handled
                elsewhere, the scaling is done twice!  The solution is  to  put
                s1 in the INTERNAL-SCALING list, which essentially means ``I've
                already incorporated scaling into the  algorithm,  so  suppress
                the multiplication by a scale factor.''

(COMMUTATIVE (name1 name2 ...))
                specifies  that  the  results   will   not   be   affected   by
                interchanging  any of the listed arguments.  When arguments are
                commutative,  Nyquist  rearranges   them   at   run-time   into
                decreasing order of sample rates.  If interpolation is in-line,
                this can dramatically reduce the amount of  code  generated  to
                handle all the different cases.  The prime example is prod.alg.

(TYPE-CHECK "code")
                specifies checking code to  be  inserted  after  argument  type
                checking  at  initialization  time.  See  downproto.alg  for an
                example where a check is made  to  guarantee  that  the  output
                sample  rate  is  not  greater  than  the  input  sample  rate.
                Otherwise an error is raised.

I.7. Generated Names
  The resulting .c file defines a number of procedures. The procedures that  do
actual  sample  computation  are  named  something like name_interp-spec_FETCH,
where name is the NAME attribute from the .alg  file,  and  interp-spec  is  an
interpolation  specification  composed of a string of the following letters: n,
s, i, and r.  One letter corresponds to  each  sound  argument,  indicating  no
interpolation (r), scaling only (s), ordinary linear interpolation with scaling
(i), and ramp (incremental) interpolation with scaling (r).  The code generator
determines  all  the  combinations  of  n,  s,  i, and r that are necessary and
generates a separate fetch function for each.

  Another function is name_toss_fetch, which is  called  when  sounds  are  not
time-aligned  and  some  initial  samples  must  be  discarded from one or more
inputs.

  The function that creates a sound is snd_make_name.    This  is  where  state
allocation  and  initialization  takes  place.    The  proper fetch function is
selected based on the sample rates and scale factors of  the  sound  arguments,
and a sound_type is returned.

  Since  Nyquist  is  a  functional language, sound operations are not normally
allowed to modify their  arguments  through  side  effects,  but  even  reading
samples  from  a sound_type causes side effects. To hide these from the Nyquist
programmer, sound_type arguments are first copied (this  only  copies  a  small
structure.  The samples themselves are on a shared list). The function snd_name
performs the necessary copies and calls snd_make_name.    It  is  the  snd_name
function that is called by XLisp.  The XLisp name for the function is SND-NAME.
Notice that the underscore in C is converted to a dash in XLisp.   Also,  XLisp
converts  identifiers  to upper case when they are read, so normally, you would
type snd-name to call the function.

I.8. Scalar Arguments
  If you want the option of passing either a number (scalar) or a signal as one
of  the arguments, you have two choices, neither of which is automated.  Choice
1 is to coerce the constant into a  signal  from  within  XLisp.    The  naming
convention  would  be to DEFUN a new function named NAME or S-NAME for ordinary
use.  The NAME function tests the  arguments  using  XLisp  functions  such  as
TYPE-OF,  NUMBERP,  and SOUNDP.  Any number is converted to a SOUND, e.g. using
CONST.  Then SND-NAME is called with all sound arguments.  The disadvantage  of
this  scheme is that scalars are expanded into a sample stream, which is slower
than having a special inner loop where the scalar is simply kept in a register,
avoiding loads, stores, and addressing overhead.

  Choice 2 is to generate a different sound operator for each case.  The naming
convention here is to append a string  of  c's  and  v's,  indicating  constant
(scalar) or variable (signal) inputs.  For example, the reson operator comes in
four variations: reson, resoncv, resonvc, and resonvv.    The  resonvc  version
implements  a resonating filter with a variable center frequency (a sound type)
and a constant bandwidth (a FLONUM).  The  RESON  function  in  Nyquist  is  an
ordinary   Lisp  function  that  checks  types  and  calls  one  of  SND-RESON,
SND-RESONCV, SND-RESONVC, or SND-RESONVV.

  Since  each  of  these  SND-  functions   performs   further   selection   of
implementation  based  on  sample  rates and the need for scaling, there are 25
different functions for computing RESON!  So far, however, Nyquist  is  smaller
than  Common  Lisp  and it's about half the size of Microsoft Word.  Hopefully,
exponential growth in memory density will outpace  linear  (as  a  function  of
programming effort) growth of Nyquist.
II. Open Sound Control and Nyquist
  Open Sound Control (OSC) is a simple protocol for communicating music control
parameters  between  software  applications  and  across  networks.  For   more
information,  see  http://www.cnmat.berkeley.edu/OpenSoundControl/. The Nyquist
implementation of Open Sound Control is simple: an array of floats can  be  set
by  OSC  messages  and read by Nyquist functions. That is about all there is to
it.

  Note: Open Sound Control must be enabled by calling (osc-enable t).  If  this
fails under Windows, see the installation instructions regarding SystemRoot.

  To  control  something in (near) real-time, you need to access a slider value
as if it a signal, or  more  properly,  a  Nyquist  SOUND  type.  The  function
snd-slider,  described  in  Section  7.6.1, takes a slider number and returns a
SOUND type representing the current value of the slider.  To  fully  understand
this  function,  you  need  to  know  something  about  how Nyquist is actually
computing sounds.

  Sounds are normally computed on demand. So the result returned by  snd-slider
does  not  immediately  compute  any  samples.  Samples  are only computed when
something tries to use this signal. At that time, the  slider  value  is  read.
Normally,  if  the  slider is used to control a sound, you will hear changes in
the sound pretty soon after the slider value changes. However, one  thing  that
can  interfere  with this is that SOUND samples are computed in blocks of about
1000 samples. When the slider value is read, the same value is used to  fill  a
block  of  1000 samples, so even if the sample rate is 44,100 Hz, the effective
slider sample rate is 44,100/1000, or 44.1 Hz. If you give the  slider  a  very
low  sample  rate,  say 1000, then slider value changes will only be noticed by
Nyquist approximately once per second. For this reason, you should normally use
the  audio  sample  rate  (typically  44,100 Hz) for the rate of the snd-slider
output SOUND. (Yes, this is terribly wasteful to represent  each  slider  value
with  1000  samples,  but Nyquist was not designed for low-latency computation,
and this is an expedient work-around.)

  In addition to reading sliders as continually changing SOUNDs,  you  can  get
the   slider   value   as  a  Lisp  FLONUM  (a  floating  point  number)  using
get-slider-value, described in Section 7.6.1. This might be useful if  you  are
computing  a  sequence  of many notes (or other sound events) and want to apply
the current slider value to the whole note or sound event.

  Note that if you store the value returned by snd-slider in  a  variable,  you
will capture the history of the slider changes. This will take a lot of memory,
so be careful.

  Suppose you write a simple expression such as (hzosc (mult 1000 (snd-slider 0
...)))  to  control  an  oscillator frequency with a slider. How long does this
sound last? The duration of hzosc is the duration of the frequency control,  so
what  is  the  duration of a slider? To avoid infinitely long signals, you must
specify a duration as one of the parameters of snd-slider.

  You might be thinking, what if I just want to tell the slider when  to  stop?
At  present,  you  cannot do that, but in the future there should be a function
that stops when its input goes to zero. Then, moving a slider to zero could end
the  signal  (and  if  you  multiplied  a  complex sound by one of these ending
functions, everything in the sound would end and be garbage collected).

  Another thing you might want to do with interactive  control  is  start  some
sound.  The  trigger  function  computes an instance of a behavior each time an
input SOUND goes from zero  to  greater-than-zero.  This  could  be  used,  for
example, to create a sequence of notes.

  The  snd-slider  function  has  some  parameters  that may be unfamiliar. The
second parameter, t0, is the starting time of the sound. This  should  normally
be  (local-to-global  0), an expression that computes the instantiation time of
the current expression. This will often be zero, but  if  you  call  snd-slider
from inside a seq or seq-rep, the starting time may not be zero.

  The srate parameter is the sample rate to return. This should normally be the
audio sample rate you are working  with,  which  is  typically  *default-sound-
srate*.

II.1. Sending Open Sound Control Messages
  A  variety  of  programs  support  OSC.  The  only OSC message interpreted by
Nyquist has an address of /slider, and two parameters: an integer slider number
and a float value, nominally from 0.0 to 1.0.

  Two  small  programs are included in the Nyquist distribution for sending OSC
messages. (Both can be found in the same directory as the nyquist  executable.)
The  first  one,  osc-test-client  sends a sequence of messages that just cause
slider 0 to ramp slowly up and down. If you run this on a command line, you can
use  "?" or "h" to get help information. There is an interactive mode that lets
you send each OSC message by typing RETURN.

II.2. The ser-to-osc Program
  The second program is ser-to-osc, a program  that  reads  serial  input  (for
example  from  a  PIC-based  microcontroller)  and sends OSC messages. Run this
command-line program from a shell (a terminal window under OS X or  Linux;  use
the  CMD  program  under Windows). You must name the serial input device on the
command line, e.g. under OS X, you might run:

    ./ser-to-osc /dev/tty.usbserial-0000103D

(Note that the program name is preceded by ``./". This tells the shell  exactly
where  to  find  the executable program in case the current directory is not on
the search path for executable programs.)  Under Windows, you might run:

    ser-to-osc com4

(Note that you do not type ``./'' in front of a windows program.)

  To use ser-to-osc, you will have to find the serial device. On the  Macintosh
and Linux, try the following:

    ls /dev/*usb*

This  will  list  all serial devices with ``usb'' in their names. Probably, one
will be a name similar to /dev/tty.usbserial-0000103D. The  ser-to-osc  program
will  echo  data  that  it  receives,  so you should know if things are working
correctly.

  Under Windows, open Control Panel from the Start menu, and  open  the  System
control  panel.  Select  the  Hardware tab and click the Device Manager button.
Look in the device list under Ports (COM & LPT). When you plug in  your  serial
or USB device, you should see a new entry appear, e.g. COM4. This is the device
name you need.

  The format for the serial input is: any non-whitespace character(s), a slider
number,  a  slider value, and a newline (control-j or ASCII 0x0A). These fields
need to be separated by tabs or spaces. An optional carriage return  (control-m
or ASCII 0x0D) preceding the ASCII 0x0A is ignored. The slider number should be
in decimal, and theh slider value is a decimal number from 0 to  255.  This  is
scaled to the range 0.0 to 1.0 (so an input of 255 translates to 1.0).

  There  is  a simple test program in demos/osc-test.lsp you can run to try out
control with Open Sound Control. There are two examples in that file. One  uses
snd-slider   to  control  the  frequency  of  an  oscillator.  The  other  uses
get-slider-value to control  the  pitch  of  grains  in  a  granular  synthesis
process.
III. Intgen
  This  documentation  describes  Intgen,  a  program for generating XLISP to C
interfaces.  Intgen works by scanning .h files with special comments  in  them.
Intgen  builds  stubs  that  implement  XLISP SUBR's.  When the SUBR is called,
arguments are type-checked and passed to the C routine declared in the .h file.
Results  are  converted  into  the  appropriate  XLISP type and returned to the
calling XLISP function.  Intgen  lets  you  add  C  functions  into  the  XLISP
environment with very little effort.

  The interface generator will take as command-line input:

   - the name of the .c file to generate (do not include the .c extension;
     e.g. write xlexten, not xlexten.c);

   - a list of .h files.

Alternatively, the command line may specify a command file from which  to  read
file names. The command file name should be preceded by "@", for example:

    intgen @sndfns.cl

reads  sndfns.cl  to get the command-line input.  Only one level of indirection
is allowed.

  The output is:

   - a single .c file with one SUBR defined for each designated routine in
     a .h file.

   - a  .h  file that declares each new C routine.  E.g. if the .c file is
     named xlexten.c, this file will be named xlextendefs.h;

   - a .h file that extends the SUBR table used by Xlisp.  E.g. if the  .c
     file is named xlexten.c, then this file is named xlextenptrs.h;

   - a  .lsp  file with lisp initialization expressions copied from the .h
     files.  This file is only generated if at  least  one  initialization
     expression is encountered.

  For example, the command line

    intgen seint ~setypes.h access.h

generates  the  file  seint.c,  using  declarations  in setypes.h and access.h.
Normally, the .h files are  included  by  the  generated  file  using  #include
commands.    A  ~ before a file means do not include the .h file.  (This may be
useful if you extend xlisp.h, which will be included anyway).   Also  generated
will be setintdefs.h and seintptrs.h.



III.0.1. Extending Xlisp
  Any number of .h files may be named on the command line to Intgen, and Intgen
will make a single .c file with interface routines for all of the .h files.  On
the  other hand, it is not necessary to put all of the extensions to Xlisp into
a single interface file.  For  example,  you  can  run  Intgen  once  to  build
interfaces  to  window manager routines, and again to build interfaces to a new
data type.  Both interfaces can be linked into Xlisp.

  To use the generated files, you must compile the .c files and link them  with
all  of  the  standard Xlisp object files.  In addition, you must edit the file
localdefs.h to contain an #include for each *defs.h file,  and  edit  the  file
localptrs.h  to include each *ptrs.h file.  For example, suppose you run Intgen
to  build  soundint.c,  fugueint.c,  and  tableint.c.    You  would  then  edit
localdefs.h to contain the following:

    #include "soundintdefs.h"
    #include "fugueintdefs.h"
    #include "tableintdefs.h"

and edit localptrs.h to contain:

    #include "soundintptrs.h"
    #include "fugueintptrs.h"
    #include "tableintptrs.h"

These  localdefs.h and localptrs.h files are in turn included by xlftab.c which
is where Xlisp builds a table of SUBRs.

  To summarize, building an interface requires just a few simple steps:

   - Write C code to be called by Xlisp interface routines.  This  C  code
     does  the  real  work, and in most cases is completely independent of
     Xlisp.

   - Add comments to .h files to  tell  Intgen  which  routines  to  build
     interfaces to, and to specify the types of the arguments.

   - Run Intgen to build interface routines.

   - Edit localptrs.h and localdefs.h to include generated .h files.

   - Compile and link Xlisp, including the new C code.

III.1. Header file format
  Each routine to be interfaced with Xlisp must be declared as follows:

    type-name routine-name(); /* LISP: (func-name type  type  ...) */
                                                      1     2
The  comment  may be on the line following the declaration, but the declaration
and the comment must each be on no more than one line.  The characters LISP: at
the  beginning  of  the  comment  mark  routines  to put in the interface.  The
comment also gives the type and  number  of  arguments.    The  function,  when
accessed  from  lisp  will  be  known  as  func-name,  which  need not bear any
relationship to routine-name.  By convention, underscores in the C routine-name
should  be  converted  to  dashes  in func-name, and func-name should be in all
capitals.  None of this is enforced or automated though.

  Legal type_names are:

LVAL            returns an Xlisp datum.

atom_type       equivalent to LVAL, but the result is expected to be an atom.

value_type      a value as used in Dannenberg's score editor.

event_type      an event as used in Dannenberg's score editor.

int             interface will convert int to Xlisp FIXNUM.

boolean         interface will convert int to  T or nil.

float or double interface converts to FLONUM.

char * or string or string_type
                interface converts to STRING.  The result string will be copied
                into the XLISP heap.

void            interface will return nil.

  It is easy to extend this list.  Any unrecognized type will be coerced to  an
int and then returned as a FIXNUM, and a warning will be issued.

  The  ``*''  after  char  must be followed by routine-name with no intervening
space.

  Parameter types may be any of the following:

FIXNUM          C routine expects an int.

FLONUM or FLOAT C routine expects a double.

STRING          C routine expects char *, the string is not copied.

VALUE           C routine expects a value_type.  (Not applicable to Fugue.)

EVENT           C routine expects an event_type.  (Not applicable to Fugue.)

ANY             C routine expects LVAL.

ATOM            C routine expects LVAL which is a lisp atom.

FILE            C routine expects FILE *.

SOUND           C routine expects a SoundPtr.

  Any of these may be followed  by  ``*'':  FIXNUM*,  FLONUM*,  STRING*,  ANY*,
FILE*,  indicating  C routine expects int *, double *, char **, LVAL *, or FILE
** .  This is basically a mechanism for returning more than one  value,  not  a
mechanism  for  clobbering  XLisp values.  In this spirit, the interface copies
the value (an int, double, char *, LVAL, or FILE *) to  a  local  variable  and
passes  the  address  of  that variable to the C routine.  On return, a list of
resulting ``*'' parameters is constructed and bound to the global XLisp  symbol
*RSLT*.   (Strings are copied.)  If the C routine is void, then the result list
is also returned by the corresponding XLisp function.

  Note 1: this does not support C routines like  strcpy  that  modify  strings,
because the C routine gets a pointer to the string in the XLisp heap.  However,
you can always add an intermediate routine that allocates space and then  calls
strcpy, or whatever.

  Note  2:  it follows that a new XLisp STRING will be created for each STRING*
parameter.

  Note 3: putting results on a (global!) symbol seems a bit  unstructured,  but
note  that  one  could  write  a  multiple-value  binding macro that hides this
ugliness from the user if desired.  In practice, I find that pulling the  extra
result values from *RSLT* when needed is perfectly acceptable.

  For  parameters  that  are  result  values  only,  the character ``^'' may be
substituted for ``*''.  In this case, the parameter is not to be passed in  the
XLisp  calling  site.  However, the address of an initialized local variable of
the given type is passed to the corresponding C  function,  and  the  resulting
value  is  passed back through *RSLT* as ordinary result parameter as described
above.  The local variables are initialized to zero or NULL.

III.2. Using #define'd macros
  If a comment of the form:

    /* LISP: type-name (routine-name-2 type-1 type-2 ...) */

appears on a line by itself and there was a #define on the previous line,  then
the preceding #define is treated as a C routine, e.g.

    #define leftshift(val, count) ((val) << (count))
    /* LISP: int (LOGSHIFT INT INT) */

will implement the LeLisp function LOGSHIFT.

  The  type-name  following ``LISP:'' should have no spaces, e.g. use ANY*, not
ANY *.

III.3. Lisp Include Files
  Include files often define constants that we would like to have around in the
Lisp  world,  but  which  are easier to initialize just by loading a text file.
Therefore, a comment of the form:

    /* LISP-SRC: (any lisp expression) */

will cause Intgen to open a file name.lsp and append

    (any lisp expression)

to name.lsp, where name is the interface name passed on the command line.    If
none of the include files examined have comments of this form, then no name.lsp
file is generated.  Note: the LISP-SRC comment must be on a new line.

III.4. Example
  This file was used for testing Intgen.  It uses a trick (ok, it's a hack)  to
interface  to  a  standard  library  macro (tolower).  Since tolower is already
defined, the macro ToLower is defined just to give Intgen a name to call.   Two
other routines, strlen and tough, are interfaced as well.

    /* igtest.h -- test interface for intgen */

    #define ToLower(c) tolower(c)
    /* LISP: int (TOLOWER FIXNUM) */

    int strlen();   /* LISP: (STRLEN STRING) */

    void tough();
      /* LISP: (TOUGH FIXNUM* FLONUM* STRING ANY FIXNUM) */

III.5. More Details
  Intgen has some compiler switches to enable/disable the use of certain types,
including VALUE and EVENT types used by Dannenberg's score  editing  work,  the
SOUND  type  used  by  Fugue,  and  DEXT  and  SEXT  types added for Dale Amon.
Enabling all of these is not likely to cause problems, and the  chances  of  an
accidental  use  of  these  types getting through the compiler and linker seems
very small.
IV. XLISP: An Object-oriented Lisp

                                  Version 2.0

                               February 6, 1988

                                      by
                              David Michael Betz
                                127 Taylor Road
                            Peterborough, NH 03458

                   Copyright (c) 1988, by David Michael Betz
                              All Rights Reserved
           Permission is granted for unrestricted non-commercial use
IV.1. Introduction
  XLISP is an experimental programming language combining some of the  features
of   Common  Lisp  with  an  object-oriented  extension  capability.    It  was
implemented to allow experimentation with object-oriented programming on  small
computers.

  Implementations  of  XLISP run on virtually every operating system.  XLISP is
completely written in the programming language C and is  easily  extended  with
user written built-in functions and classes.  It is available in source form to
non-commercial users.

  Many Common Lisp functions are built into XLISP.  In addition, XLISP  defines
the  objects Object and Class as primitives.  Object is the only class that has
no superclass and hence is the root of the class hierarchy tree.  Class is  the
class  of  which  all  classes  are instances (it is the only object that is an
instance of itself).

  This document is a brief description of XLISP.  It assumes some knowledge  of
LISP and some understanding of the concepts of object-oriented programming.

  I recommend the book Lisp by Winston and Horn and published by Addison Wesley
for learning Lisp.  The first edition of this book is based on MacLisp and  the
second edition is based on Common Lisp.

  You  will  probably  also  need  a  copy  of Common Lisp: The Language by Guy
L. Steele, Jr., published by Digital Press to use as a reference  for  some  of
the Common Lisp functions that are described only briefly in this document.

IV.2. A Note From The Author
  If  you have any problems with XLISP, feel free to contact me [me being David
Betz - RBD] for help or advice.  Please remember that since XLISP is  available
in  source  form  in  a  high  level language, many users [e.g. that Dannenberg
fellow - RBD] have been making versions available on a variety of machines.  If
you call to report a problem with a specific version, I may not be able to help
you if that version runs on a machine to which I don't  have  access.    Please
have  the version number of the version that you are running readily accessible
before calling me.

  If you find a bug in XLISP, first try to  fix  the  bug  yourself  using  the
source  code  provided.   If you are successful in fixing the bug, send the bug
report along with the fix to me.  If you don't have access to a C  compiler  or
are  unable  to fix a bug, please send the bug report to me and I'll try to fix
it.

  Any suggestions for improvements will be welcomed.  Feel free to  extend  the
language  in  whatever  way  suits  your needs.  However, PLEASE DO NOT RELEASE
ENHANCED VERSIONS WITHOUT CHECKING WITH ME FIRST!!  I  would  like  to  be  the
clearing  house  for  new features added to XLISP.  If you want to add features
for your own personal use, go ahead.  But,  if  you  want  to  distribute  your
enhanced  version, contact me first.  Please remember that the goal of XLISP is
to provide a language to learn and experiment  with  LISP  and  object-oriented
programming on small computers.  I don't want it to get so big that it requires
megabytes of memory to run.

IV.3. XLISP Command Loop
  When XLISP is started, it first tries to load the  workspace  xlisp.wks  from
the  current  directory.    If that file doesn't exist, XLISP builds an initial
workspace, empty except for the built-in functions and symbols.

  Then XLISP attempts to load init.lsp from the current  directory.    It  then
loads  any  files named as parameters on the command line (after appending .lsp
to their names).

  XLISP then issues the following prompt:

            >

This indicates that XLISP is waiting for an expression to be typed.

  When a complete expression has been entered, XLISP attempts to evaluate  that
expression.   If the expression evaluates successfully, XLISP prints the result
and then returns to the initial prompt waiting for  another  expression  to  be
typed.

IV.4. Special Characters
  When  XLISP  is  running  from  a  console,  some  control  characters invoke
operations:

   - Backspace and Delete characters erase the previous character  on  the
     input line (if any).

   - Control-U erases the entire input line.

   - Control-C executes the TOP-LEVEL function.

   - Control-G executes the CLEAN-UP function.

   - Control-P executes the CONTINUE function.

   - Control-B   stops  execution  and  enters  the  break  command  loop.
     Execution can be continued by typing Control-P or (CONTINUE).

   - Control-E turns on character echoing (Linux and Mac OS X only).

   - Control-F turns off character echoing (Linux and Mac OS X only).

   - Control-T evaluates the INFO function.

IV.5. Break Command Loop
  When XLISP encounters an error while evaluating an expression, it attempts to
handle the error in the following way:

  If  the  symbol *breakenable* is true, the message corresponding to the error
is printed.  If the error is correctable, the correction message is printed.

  If the symbol *tracenable* is true, a trace back is printed.  The  number  of
entries  printed  depends  on  the  value  of the symbol *tracelimit*.  If this
symbol is set to something other than a number, the entire trace back stack  is
printed.

  XLISP  then  enters  a  read/eval/print loop to allow the user to examine the
state of the interpreter in the context of the error.  This loop  differs  from
the  normal  top-level  read/eval/print  loop  in  that if the user invokes the
function continue, XLISP will continue from a correctable error.  If  the  user
invokes  the  function  clean-up, XLISP will abort the break loop and return to
the top level or the next lower numbered break loop.  When  in  a  break  loop,
XLISP prefixes the break level to the normal prompt.

  If  the  symbol  *breakenable*  is  nil, XLISP looks for a surrounding errset
function.  If one is found, XLISP examines the value of the  print  flag.    If
this flag is true, the error message is printed.  In any case, XLISP causes the
errset function call to return nil.

  If there is no surrounding errset function, XLISP prints  the  error  message
and returns to the top level.

IV.6. Data Types
  There are several different data types available to XLISP programmers.

   - lists

   - symbols

   - strings

   - integers

   - characters

   - floats

   - objects

   - arrays

   - streams

   - subrs (built-in functions)

   - fsubrs (special forms)

   - closures (user defined functions)

IV.7. The Evaluator
  The process of evaluation in XLISP:

   - Strings,  integers,  characters,  floats,  objects,  arrays, streams,
     subrs, fsubrs and closures evaluate to themselves.

   - Symbols act as variables and are evaluated by  retrieving  the  value
     associated with their current binding.

   - Lists  are  evaluated  by examining the first element of the list and
     then taking one of the following actions:

        * If it is a symbol, the  functional  binding  of  the  symbol  is
          retrieved.

        * If  it  is a lambda expression, a closure is constructed for the
          function described by the lambda expression.

        * If it is a subr, fsubr or closure, it stands for itself.

        * Any other value is an error.

     Then, the value produced by the previous step is examined:

        * If it is a subr or closure,  the  remaining  list  elements  are
          evaluated and the subr or closure is called with these evaluated
          expressions as arguments.

        * If it is an fsubr, the fsubr is called using the remaining  list
          elements as arguments (unevaluated).

        * If it is a macro, the macro is expanded using the remaining list
          elements as arguments (unevaluated).   The  macro  expansion  is
          then evaluated in place of the original macro call.

IV.8. Lexical Conventions
  The following conventions must be followed when entering XLISP programs:

  Comments  in XLISP code begin with a semi-colon character and continue to the
end of the line.

  Symbol names in XLISP can consist of  any  sequence  of  non-blank  printable
characters except the following:

                    ( ) ' ` , " ;

Uppercase  and  lowercase characters are not distinguished within symbol names.
All lowercase characters are mapped to uppercase on input.

  Integer literals consist of a sequence of digits optionally beginning with  a
+ or -.  The range of values an integer can represent is limited by the size of
a C long on the machine on which XLISP is running.

  Floating point literals consist of a sequence of digits optionally  beginning
with  a  + or - and including an embedded decimal point.  The range of values a
floating point number can represent is limited by the size of a C float (double
on machines with 32 bit addresses) on the machine on which XLISP is running.

  Literal  strings  are  sequences  of  characters surrounded by double quotes.
Within quoted strings the  ``\''  character  is  used  to  allow  non-printable
characters to be included.  The codes recognized are:

   - \\ means the character ``\''

   - \n means newline

   - \t means tab

   - \r means return

   - \f means form feed

   - \nnn means the character whose octal code is nnn

IV.9. Readtables
  The  behavior  of  the  reader  is  controlled  by  a data structure called a
readtable.  The reader uses  the  symbol  *readtable*  to  locate  the  current
readtable.   This table controls the interpretation of input characters.  It is
an array with 128 entries, one for each of the ASCII  character  codes.    Each
entry contains one of the following things:

   - NIL M Indicating an invalid character

   - :CONSTITUENT M Indicating a symbol constituent

   - :WHITE-SPACE M Indicating a whitespace character

   - (:TMACRO . fun) M Terminating readmacro

   - (:NMACRO . fun) M Non-terminating readmacro

   - :SESCAPE M Single escape character ('\')

   - :MESCAPE M Multiple escape character ('|')

  In  the  case  of :TMACRO and :NMACRO, the fun component is a function.  This
can either be a built-in readmacro  function  or  a  lambda  expression.    The
function  should  take  two  parameters.  The first is the input stream and the
second is the character that caused the  invocation  of  the  readmacro.    The
readmacro  function  should return NIL to indicate that the character should be
treated as white space or  a  value  consed  with  NIL  to  indicate  that  the
readmacro should be treated as an occurence of the specified value.  Of course,
the readmacro code is free to read additional characters from the input stream.

  XLISP defines several useful read macros:

   - '<expr> == (quote <expr>)

   - #'<expr> == (function <expr>)

   - #(<expr>...)  == an array of the specified expressions

   - #x<hdigits> == a hexadecimal number (0-9,A-F)

   - #o<odigits> == an octal number (0-7)

   - #b<bdigits> == a binary number (0-1)

   - #\<char> == the ASCII code of the character

   - #| ... |# == a comment

   - #:<symbol> == an uninterned symbol

   - `<expr> == (backquote <expr>)

   - ,<expr> == (comma <expr>)

   - ,@<expr> == (comma-at <expr>)

IV.10. Lambda Lists
  There are several forms in XLISP that  require  that  a  ``lambda  list''  be
specified.    A  lambda  list  is  a  definition of the arguments accepted by a
function.  There are four different types of arguments.

  The lambda list starts with required arguments.  Required arguments  must  be
specified in every call to the function.

  The  required  arguments  are  followed by the &optional arguments.  Optional
arguments may be provided or omitted in a call.  An  initialization  expression
may  be specified to provide a default value for an &optional argument if it is
omitted from a call.  If no initialization expression is specified, an  omitted
argument  is  initialized to NIL.  It is also possible to provide the name of a
supplied-p variable that can be used to determine if a call  provided  a  value
for  the  argument or if the initialization expression was used.  If specified,
the supplied- p variable will be bound to T if a value  was  specified  in  the
call and NIL if the default value was used.

  The  &optional  arguments  are  followed  by  the  &rest argument.  The &rest
argument gets bound to the remainder of the argument list  after  the  required
and &optional arguments have been removed.

  The  &rest  argument  is  followed  by  the  &key  arguments.  When a keyword
argument is passed to a function, a pair of  values  appears  in  the  argument
list.   The first expression in the pair should evaluate to a keyword symbol (a
symbol that begins with a ``:'').  The value of the second  expression  is  the
value  of  the  keyword argument.  Like &optional arguments, &key arguments can
have initialization expressions and supplied-p variables.  In addition,  it  is
possible  to  specify the keyword to be used in a function call.  If no keyword
is specified, the keyword obtained by adding a ``:'' to the  beginning  of  the
keyword  argument  symbol  is  used.    In other words, if the keyword argument
symbol is foo, the keyword will be ':foo.

  The &key arguments are followed by the  &aux  variables.    These  are  local
variables  that  are  bound  during the evaluation of the function body.  It is
possible to have initialization expressions for the &aux variables.

  Here is the complete syntax for lambda lists:

                    (rarg...
                     [&optional [oarg | (oarg [init [svar]])]...]
                     [&rest rarg]
                     [&key
                       [karg | ([karg | (key karg)] [init [svar]])]...
                       &allow-other-keys]
                     [&aux
                       [aux | (aux [init])]...])

                where:

                    rarg is a required argument symbol
                    oarg is an &optional argument symbol
                    rarg is the &rest argument symbol
                    karg is a &key argument symbol
                    key is a keyword symbol
                    aux is an auxiliary variable symbol
                    init is an initialization expression
                    svar is a supplied-p variable symbol

IV.11. Objects
  Definitions:

   - selector M a symbol used to select an appropriate method

   - message M a selector and a list of actual arguments

   - method M the code that implements a message

Since XLISP was created to  provide  a  simple  basis  for  experimenting  with
object-oriented  programming,  one  of  the  primitive  data  types included is
object.  In XLISP, an object consists of a data structure containing a  pointer
to the object's class as well as an array containing the values of the object's
instance variables.

  Officially, there is no way to see inside an object (look at  the  values  of
its  instance  variables).    The  only way to communicate with an object is by
sending it a message.

  You can send a message to an object using the send function.   This  function
takes  the  object  as  its  first argument, the message selector as its second
argument (which must be a symbol) and the message arguments  as  its  remaining
arguments.

  The  send  function determines the class of the receiving object and attempts
to find a method corresponding to the message selector in the set  of  messages
defined  for that class.  If the message is not found in the object's class and
the class has a super-class, the search continues by looking  at  the  messages
defined  for  the  super-class.  This process continues from one super-class to
the next until a method for the message is found.  If no method  is  found,  an
error occurs.

  When  a  method  is  found,  the  evaluator binds the receiving object to the
symbol self and evaluates the  method  using  the  remaining  elements  of  the
original list as arguments to the method.  These arguments are always evaluated
prior to being bound to their corresponding formal arguments.   The  result  of
evaluating the method becomes the result of the expression.

  Within  the  body of a method, a message can be sent to the current object by
calling the (send self ...). The method lookup starts with the  object's  class
regardless of the class containing the current method.

  Sometimes  it  is  desirable  to invoke a general method in a superclass even
when it is overridden by a more specific method in a subclass.    This  can  be
accomplished  by  calling  send-super,  which  begins  the method lookup in the
superclass of the class defining the current method rather than in the class of
the current object.

  The send-super function takes a selector as its first argument (which must be
a symbol) and the message arguments as its  remaining  arguments.  Notice  that
send-super can only be sent from within a method, and the target of the message
is always the current object (self). (send-super ...) is similar to (send  self
...) except that method lookup begins in the superclass of the class containing
the current method rather than the class of the current object.
IV.12. The ``Object'' Class
  Object M the top of the class hierarchy.

  Messages:
:show M show an object's instance variables.
     returns M the object

:class M return the class of an object
     returns M the class of the object

:isa(:isa) class M test if object inherits from class
     returns M t if object is an instance of class  or  a  subclass  of  class,
          otherwise nil

:isnew M the default object initialization routine
     returns M the object

IV.13. The ``Class'' Class
  Class M class of all object classes (including itself)

  Messages:
:new M create a new instance of a class
     returns M the new class object

:isnew ivars [cvars [super]] M initialize a new class
     ivars M the list of instance variable symbols
     cvars M the list of class variable symbols
     super M the superclass (default is object)
     returns M the new class object

:answer msg fargs code M add a message to a class
     msg M the message symbol
     fargs M the formal argument list (lambda list)
     code M a list of executable expressions
     returns M the object

  When  a  new instance of a class is created by sending the message :new to an
existing class, the message :isnew followed by whatever parameters were  passed
to the :new message is sent to the newly created object.

  When  a new class is created by sending the :new message to the object Class,
an optional parameter may be specified indicating the  superclass  of  the  new
class.    If  this  parameter  is  omitted, the new class will be a subclass of
Object.  A class inherits all instance variables, class variables, and  methods
from its super-class.

IV.14. Profiling
  The  Xlisp  2.0  release  has  been extended with a profiling facility, which
counts how many times and  where  eval  is  executed.    A  separate  count  is
maintained for each named function, closure, or macro, and a count indicates an
eval in the immediately  (lexically)  enclosing  named  function,  closure,  or
macro.    Thus,  the count gives an indication of the amount of time spent in a
function, not counting nested function  calls.    The  list  of  all  functions
executed  is  maintained  on the global *profile* variable.  These functions in
turn have *profile* properties, which maintain the counts.  The profile  system
merely increments counters and puts symbols on the *profile* list.  It is up to
the user to initialize data and gather results.  Profiling is turned on or  off
with the profile function.  Unfortunately, methods cannot be profiled with this
facility.

IV.15. Symbols

   - self M the current object (within a method context)

   - *obarray* M the object hash table

   - *standard-input* M the standard input stream

   - *standard-output* M the standard output stream

   - *error-output* M the error output stream

   - *trace-output* M the trace output stream

   - *debug-io* M the debug i/o stream

   - *breakenable* M flag controlling entering break loop on errors

   - *tracelist* M list of names of functions to trace

   - *tracenable* M enable trace back printout on errors

   - *tracelimit* M number of levels of trace back information

   - *evalhook* M user substitute for the evaluator function

   - *applyhook* M (not yet implemented)

   - *readtable* M the current readtable

   - *unbound* M indicator for unbound symbols

   - *gc-flag* M controls the printing of gc messages

   - *gc-hook* M function to call after garbage collection

   - *integer-format* M format for printing integers (``%d'' or ``%ld'')

   - *float-format* M format for printing floats (``%g'')

   - *print-case* M symbol output case (:upcase or :downcase)

  There are several symbols  maintained  by  the  read/eval/print  loop.    The
symbols  +,  ++,  and +++ are bound to the most recent three input expressions.
The symbols *, ** and *** are bound to the most  recent  three  results.    The
symbol  - is bound to the expression currently being evaluated.  It becomes the
value of + at the end of the evaluation.

IV.16. Evaluation Functions
(eval expr) M evaluate an xlisp expression
     expr M the expression to be evaluated
     returns M the result of evaluating the expression

(apply fun args) M apply a function to a list of arguments
     fun M the function to apply (or function symbol)
     args M the argument list
     returns M the result of applying the function to the arguments

(funcall fun arg...) M call a function with arguments
     fun M the function to call (or function symbol)
     arg M arguments to pass to the function
     returns M the result of calling the function with the arguments

(quote expr) M return an expression unevaluated
     expr M the expression to be quoted (quoted)
     returns M expr unevaluated

(function expr) M get the functional interpretation
     expr M the symbol or lambda expression (quoted)
     returns M the functional interpretation

(backquote expr) M fill in a template
     expr M the template
     returns M a copy of the template with comma and comma-at
     expressions expanded

(lambda args expr...) M make a function closure
     args M formal argument list (lambda list) (quoted)
     expr M expressions of the function body
     returns M the function closure

(get-lambda-expression closure) M get the lambda expression
     closure M the closure
     returns M the original lambda expression

(macroexpand form) M recursively expand macro calls
     form M the form to expand
     returns M the macro expansion

(macroexpand-1 form) M expand a macro call
     form M the macro call form
     returns M the macro expansion


IV.17. Symbol Functions
(set sym expr) M set the value of a symbol
     sym M the symbol being set
     expr M the new value
     returns M the new value

(setq [sym expr]...) M set the value of a symbol
     sym M the symbol being set (quoted)
     expr M the new value
     returns M the new value

(psetq [sym expr]...)  M parallel version of setq
     sym M the symbol being set (quoted)
     expr M the new value
     returns M the new value

(setf [place expr]...)  M set the value of a field
     place M the field specifier (quoted):
          sym M set value of a symbol
          (car expr) M set car of a cons node
          (cdr expr) M set cdr of a cons node
          (nth n expr) M set nth car of a list
          (aref expr n) M set nth element of an array
          (get sym prop) M set value of a property
          (symbol-value sym) M set value of a symbol
          (symbol-function sym) M set functional value of a symbol
          (symbol-plist sym) M set property list of a symbol
     expr M the new value
     returns M the new value

(defun sym fargs expr...)  M define a function
(defmacro sym fargs expr...) M define a macro
     sym M symbol being defined (quoted)
     fargs M formal argument list (lambda list) (quoted)
     expr M expressions constituting the body of the
     function (quoted) returns M the function symbol

(gensym [tag]) M generate a symbol
     tag M string or number
     returns M the new symbol

(intern pname) M make an interned symbol
     pname M the symbol's print name string
     returns M the new symbol

(make-symbol pname) M make an uninterned symbol
     pname M the symbol's print name string
     returns M the new symbol

(symbol-name sym) M get the print name of a symbol
     sym M the symbol
     returns M the symbol's print name

(symbol-value sym) M get the value of a symbol
     sym M the symbol
     returns M the symbol's value

(symbol-function sym) M get the functional value of a symbol
     sym M the symbol
     returns M the symbol's functional value

(symbol-plist sym) M get the property list of a symbol
     sym M the symbol
     returns M the symbol's property list

(hash sym n) M compute the hash index for a symbol
     sym M the symbol or string
     n M the table size (integer)
     returns M the hash index (integer)


IV.18. Property List Functions
(get sym prop) M get the value of a property
     sym M the symbol
     prop M the property symbol
     returns M the property value or nil

(putprop sym val prop) M put a property onto a property list
     sym M the symbol
     val M the property value
     prop M the property symbol
     returns M the property value

(remprop sym prop) M remove a property
     sym M the symbol
     prop M the property symbol
     returns M nil


IV.19. Array Functions
(aref array n) M get the nth element of an array
     array M the array
     n M the array index (integer)
     returns M the value of the array element

(make-array size) M make a new array
     size M the size of the new array (integer)
     returns M the new array

(vector expr...)  M make an initialized vector
     expr M the vector elements
     returns M the new vector


IV.20. List Functions
(car expr) M return the car of a list node
     expr M the list node
     returns M the car of the list node

(cdr expr) M return the cdr of a list node
     expr M the list node
     returns M the cdr of the list node

(cxxr expr) M all cxxr combinations

(cxxxr expr) M all cxxxr combinations

(cxxxxr expr) M all cxxxxr combinations

(first expr) M a synonym for car

(second expr) M a synonym for cadr

(third expr) M a synonym for caddr

(fourth expr) M a synonym for cadddr

(rest expr) M a synonym for cdr

(cons expr1 expr2) M construct a new list node
     expr1 M the car of the new list node
     expr2 M the cdr of the new list node
     returns M the new list node

(list expr...)  M create a list of values
     expr M expressions to be combined into a list
     returns M the new list

(append expr...)  M append lists
     expr M lists whose elements are to be appended
     returns M the new list

(reverse expr) M reverse a list
     expr M the list to reverse
     returns M a new list in the reverse order

(last list) M return the last list node of a list
     list M the list
     returns M the last list node in the list

(member expr list &key :test :test-not) M find an expression in a list
     expr M the expression to find
     list M the list to search
     :test M the test function (defaults to eql)
     :test-not M the test function (sense inverted)
     returns M the remainder of the list starting with the expression

(assoc expr alist &key :test :test-not) M find an expression in an a-list
     expr M the expression to find
     alist M the association list
     :test M the test function (defaults to eql)
     :test-not M the test function (sense inverted)
     returns M the alist entry or nil

(remove expr list &key :test :test-not) M remove elements from a list
     expr M the element to remove
     list M the list
     :test M the test function (defaults to eql)
     :test-not M the test function (sense inverted)
     returns M copy of list with matching expressions removed

(remove-if test list) M remove elements that pass test
     test M the test predicate
     list M the list
     returns M copy of list with matching elements removed

(remove-if-not test list) M remove elements that fail test
     test M the test predicate
     list M the list
     returns M copy of list with non-matching elements removed

(length expr) M find the length of a list, vector or string
     expr M the list, vector or string
     returns M the length of the list, vector or string

(nth n list) M return the nth element of a list
     n M the number of the element to return (zero origin)
     list M the list
     returns M the nth element or nil if the list isn't that long

(nthcdr n list) M return the nth cdr of a list
     n M the number of the element to return (zero origin)
     list M the list
     returns M the nth cdr or nil if the list isn't that long

(mapc fcn list1 list...)  M apply function to successive cars
     fcn M the function or function name
     listn M a list for each argument of the function
     returns M the first list of arguments

(mapcar fcn list1 list...)  M apply function to successive cars
     fcn M the function or function name
     listn M a list for each argument of the function
     returns M a list of the values returned

(mapl fcn list1 list...)  M apply function to successive cdrs
     fcn M the function or function name
     listn M a list for each argument of the function
     returns M the first list of arguments

(maplist fcn list1 list...)  M apply function to successive cdrs
     fcn M the function or function name
     listn M a list for each argument of the function
     returns M a list of the values returned

(subst to from expr &key :test :test-not) M substitute expressions
     to M the new expression
     from M the old expression
     expr M the expression in which to do the substitutions
     :test M the test function (defaults to eql)
     :test-not M the test function (sense inverted)
     returns M the expression with substitutions

(sublis alist expr &key :test :test-not) M substitute with an a-list
     alist M the association list
     expr M the expression in which to do the substitutions
     :test M the test function (defaults to eql)
     :test-not M the test function (sense inverted)
     returns M the expression with substitutions


IV.21. Destructive List Functions
(rplaca list expr) M replace the car of a list node
     list M the list node
     expr M the new value for the car of the list node
     returns M the list node after updating the car

(rplacd list expr) M replace the cdr of a list node
     list M the list node
     expr M the new value for the cdr of the list node
     returns M the list node after updating the cdr

(nconc list...)  M destructively concatenate lists
     list M lists to concatenate
     returns M the result of concatenating the lists
(delete expr &key :test :test-not) M delete elements from a list
     expr M the element to delete
     list M the list
     :test M the test function (defaults to eql)
     :test-not M the test function (sense inverted)
     returns M the list with the matching expressions deleted

(delete-if test list) M delete elements that pass test
     test M the test predicate
     list M the list
     returns M the list with matching elements deleted

(delete-if-not test list) M delete elements that fail test
     test M the test predicate
     list M the list
     returns M the list with non-matching elements deleted

(sort list test) M sort a list
     list M the list to sort
     test M the comparison function
     returns M the sorted list


IV.22. Predicate Functions
(atom expr) M is this an atom?
     expr M the expression to check
     returns M t if the value is an atom, nil otherwise

(symbolp expr) M is this a symbol?
     expr M the expression to check
     returns M t if the expression is a symbol, nil otherwise

(numberp expr) M is this a number?
     expr M the expression to check
     returns M t if the expression is a number, nil otherwise

(null expr) M is this an empty list?
     expr M the list to check
     returns M t if the list is empty, nil otherwise

(not expr) M is this false?
     expr M the expression to check
     return M t if the value is nil, nil otherwise

(listp expr) M is this a list?
     expr M the expression to check
     returns M t if the value is a cons or nil, nil otherwise

(endp list) M is this the end of a list
     list M the list
     returns M t if the value is nil, nil otherwise

(consp expr) M is this a non-empty list?
     expr M the expression to check
     returns M t if the value is a cons, nil otherwise

(integerp expr) M is this an integer?
     expr M the expression to check
     returns M t if the value is an integer, nil otherwise

(floatp expr) M is this a float?
     expr M the expression to check
     returns M t if the value is a float, nil otherwise

(stringp expr) M is this a string?
     expr M the expression to check
     returns M t if the value is a string, nil otherwise

(characterp expr) M is this a character?
     expr M the expression to check
     returns M t if the value is a character, nil otherwise

(arrayp expr) M is this an array?
     expr M the expression to check
     returns M t if the value is an array, nil otherwise

(streamp expr) M is this a stream?
     expr M the expression to check
     returns M t if the value is a stream, nil otherwise

(objectp expr) M is this an object?
     expr M the expression to check
     returns M t if the value is an object, nil otherwise

(filep expr)(This is not part of standard XLISP nor  is  it  built-in.  Nyquist
     defines it though.)  M is this a file?
     expr M the expression to check
     returns M t if the value is an object, nil otherwise

(boundp sym) M is a value bound to this symbol?
     sym M the symbol
     returns M t if a value is bound to the symbol, nil otherwise

(fboundp sym) M is a functional value bound to this symbol?
     sym M the symbol
     returns M t if a functional value is bound to the symbol,
     nil otherwise

(minusp expr) M is this number negative?
     expr M the number to test
     returns M t if the number is negative, nil otherwise

(zerop expr) M is this number zero?
     expr M the number to test
     returns M t if the number is zero, nil otherwise

(plusp expr) M is this number positive?
     expr M the number to test
     returns M t if the number is positive, nil otherwise

(evenp expr) M is this integer even?
     expr M the integer to test
     returns M t if the integer is even, nil otherwise

(oddp expr) M is this integer odd?
     expr M the integer to test
     returns M t if the integer is odd, nil otherwise

(eq expr1 expr2) M are the expressions identical?
     expr1 M the first expression
     expr2 M the second expression
     returns M t if they are equal, nil otherwise

(eql expr1 expr2) M are the expressions identical? (works with all numbers)
     expr1 M the first expression
     expr2 M the second expression
     returns M t if they are equal, nil otherwise

(equal expr1 expr2) M are the expressions equal?
     expr1 M the first expression
     expr2 M the second expression
     returns M t if they are equal, nil otherwise


IV.23. Control Constructs
(cond pair...)  M evaluate conditionally
     pair M pair consisting of:
          (pred expr...)
     where:
          pred M is a predicate expression
          expr M evaluated if the predicate is not nil
     returns M the value of the first expression whose predicate is not nil

(and expr...)  M the logical and of a list of expressions
     expr M the expressions to be anded
     returns  M  nil if any expression evaluates to nil, otherwise the value of
          the last expression (evaluation of expressions stops after the  first
          expression that evaluates to nil)

(or expr...)  M the logical or of a list of expressions
     expr M the expressions to be ored
     returns  M  nil if all expressions evaluate to nil, otherwise the value of
          the first non-nil expression (evaluation of expressions  stops  after
          the first expression that does not evaluate to nil)

(if texpr expr1 [expr2]) M evaluate expressions conditionally
     texpr M the test expression
     expr1 M the expression to be evaluated if texpr is non-nil
     expr2 M the expression to be evaluated if texpr is nil
     returns M the value of the selected expression

(when texpr expr...)  M evaluate only when a condition is true
     texpr M the test expression
     expr M the expression(s) to be evaluated if texpr is non-nil
     returns M the value of the last expression or nil

(unless texpr expr...)  M evaluate only when a condition is false
     texpr M the test expression
     expr M the expression(s) to be evaluated if texpr is nil
     returns M the value of the last expression or nil

(case expr case...)  M select by case
     expr M the selection expression
     case M pair consisting of:
          (value expr...)
     where:
          value M is a single expression or a list of expressions (unevaluated)
          expr M are expressions to execute if the case matches
     returns M the value of the last expression of the matching case

(let (binding...) expr...)  M create local bindings
(let* (binding...) expr...)  M let with sequential binding
     binding M the variable bindings each of which is either:
          1) a symbol (which is initialized to nil)
          2)  a  list whose car is a symbol and whose cadr is an initialization
               expression
     expr M the expressions to be evaluated
     returns M the value of the last expression

(flet (binding...) expr...)  M create local functions
(labels (binding...) expr...) M flet with recursive functions
(macrolet (binding...) expr...) M create local macros
     binding M the function bindings each of which is:
          (sym fargs expr...)
     where:
          sym M the function/macro name
          fargs M formal argument list (lambda list)
          expr M expressions constituting the body of the function/macro
     expr M the expressions to be evaluated
     returns M the value of the last expression

(catch sym expr...)  M evaluate expressions and catch throws
     sym M the catch tag
     expr M expressions to evaluate
     returns M the value of the last expression the throw expression

(throw sym [expr]) M throw to a catch
     sym M the catch tag
     expr M the value for the catch to return (defaults to nil)
     returns M never returns

(unwind-protect expr cexpr...)  M protect evaluation of an expression
     expr M the expression to protect
     cexpr M the cleanup expressions
     returns M the value of the expression
     Note:  unwind-protect guarantees to execute the cleanup  expressions  even
          if  a  non-local  exit  terminates  the  evaluation  of the protected
          expression


IV.24. Looping Constructs
(loop expr...)  M basic looping form
     expr M the body of the loop
     returns M never returns (must use non-local exit)

(do (binding...) (texpr rexpr...) expr...)  (do* (binding...) (texpr  rexpr...)
     expr...)
     binding M the variable bindings each of which is either:
          1) a symbol (which is initialized to nil)
          2) a list of the form: (sym init [step]) where:
               sym M is the symbol to bind
               init M is the initial value of the symbol
               step M is a step expression
     texpr M the termination test expression
     rexpr M result expressions (the default is nil)
     expr M the body of the loop (treated like an implicit prog)
     returns M the value of the last result expression

(dolist (sym expr [rexpr]) expr...)  M loop through a list
     sym M the symbol to bind to each list element
     expr M the list expression
     rexpr M the result expression (the default is nil)
     expr M the body of the loop (treated like an implicit prog)

(dotimes (sym expr [rexpr]) expr...)  M loop from zero to n-1
     sym M the symbol to bind to each value from 0 to n-1
     expr M the number of times to loop
     rexpr M the result expression (the default is nil)
     expr M the body of the loop (treated like an implicit prog)


IV.25. The Program Feature
(prog (binding...) expr...)  M the program feature
(prog* (binding...) expr...)  M prog with sequential binding
     binding M the variable bindings each of which is either:
          1) a symbol (which is initialized to nil)
          2)  a  list whose car is a symbol and whose cadr is an initialization
               expression
     expr M expressions to evaluate or tags (symbols)
     returns M nil or the argument passed to the return function

(block name expr...)  M named block
     name M the block name (symbol)
     expr M the block body
     returns M the value of the last expression

(return [expr]) M cause a prog construct to return a value
     expr M the value (defaults to nil)
     returns M never returns

(return-from name [value]) M return from a named block
     name M the block name (symbol)
     value M the value to return (defaults to nil)
     returns M never returns

(tagbody expr...)  M block with labels
     expr M expression(s) to evaluate or tags (symbols)
     returns M nil

(go sym) M go to a tag within a tagbody or prog
     sym M the tag (quoted)
     returns M never returns

(progv slist vlist expr...)  M dynamically bind symbols
     slist M list of symbols
     vlist M list of values to bind to the symbols
     expr M expression(s) to evaluate
     returns M the value of the last expression

(prog1 expr1 expr...)  M execute expressions sequentially
     expr1 M the first expression to evaluate
     expr M the remaining expressions to evaluate
     returns M the value of the first expression

(prog2 expr1 expr2 expr...)  M execute expressions sequentially
     expr1 M the first expression to evaluate
     expr2 M the second expression to evaluate
     expr M the remaining expressions to evaluate
     returns M the value of the second expression

(progn expr...)  M execute expressions sequentially
     expr M the expressions to evaluate
     returns M the value of the last expression (or nil)


IV.26. Debugging and Error Handling
(trace sym) M add a function to the trace list
     sym M the function to add (quoted)
     returns M the trace list

(untrace sym) M remove a function from the trace list
     sym M the function to remove (quoted)
     returns M the trace list

(error emsg [arg]) M signal a non-correctable error
     emsg M the error message string
     arg M the argument expression (printed after the message)
     returns M never returns

(cerror cmsg emsg [arg]) M signal a correctable error
     cmsg M the continue message string
     emsg M the error message string
     arg M the argument expression (printed after the message)
     returns M nil when continued from the break loop

(break [bmsg [arg]]) M enter a break loop
     bmsg M the break message string (defaults to **break**)
     arg M the argument expression (printed after the message)
     returns M nil when continued from the break loop

(clean-up) M clean-up after an error
     returns M never returns

(top-level) M clean-up after an error and return to the top level
     returns M never returns

(continue) M continue from a correctable error
     returns M never returns

(errset expr [pflag]) M trap errors
     expr M the expression to execute
     pflag M flag to control printing of the error message
     returns M the value of the last expression consed with nil
     or nil on error

(baktrace [n]) M print n levels of trace back information
     n M the number of levels (defaults to all levels)
     returns M nil

(evalhook expr ehook ahook [env]) M evaluate with hooks
     expr M the expression to evaluate
     ehook M the value for *evalhook*
     ahook M the value for *applyhook*
     env M the environment (default is nil)
     returns M the result of evaluating the expression

(profile flag)(This is not a standard XLISP 2.0 function.)  M turn profiling on
     or off.
     flag M nil turns profiling off, otherwise on
     returns M the previous state of profiling.


IV.27. Arithmetic Functions
(truncate expr) M truncates a floating point number to an integer
     expr M the number
     returns M the result of truncating the number

(float expr) M converts an integer to a floating point number
     expr M the number
     returns M the result of floating the integer

(+ expr...)  M add a list of numbers
     expr M the numbers
     returns M the result of the addition

(- expr...)  M subtract a list of numbers or negate a single number
     expr M the numbers
     returns M the result of the subtraction

(* expr...)  M multiply a list of numbers
     expr M the numbers
     returns M the result of the multiplication

(/ expr...)  M divide a list of numbers
     expr M the numbers
     returns M the result of the division

(1+ expr) M add one to a number
     expr M the number
     returns M the number plus one

(1- expr) M subtract one from a number
     expr M the number
     returns M the number minus one

(rem expr...)  M remainder of a list of numbers
     expr M the numbers
     returns M the result of the remainder operation

(min expr...)  M the smallest of a list of numbers
     expr M the expressions to be checked
     returns M the smallest number in the list

(max expr...)  M the largest of a list of numbers
     expr M the expressions to be checked
     returns M the largest number in the list

(abs expr) M the absolute value of a number
     expr M the number
     returns M the absolute value of the number

(gcd n1 n2...)  M compute the greatest common divisor
     n1 M the first number (integer)
     n2 M the second number(s) (integer)
     returns M the greatest common divisor

(random n) M compute a random number between 0 and n-1 inclusive
     n M the upper bound (integer)
     returns M a random number

(rrandom) M compute a random real number between 0 and 1 inclusive
     returns M a random floating point number

(sin expr) M compute the sine of a number
     expr M the floating point number
     returns M the sine of the number

(cos expr) M compute the cosine of a number
     expr M the floating point number
     returns M the cosine of the number

(tan expr) M compute the tangent of a number
     expr M the floating point number
     returns M the tangent of the number

(atan  expr [expr2])(This is not a standard XLISP 2.0 function.)  M compute the
     arctangent
     expr M the value of x
     expr2 M the value of y (default value is 1.0)
     returns M the arctangent of x/y

(expt x-expr y-expr) M compute x to the y power
     x-expr M the floating point number
     y-expr M the floating point exponent
     returns M x to the y power

(exp x-expr) M compute e to the x power
     x-expr M the floating point number
     returns M e to the x power

(sqrt expr) M compute the square root of a number
     expr M the floating point number
     returns M the square root of the number

(< n1 n2...)  M test for less than
(<= n1 n2...) M test for less than or equal to
(= n1 n2...)  M test for equal to
(/= n1 n2...) M test for not equal to
(>= n1 n2...) M test for greater than or equal to
(> n1 n2...) M test for greater than
     n1 M the first number to compare
     n2 M the second number to compare
     returns M t if the results of comparing n1 with n2, n2 with n3, etc.,  are
          all true.


IV.28. Bitwise Logical Functions
(logand expr...) M the bitwise and of a list of numbers
     expr M the numbers
     returns M the result of the and operation

(logior expr...)  M the bitwise inclusive or of a list of numbers
     expr M the numbers
     returns M the result of the inclusive or operation

(logxor expr...)  M the bitwise exclusive or of a list of numbers
     expr M the numbers
     returns M the result of the exclusive or operation

(lognot expr) M the bitwise not of a number
     expr M the number
     returns M the bitwise inversion of number


IV.29. String Functions
(string expr) M make a string from an integer ascii value
     expr M the integer
     returns M a one character string

(string-search  pat  str  &key  :start  :end)(This  is not a standard XLISP 2.0
     function.)  M search for pattern in string
     pat M a string to search for
     str M the string to be searched
     :start M the starting offset in str
     :end M the ending offset + 1
     returns M index of pat in str or NIL if not found

(string-trim bag str) M trim both ends of a string
     bag M a string containing characters to trim
     str M the string to trim
     returns M a trimed copy of the string

(string-left-trim bag str) M trim the left end of a string
     bag M a string containing characters to trim
     str M the string to trim
     returns M a trimed copy of the string

(string-right-trim bag str) M trim the right end of a string
     bag M a string containing characters to trim
     str M the string to trim
     returns M a trimed copy of the string

(string-upcase str &key :start :end) M convert to uppercase
     str M the string
     :start M the starting offset
     :end M the ending offset + 1
     returns M a converted copy of the string

(string-downcase str &key :start :end) M convert to lowercase
     str M the string
     :start M the starting offset
     :end M the ending offset + 1
     returns M a converted copy of the string

(nstring-upcase str &key :start :end) M convert to uppercase
     str M the string
     :start M the starting offset
     :end M the ending offset + 1
     returns M the converted string (not a copy)

(nstring-downcase str &key :start :end) M convert to lowercase
     str M the string
     :start M the starting offset
     :end M the ending offset + 1
     returns M the converted string (not a copy)

(strcat expr...)  M concatenate strings
     expr M the strings to concatenate
     returns M the result of concatenating the strings

(subseq string start [end]) M extract a substring
     string M the string
     start M the starting position (zero origin)
     end M the ending position + 1 (defaults to end)
     returns M substring between start and end

(string< str1 str2 &key :start1 :end1 :start2 :end2) (string<= str1  str2  &key
     :start1 :end1 :start2 :end2)
(string= str1 str2 &key :start1 :end1 :start2 :end2)
(string/= str1 str2 &key :start1 :end1 :start2 :end2)
(string>= str1 str2 &key :start1 :end1 :start2 :end2)
(string> str1 str2 &key :start1 :end1 :start2 :end2)
     str1 M the first string to compare
     str2 M the second string to compare
     :start1 M first substring starting offset
     :end1 M first substring ending offset + 1
     :start2 M second substring starting offset
     :end2 M second substring ending offset + 1
     returns M t if predicate is true, nil otherwise
     Note: case is significant with these comparison functions.

(string-lessp str1 str2 &key :start1 :end1 :start2 :end2)
(string-not-greaterp str1 str2 &key :start1 :end1 :start2 :end2)
(string-equalp str1 str2 &key :start1 :end1 :start2 :end2)
(string-not-equalp str1 str2 &key :start1 :end1 :start2 :end2)
(string-not-lessp str1 str2 &key :start1 :end1 :start2 :end2)
(string-greaterp str1 str2 &key :start1 :end1 :start2 :end2)
     str1 M the first string to compare
     str2 M the second string to compare
     :start1 M first substring starting offset
     :end1 M first substring ending offset + 1
     :start2 M second substring starting offset
     :end2 M second substring ending offset + 1
     returns M t if predicate is true, nil otherwise
     Note: case is not significant with these comparison functions.


IV.30. Character Functions
(char string index) M extract a character from a string
     string M the string
     index M the string index (zero relative)
     returns M the ascii code of the character

(upper-case-p chr) M is this an upper case character?
     chr M the character
     returns M t if the character is upper case, nil otherwise

(lower-case-p chr) M is this a lower case character?
     chr M the character
     returns M t if the character is lower case, nil otherwise

(both-case-p chr) M is this an alphabetic (either case) character?
     chr M the character
     returns M t if the character is alphabetic, nil otherwise

(digit-char-p chr) M is this a digit character?
     chr M the character
     returns M the digit weight if character is a digit, nil otherwise

(char-code chr) M get the ascii code of a character
     chr M the character
     returns M the ascii character code (integer)

(code-char code) M get the character with a specified ascii code
     code M the ascii code (integer)
     returns M the character with that code or nil

(char-upcase chr) M convert a character to upper case
     chr M the character
     returns M the upper case character

(char-downcase chr) M convert a character to lower case
     chr M the character
     returns M the lower case character

(digit-char n) M convert a digit weight to a digit
     n M the digit weight (integer)
     returns M the digit character or nil

(char-int chr) M convert a character to an integer
     chr M the character
     returns M the ascii character code

(int-char int) M convert an integer to a character
     int M the ascii character code
     returns M the character with that code

(char< chr1 chr2...)
(char<= chr1 chr2...)
(char= chr1 chr2...)
(char/= chr1 chr2...)
(char>= chr1 chr2...)
(char> chr1 chr2...)
     chr1 M the first character to compare
     chr2 M the second character(s) to compare
     returns M t if predicate is true, nil otherwise
     Note: case is significant with these comparison functions.

(char-lessp chr1 chr2...)
(char-not-greaterp chr1 chr2...)
(char-equalp chr1 chr2...)
(char-not-equalp chr1 chr2...)
(char-not-lessp chr1 chr2...)
(char-greaterp chr1 chr2...)
     chr1 M the first string to compare
     chr2 M the second string(s) to compare
     returns M t if predicate is true, nil otherwise
     Note: case is not significant with these comparison functions.


IV.31. Input/Output Functions
(read [stream [eof [rflag]]]) M read an expression
     stream M the input stream (default is standard input)
     eof M the value to return on end of file (default is nil)
     rflag M recursive read flag (default is nil)
     returns M the expression read

(print expr [stream]) M print an expression on a new line
     expr M the expression to be printed
     stream M the output stream (default is standard output)
     returns M the expression

(prin1 expr [stream]) M print an expression
     expr M the expression to be printed
     stream M the output stream (default is standard output)
     returns M the expression

(princ expr [stream]) M print an expression without quoting
     expr M the expressions to be printed
     stream M the output stream (default is standard output)
     returns M the expression

(pprint expr [stream]) M pretty print an expression
     expr M the expressions to be printed
     stream M the output stream (default is standard output)
     returns M the expression

(terpri [stream]) M terminate the current print line
     stream M the output stream (default is standard output)
     returns M nil

(flatsize expr) M length of printed representation using prin1
     expr M the expression
     returns M the length

(flatc expr) M length of printed representation using princ
     expr M the expression
     returns M the length


IV.32. The Format Function
(format stream fmt arg...)  M do formated output
     stream M the output stream
     fmt M the format string
     arg M the format arguments
     returns M output string if stream is nil, nil otherwise

  The  format  string  can contain characters that should be copied directly to
the output and formatting directives.  The formatting directives are:

    ~A M print next argument using princ
    ~S M print next argument using prin1
    ~% M start a new line
    ~~ M print a tilde character
    ~<newline> M ignore this one newline and white space on the
    next line up to the first non-white-space character or newline. This
    allows strings to continue across multiple lines

IV.33. File I/O Functions
  Note that files are ordinarily opened as text. Binary files (such as standard
midi files) must be opened with open-binary on non-unix systems.
(open fname &key :direction) M open a file stream
     fname M the file name string or symbol
     :direction M :input or :output (default is :input)
     returns M a stream

(open-binary fname &key :direction) M open a binary file stream
     fname M the file name string or symbol
     :direction M :input or :output (default is :input)
     returns M a stream

(close stream) M close a file stream
     stream M the stream
     returns M nil

(setdir  path)(This  is  not  a  standard  XLISP  2.0  function.) M set current
     directory
     path M the path of the new directory
     returns M the resulting full path, e.g.  (setdir  ".")  gets  the  current
          working directory, or nil if an error occurs

(listdir  path)(This  is  not a standard XLISP 2.0 function.) M get a directory
     listing
     path M the path of the directory to be listed
     returns M list of filenames in the directory

(get-temp-path)(This is not a standard XLISP 2.0 function.) M get a path  where
     a  temporary  file  can  be  created.  Under  Windows,  this  is  based on
     environment variables. If XLISP is running as a sub-process to  Java,  the
     environment  may  not  exist,  in  which  case  the  default result is the
     unfortunate choice c:\windows\.
     returns M the resulting full path as a string

(get-user)(This is not a standard XLISP 2.0 function.) M get the  user  ID.  In
     Unix  systems  (including  OS  X and Linux), this is the value of the USER
     environment variable. In Windows,  this  is  currently  just  ``nyquist'',
     which  is  also  returned  if the environment variable cannot be accessed.
     This function is used to avoid the case of two users creating files of the
     same name in the same temp directory.
     returns M the string naming the user

(find-in-xlisp-path  filename)(This  is  not  a standard XLISP 2.0 function.) M
     search the XLISP search path (e.g. XLISPPATH  from  the  environment)  for
     filename.  If filename is not found as is, and there is no file extension,
     append ".lsp" to filename and search again. The current directory  is  not
     searched.
     filename M the name of the file to search for
     returns M a full path name to the first occurrence found

(read-char [stream]) M read a character from a stream
     stream M the input stream (default is standard input)
     returns M the character

(peek-char [flag [stream]]) M peek at the next character
     flag M flag for skipping white space (default is nil)
     stream M the input stream (default is standard input)
     returns M the character (integer)

(write-char ch [stream]) M write a character to a stream
     ch M the character to write
     stream M the output stream (default is standard output)
     returns M the character

(read-int [stream [length]]) M read a binary integer from a stream
     stream M the input stream (default is standard input)
     length M the length of the integer in bytes (default is 4)
     returns M the integer
     Note:  Integers  are  assumed to be big-endian (high-order byte first) and
          signed, regardless of the platform. To read little-endian format, use
          a  negative  number  for  the  length,  e.g.  -4 indicates a 4-bytes,
          low-order byte first. The file should be opened in binary mode.

(write-int ch [stream [length]]) M write a binary integer to a stream
     ch M the character to write
     stream M the output stream (default is standard output)
     length M the length of the integer in bytes (default is 4)
     returns M the integer
     Note: Integers are assumed to be big-endian (high-order  byte  first)  and
          signed, regardless of the platform. To write in little-endian format,
          use a negative number for the length, e.g. -4  indicates  a  4-bytes,
          low-order byte first. The file should be opened in binary mode.

(read-float  [stream  [length]])  M  read a binary floating-point number from a
     stream
     stream M the input stream (default is standard input)
     length M the length of the float in bytes (default is 4, legal values  are
          -4, -8, 4, and 8)
     returns M the integer
     Note:  Floats  are  assumed  to  be big-endian (high-order byte first) and
          signed, regardless of the platform. To read little-endian format, use
          a  negative  number  for  the  length,  e.g.  -4 indicates a 4-bytes,
          low-order byte first. The file should be opened in binary mode.

(write-float ch [stream [length]]) M write a binary floating-point number to  a
     stream
     ch M the character to write
     stream M the output stream (default is standard output)
     length  M the length of the float in bytes (default is 4, legal values are
          -4, -8, 4, and 8)
     returns M the integer
     Note: Floats are assumed to be  big-endian  (high-order  byte  first)  and
          signed, regardless of the platform. To write in little-endian format,
          use a negative number for the length, e.g. -4  indicates  a  4-bytes,
          low-order byte first. The file should be opened in binary mode.

(read-line [stream]) M read a line from a stream
     stream M the input stream (default is standard input)
     returns M the string

(read-byte [stream]) M read a byte from a stream
     stream M the input stream (default is standard input)
     returns M the byte (integer)

(write-byte byte [stream]) M write a byte to a stream
     byte M the byte to write (integer)
     stream M the output stream (default is standard output)
     returns M the byte (integer)


IV.34. String Stream Functions
  These  functions  operate  on  unnamed  streams.    An  unnamed output stream
collects characters sent to it when it is used as the destination of any output
function.    The  functions get-output-stream-string and get-output-stream-list
return a string or a list of characters.

  An unnamed input stream is setup with the  make-string-input-stream  function
and  returns  each character of the string when it is used as the source of any
input function.

(make-string-input-stream str [start [end]])
     str M the string
     start M the starting offset
     end M the ending offset + 1
     returns M an unnamed stream that reads from the string

(make-string-output-stream)
     returns M an unnamed output stream

(get-output-stream-string stream)
     stream M the output stream
     returns M the output so far as a string
     Note:  the output stream is emptied by this function

(get-output-stream-list stream)
     stream M the output stream
     returns M the output so far as a list
     Note:  the output stream is emptied by this function


IV.35. System Functions
  Note: the load  function  first  tries  to  load  a  file  from  the  current
directory.  A  .lsp  extension is added if there is not already an alphanumeric
extension following a period.  If that fails, XLISP searches the path, which is
obtained    from    the    XLISPPATH   environment   variable   in   Unix   and
HKEY_LOCAL_MACHINE\SOFTWARE\CMU\Nyquist\XLISPPATH under Win32.  (The  Macintosh
version has no search path.)
(load fname &key :verbose :print) M load a source file
     fname M the filename string or symbol
     :verbose M the verbose flag (default is t)
     :print M the print flag (default is nil)
     returns M the filename

(save fname) M save workspace to a file
     fname M the filename string or symbol
     returns M t if workspace was written, nil otherwise

(restore fname) M restore workspace from a file
     fname M the filename string or symbol
     returns M nil on failure, otherwise never returns

(dribble [fname]) M create a file with a transcript of a session
     fname M file name string or symbol (if missing, close current transcript)
     returns M t if the transcript is opened, nil if it is closed

(gc) M force garbage collection
     returns M nil

(expand num) M expand memory by adding segments
     num M the number of segments to add
     returns M the number of segments added

(alloc num) M change number of nodes to allocate in each segment
     num M the number of nodes to allocate
     returns M the old number of nodes to allocate

(info) M show information about memory usage.
     returns M nil

(room) M show memory allocation statistics
     returns M nil

(type-of expr) M returns the type of the expression
     expr M the expression to return the type of
     returns M nil if the value is nil otherwise one of the symbols:
          SYMBOL M for symbols
          OBJECT M for objects
          CONS M for conses
          SUBR M for built-in functions
          FSUBR M for special forms
          CLOSURE M for defined functions
          STRING M for strings
          FIXNUM M for integers
          FLONUM M for floating point numbers
          CHARACTER M for characters
          FILE-STREAM M for file pointers
          UNNAMED-STREAM M for unnamed streams
          ARRAY M for arrays

(peek addrs) M peek at a location in memory
     addrs M the address to peek at (integer)
     returns M the value at the specified address (integer)

(poke addrs value) M poke a value into memory
     addrs M the address to poke (integer)
     value M the value to poke into the address (integer)
     returns M the value

(bigendianp) M is this a big-endian machine?
     returns M T if this a big-endian architecture, storing the high-order byte
          of an integer at the lowest byte address of the  integer;  otherwise,
          NIL.  (This is not a standard XLISP 2.0 function.)

(address-of expr) M get the address of an xlisp node
     expr M the node
     returns M the address of the node (integer)

(exit) M exit xlisp
     returns M never returns

(setup-console) M set default console attributes
     returns M NIL
     Note:  Under Windows, Nyquist normally starts up in a medium-sized console
          window with black text and a white background, with a window title of
          ``Nyquist.''  This  is normally accomplished by calling setup-console
          in system.lsp. In Nyquist, you can avoid  this  behavior  by  setting
          *setup-console* to NIL in your init.lsp file. If setup-console is not
          called, Nyquist uses standard input and output as is.  This  is  what
          you want if you are running Nyquist inside of emacs, for example.

(echoenabled flag) M turn console input echoing on or off
     flag M T to enable echo, NIL to disable
     returns M NIL
     Note:  This  function  is  only  implemented  under Linux and Mac OS X. If
          Nyquist I/O is redirected through pipes, the Windows version does not
          echo  the  input, but the Linux and Mac versions do. You can turn off
          echoing with this  function.  Under  windows  it  is  defined  to  do
          nothing.

IV.36. File I/O Functions



IV.36.1. Input from a File
  To  open  a  file  for input, use the open function with the keyword argument
:direction set to :input.  To open a file for output,  use  the  open  function
with the keyword argument :direction set to :output.  The open function takes a
single required argument which is the name of the file to be opened.  This name
can  be  in  the  form  of  a string or a symbol.  The open function returns an
object of type FILE-STREAM if it succeeds in opening the specified  file.    It
returns  the  value  nil  if  it fails.  In order to manipulate the file, it is
necessary to save the value returned by the open function.    This  is  usually
done  by assigning it to a variable with the setq special form or by binding it
using let or let*.  Here is an example:

    (setq fp (open "init.lsp" :direction :input))

Evaluating this expression will result in the file init.lsp being opened.   The
file  object that will be returned by the open function will be assigned to the
variable fp.

  It is now possible to use the file for input.  To read an expression from the
file,  just supply the value of the fp variable as the optional stream argument
to read.

    (read fp)

Evaluating this expression will result in reading the first expression from the
file  init.lsp.    The  expression  will  be returned as the result of the read
function.  More expressions can be read from the file using  further  calls  to
the  read  function.    When  there  are  no more expressions to read, the read
function will return nil (or whatever value was supplied as the second argument
to read).

  Once  you  are done reading from the file, you should close it.  To close the
file, use the following expression:

    (close fp)

Evaluating this expression will cause the file to be closed.
IV.36.2. Output to a File
  Writing to a file is pretty much the same as reading from one.  You  need  to
open  the  file  first.  This time you should use the open function to indicate
that you will do output to the file.  For example:

    (setq fp (open "test.dat" :direction :output))

Evaluating this expression will open the file test.dat for output.  If the file
already  exists, its current contents will be discarded.  If it doesn't already
exist, it will be created.  In any case, a FILE-STREAM object will be  returned
by the OPEN function.  This file object will be assigned to the fp variable.

  It  is  now  possible  to write to this file by supplying the value of the fp
variable as the optional stream parameter in the print function.

    (print "Hello there" fp)

Evaluating this expression will result in  the  string  ``Hello  there''  being
written  to  the file test.dat.  More data can be written to the file using the
same technique.

  Once you are done writing to the file, you  should  close  it.    Closing  an
output file is just like closing an input file.

    (close fp)

Evaluating this expression will close the output file and make it permanent.



IV.36.3. A Slightly More Complicated File Example
  This  example  shows  how  to open a file, read each Lisp expression from the
file and print it.  It demonstrates the  use  of  files  and  the  use  of  the
optional stream argument to the read function.

    (do* ((fp (open "test.dat" :direction :input))
          (ex (read fp) (read fp)))
         ((null ex) nil)
      (print ex))
                                  REFERENCES

[Dannenberg 89]
               Dannenberg, R. B. and C. L. Fraley.  Fugue: Composition and
Sound Synthesis With Lazy Evaluation and Behavioral Abstraction.  In T. Wells
and D. Butler (editor), Proceedings of the 1989 International Computer Music
Conference, pages 76-79.  International Computer Music Association, San
Francisco, 1989.

[Touretzky 84] Touretzky, David S.  LISP: a gentle introduction to symbolic
computation.  Harper & Row, New York, 1984.
Index


                          Begin   13                Do*   64
!   13, 33                Behavioral abstraction   6Dolby Pro-Logic   49
!=   13                   Behaviors   18            Dolby Surround   49
!Call   37                Bell sound   4            Dolist   64
!Clock   36               Bernoulli     distributionDoppler effect   49
!csec   35                        43                Dot   33
!Def   36                 Bernoulli-dist   43       Dotimes   64
!End   37                 Beta distribution   43    Dotted durations   3
!msec   35                Beta-dist   43            Dribble   67
!Ramp   36                Big endian   67           Drum   50
!Rate   34                Bigendianp   67           Drum machine   4
!Seti   37                Bilateral      exponentialDrum samples   4
!Setv   37                        distribution   42 Drum sound   4
!Tempo   34               Bilateral-exponential-distDrum-loop   50
                                  42                DSP in Lisp   4
#   (Adagio  articulation)Binary files   66         Dtmf   49
        34                Binomial distribution   43Dtmf-tone   49
#?, sal   13              Binomial-dist   43        Dubugging   27
#define'd macros   56     Biquad   21               Duration   33
#f   13                   Biquad-m   21             Duration notation   3
#t   13                   Bitwise  Logical FunctionsDuration of another  sound
                                  65                        26
%   (Adagio   thirtysecondBlank   33                DX7   33
        note)   33        Block   64                Dynamic markings   34
%   13                    Both-case-p   65
                          Boundp   63               Echo   21
&   13                    Bowed   22                Echoenabled   67
&=   15                   Bowed-freq   22           Effect,      reverberation
                          Brass sound   4                   22, 22
*   13, 64                Break   59, 64            Effect, chorus    22,  28,
*=   15                   Build-harmonic   2, 18            48
*A4-Hertz*   17, 31       Buzz   19                 Effect, flange   48
*applyhook*   61                                    Effect,  pitch shift   22,
*autonorm*   31           Call command   37                 28
*autonorm-max-samples*    Car   62                  Effect,      reverberation
        31                Case   33, 63                     29, 49
*autonorm-previous-peak*  Case-insensitive   13     Effect, stereo   49
        31                Catch   64                Effect, stereo pan   49
*autonorm-target*   31    Cauchy distribution   42  Effect, swap channels   49
*autonorm-type*   31      Cauchy-dist   42          Effect, widen   49
*autonormflag*   31       Cdr   62                  Effects, phaser   48
*breakenable*   31, 59, 61Cerror   64               EIghth note   3, 33
*control-srate*     6, 24,Change directory   66     Emacs,  using Nyquist with
        31                Char   65                         67
*debug-io*   61           Char-code   65            Empty list   13
*default-control-srate*   Char-downcase   66        End   13
        31                Char-equalp   66          End command   37
*default-plot-file*   26  Char-greaterp   66        Endian   67
*default-sf-bits*   31    Char-int   66             Endless tones   4
*default-sf-dir*   24, 31 Char-lessp   66           Endp   63
*default-sf-format*   31  Char-not-equalp   66      Env   3, 18
*default-sf-srate*     25,Char-not-greaterp   66    Env-note   3
        31                Char-not-lessp   66       Envelope   3
*default-sound-srate*   31Char-upcase   66          Envelope follower   17, 27
*error-output*   61       Char/=   66               Envelope generator   21
*evalhook*   61           Char<   66                Envelopes   3
*file-separator*   31     Char<=   66               Environment   6
*float-format*   61       Char=   66                Eq   63
*gc-flag*   61            Char>   66                Eq-band   21
*gc-hook*   61            Char>=   66               Eq-highshelf   21
*integer-format*   61     Character Functions   65  Eq-lowshelf   21
*loud*   6                Characterp   63           Eql   63
*obarray*   61            Chdir, sal   13           Equal   63
*print-case*   61         Chorus   22, 27, 28, 48   Equalization   21, 48
*readtable*   60, 61      Clarinet   22             Error   64
*rslt*   31, 56           Clarinet sound   4        Error Handling   64
*sound-srate*   6, 24, 31 Clarinet-all   22         Errors   iii
*soundenable*   31        Clarinet-freq   22        Errset   64
*standard-input*   61     Class   61                Estimate frequency   23
*standard-output*   61    Class class   61          Eval   61
*start*   6               Clean-up   64             Eval pattern   41
*stop*   6                Clip   10, 23, 26         Evalhook   64
*sustain*   6             Clipping repair   48      Evaluation functions   61
*table*   31              Clock   36                Evaluator   59
*trace-output*   61       Clock command   36        Evenp   63
*tracelimit*   59, 61     Close   66                Event-dur   45
*tracelist*   61          Co-termination   26       Event-end   45
*tracenable*   31, 59, 61 Code-char   66            Event-expression   45
*transpose*   6           Comb   21                 Event-get-attr   45
*unbound*   61            Comb filter   21          Event-has-attr   45
*warp*   6, 23            Combination   24          Event-set-attr   45
                          Command Loop   59         Event-set-dur   45
+   13, 64                Commas   35               Event-set-expression   45
+=   15                   Comment   33              Event-set-time   45
                          Comments   13             Event-time   45
, (Adagio)   35           Compose   27              Exclamation point   33
                          Compress   48             Exec statement, sal   14
-   13, 64                Compress-map   48         Exit   67
                          Compressor   17           Exit statement, sal   15
. (Adagio)   33           Concatenate strings   65  Exp   65
                          Cond   63                 Exp-dec   18
/   13, 64                Conditional    expression,Expand   67
/=   65                           sal   13          Exponent   39
                          Configure nyquist   1     Exponential   23
1+   64                   Congen   21               Exponential   distribution
1-   64                   Cons   62                         42
                          Console, XLISP   67       Exponential envelope   18
:answer   61              Consp   63                Exponential-dist   42
:class   61               Const   18                Expr-get-attr   45
:isnew   61               Constant function   18    Expr-has-attr   45
:new   61                 Continue   64             Expr-set-attr   45
:show   61                Continuous-control-warp   Expression pattern   41
                                  23                Expressions, sal   13
; (Adagio)   35           Continuous-sound-warp   24Expt   65
                          Contour generator   21    Extending Xlisp   56
<   13, 65                Control   18              Extract   24
<=   13, 15, 65           Control change   35       Extract-abs   24
                          Control characters,  XLISP
=   13, 65                        59                F (Adagio dynamic)   34
                          Control Constructs   63   F (Adagio Flat)   33
>   13, 65                Control-srate-abs   24    Fast   fourier   transform
>=   13, 15, 65           Control-warp   18                 tutorial   32
                          Convert   sound  to  arrayFboundp   63
@   13                            17                Feedback   FM   Oscillator
@=   15                   Convolution   21                  19
@@   13                   Convolve   21             Feedback-delay   21
                          Copier pattern   41       Feel factor   46
A440   17                 Cos   65                  FF (Adagio dynamic)   34
Abs   65                  Cue   18                  FFF (Adagio dynamic)   34
Abs-env   23              Cue-file   18             Fft   32
Absolute stretch, sal   13Current-path   39         Fft tutorial   32
Absolute time  shift,  salCxxr   62                 File  I/O  Functions   66,
        13                Cxxxr   62                        67
Absolute value   23, 26   Cxxxxr   62               Filep   63
Access samples   16       Cycle pattern   40        Filter example   11
Accidentals   33                                    Finally clause, sal   14
Accumulate pattern   41   Data Types   59           Find string   65
Adagio   33               Db-average   48           Find-in-xlisp-path   66
Add offset to sound   26  Db-to-linear   17         FIR filter   21
Add to file samples   25  DB0   3                   First   62
Add-action-to-workspace   DB1   3                   First derivative   19
        46                DB10   3                  Flange   48
Add-to-workspace   46     Debugging   17, 26, 39, 64Flange effect   48
Additive synthesis,  gongsDecf   39                 Flat   33
        3                 Decrement   39            Flatc   66
Address-of   67           Default durations   34    Flatsize   66
Aftertouch   35           Default   34              Flet   63
Agc   48                  Default sample rate   7   Float   64
Algorithmic    CompositionDefault     sound     fileFloatp   63
        40                        directory   24    Flute   22
All pass filter   20      Default time   33         Flute sound   4
Alloc   67                Define function   14      Flute-all   22
Allpass2   21             Define variable   13      Flute-freq   22
Allpoles-from-lpc   38    Defining Behaviors   7    FM synthesis   11
Alpass   20               Defmacro   61             Fmfb   19
Alpass filter   20        Defun   61                Fmlfo   18
Amosc   19                Delay   21                Fmosc   19
Analog synthesizer   50   Delay, variable   27      Follow   17
And   63                  Delete   62               Follower   27
Append   62               Delete-if   63            Force-srate   18
Apply   61                Delete-if-not   63        Format   66
Apply-banded-bass-boost   Demos, bell sound   4     Fourth   62
        49                Demos, distortion   21    Frequency analysis   23
Apply-banded-delay   49   Demos, drum machine   4   Frequency Modulation   10
Apply-banded-treble-boost Demos, drum sound   4     Full path name   39
        49                Demos, fft   32           Funcall   61
Approximation   20        Demos, FM   11            Function   61
Arc-sine-dist   42        Demos, FM synthesis   4   Function calls, sal   13
Arcsine distribution   42 Demos, formants   4       Function, sal   14
Aref   62                 Demos, gong sound   3     Fundamenal       frequency
Areson   21               Demos, lpc   38                   estimation   23
Args   39                 Demos, midi   33
Arguments   to   a    lispDemos, piano   48         Gain   48
        function   39     Demos, pitch change   27  Gamma-dist   42
Arithmetic Functions   64 Demos,   rhythmic  patternGate   17, 27
Array from sound   17             4                 Gaussian distribution   42
Array Functions   62      Demos, ring modulation   3Gaussian-dist   42
Array notation, sal   13  Demos,    sample-by-sampleGc   67
Arrayp   63                       4                 Gcd   65
Articulation   33, 34     Demos,   scratch  tutorialGEN05   20
Assoc   62                        11                Gensym   61
Asterisk   33             Demos, Shepard tones   21 Geometric     distribution
At   23                   Demos,  spectral  analysis        43
At Transformation   7             of a chord   3    Geometric-dist   43
At, sal   13              Demos,   voice   synthesisGet   62
At-abs   23                       21                Get char   66
At-abs, sal   13          Demos, wind sound   11    Get-duration   17
Atan   65                 Derivative   19           Get-lambda-expression   61
Atom   63                 Describe   46             Get-loud   17
Atone   21                Destructive List FunctionsGet-output-stream-list
Attributes   33                   62                        67
Automatic   gain   controlDeveloping code   39      Get-output-stream-string
        48                Diff   24                         67
Autonorm-off   10, 24, 25 Difference   47           Get-slider-value   26
Autonorm-on   10, 24, 25  Difference of sounds   24 Get-sustain   17
Average   26              Digit-char   66           Get-temp-path   66
                          Digit-char-p   65         Get-transpose   17
Backquote   61            Directory listing   66    Get-user   66
Backward   48             Directory,  default  soundGet-warp   17
Baktrace   64                     file   24         Global Variables   31
Banded bass boost   49    Display   statement,   salGlobal variables, sal   13
Banded delay   49                 14                Go   64
Banded treble boost   49  Distortion tutorial   21  Gong sounds   3
Bandfx.lsp   48           Distributions, probabilityGranular synthesis   49
Bandpass filter   21              42                Graphical equalizer   48
Bandpass2   21            Division   23             Grindef   39
Bartok   35               Do   64
H (Adagio Half note)   33 Mkwave   2                Qt   3
H   3                     Modalbar   22             Quantize   23
Half note   3, 33         Modulation wheel   35     Quarter note   3, 33
Harmonic   18             Modulo (rem) function   64Quote   61
Hash   62                 Mono to stereo   49
Hd   3                    Moog   50                 R (Adagio Rest)   33
Header file format   56   Moving average   26       Ramp   23
Heap pattern   41         MP (Adagio dynamic)   34  Random   39, 42, 65
High-pass filter   21     Mult   3, 18, 24          Random pattern   40
Highpass2   21            Multichannel Sounds   16  Rate   33, 34
Highpass4   22            Multiple band effects   48Read   66
Highpass6   22            Multiple commands   35    Read directory   66
Highpass8   22            Multiple tempi   36       Read macros   60
Hp   21                   Multiplication   27       Read samples   16
Ht   3                    Multiply signals   24     Read   samples  from  file
Hyperbolic-cosine-dist                                      25
        42                N (Adagio Next)   33      Read  samples  in  reverse
Hz-to-step   17           Natural   33                      48
Hzosc   19                Natural log   23          Read-byte   67
                          Nband   48                Read-char   66
I (Adagio eIght note)   33Nband-range   48          Read-float   66
I   3                     Nconc   62                Read-int   66
Id   3                    Nested Transformations   7Read-line   67
If   63                   Next Adagio command   33  Readtables   60
If statement, sal   14    Next in pattern   40      Real-random   39
Ifft   32                 Next pattern   40         Recip   23
Incf   39                 Noise   23                Reciprocal   23
Increment   39            Noise gate   27           Registry   1
Info   67                 Noise-gate   17           Rem   64
Input from a File   67    Normalization   10        Remainder   64
Input/Output     FunctionsNot   63                  Remove   62
        66                Not  enough   memory   forRemove-if   62
Installation   1                  normalization   10Remove-if-not   62
Int-char   66             Notch filter   21         Remprop   62
Integerp   63             Notch2   21               Replace file samples   25
Integrate   19            Note   3                  Resample   18
Intern   61               Note list   24            Resampling   18, 27
Interoperability, sal  andNrev   22                 Rescaling   10
        lisp   15         Nstring-downcase   65     Resolution   35
Interpolate   46          Nstring-upcase   65       Reson   21
Intersection   47         Nth   62                  Rest   23, 62
Intgen   56               Nthcdr   62               Restore   67
Inverse   27              Null   63                 Rests   33
Inverse fft   32          Numberp   63              Return   64
It   3                    Ny:all   3                Return statement, sal   15
                                                    Return-from   64
Jcrev   22                O (Adagio control)   35   Reverb   22, 29, 49
Jitter   46               Object   61               Reverse   62
                          Object Class   61         Reverse, sound   48
K (Adagio control)   35   Objectp   63              Ring modulation   3
Karplus-Strong   19       Objects   60              Risset   3
Karplus-Strong   synthesisOctave specification   33 Rms   23, 26
        4                 Oddp   63                 Room   67
Keyword parameters   44   Offset   46               Rplaca   62
                          Offset to a sound   26    Rplacd   62
Labels   63               Omissions   iii           Rrandom   65
Lambda   61               Oneshot   27
Lambda Lists   60         Open   66                 S (Adagio Sharp)   33
Last   62                 Open  sound  control   18,S  (Adagio Sixteenth note)
Latency   18                      55                        33
Legato   24, 34           Open-binary   66          S   3
Length   62               Or   63                   S-abs   23
Length pattern   41       Osc   2, 18, 19           S-add-to   25
Length-of-beat   50       Osc-enable   18           S-exp   23
Let   63                  Osc-note   23             S-log   23
Let*   63                 Osc-pulse   19            S-max   10, 23
Lexical conventions   59  Osc-saw   19              S-min   10, 23
LF (Adagio dynamic)   34  Osc-tri   19              S-overwrite   25
Lf   3                    Output  samples  to   fileS-plot   26
LFF (Adagio dynamic)   34         25                S-print-tree   26
Lff   3                   Output to a File   68     S-read   25
LFFF (Adagio dynamic)   34Overlap   24              S-read-reverse   48
Lfff   3                  Overwrite samples   25    S-rest   23
Lfo   18                                            S-reverse   48
Libraries   48            P (Adagio dynamic)   34   S-save   25
Limit   23                P (Adagio Pitch)   33     S-sqrt   23
Limiter   17              Palindrome pattern   40   SAL   13
Line pattern   40         Pan   18, 49              Sal and lisp   15
Linear distribution   42  Pan, stereo   49          Sal expressions   13
Linear interpolation   46 Parameters, keyword   44  Sample interpolation   27
Linear Prediction   38    Params-scale   46         Sample rate, forcing   18
Linear prediction tutorialParams-transpose   46     Sample rates   7
        38                Partial   19              Sampler   19
Linear-dist   42          Path, current   39        Samples   16, 17
Linear-to-db   17         Pattern, length   41      Samples, reading   16
Lisp DSP   4              Pattern, window   41      Sampling rate   17
Lisp Include Files   57   Pattern, accumulate   41  Save   67
List   62                 Pattern, copier   41      Save samples to file   25
List directory   66       Pattern, cycle   40       Save-lpc-file   38
List Functions   62       Pattern, eval   41        Save-workspace   46
Listdir   66              Pattern, expression   41  Saving Sound Files   10
Listing  of  lisp functionPattern, heap   41        Sawtooth oscillator   19
        39                Pattern, line   40        Sawtooth wave   2
Listp   63                Pattern, markov   41      Sax   22
Little endian   67        Pattern, palindrome   40  Sax-all   22
LMF (Adagio dynamic)   34 Pattern, product   41     Sax-freq   22
Lmf   3                   Pattern, random   40      Scale   18
LMP (Adagio dynamic)   34 Pattern, sum   41         Scale-db   18
Lmp   3                   Patternp   46             Scale-srate   18
Load   67                 Peak   27                 Scan directory   66
Load statement, sal   14  Peak amplitude   10       Score   24
Local-to-global   18      Peak,   maximum  amplitudeScore manipulation   45
Log   17                          27                Score, musical   3
Log function   17         Peek   67                 Score-adjacent-events   46
Logand   65               Peek-char   66            Score-append   45
Logical-stop   16         Period estimation   23    Score-apply   46
Logior   65               Phaser   48               Score-filter   45
Logistic distribution   42Physical model   4        Score-filter-length   46
Logistic-dist   42        Piano synthesizer   48    Score-filter-overlap   46
Lognot   65               Piano synthesizer tutorialScore-gen   44
Logorithm   23                    48                Score-get-begin   45
Logxor   65               Piano-midi   48           Score-get-end   45
Loop   64                 Piano-midi2file   48      Score-indexof   46
Loop examples, sal   14   Piano-note   48           Score-last-indexof   46
Loop statement, sal   14  Piano-note-2   48         Score-merge   45
Looping Constructs   64   Piece-wise   20           Score-must-have-begin-end
Loud   24                 Piece-wise linear   27            45
Loud-abs   24             Pitch   33                Score-play   46
Loudness   33, 34         Pitch bend   35           Score-print   46
Low-frequency   oscillatorPitch detection   23      Score-randomize-start   46
        18                Pitch notation   3        Score-read-smf   46
Low-pass filter   21, 29  Pitch shift   22, 28      Score-repeat   46
Lower-case-p   65         Pitch shifting   27       Score-scale   45
Lowpass2   21             Pitshift   22             Score-select   45
Lowpass4   21             Pl-center   49            Score-set-begin   45
Lowpass6   21             Pl-doppler   49           Score-set-end   45
Lowpass8   22             Pl-left   49              Score-shift   45
LP (Adagio dynamic)   34  Pl-pan2d   49             Score-sort   45
Lp   3, 21                Pl-position   49          Score-sorted   45
LPC   38                  Pl-rear   49              Score-stretch   45
Lpc tutorial   38         Pl-right   49             Score-stretch-to-length
Lpc-frame-err   38        Play   2, 24                      46
Lpc-frame-filter-coefs    Play in reverse   48      Score-sustain   45
        38                Play-file   25            Score-transpose   45
Lpc-frame-rms1   38       Pluck   19                Score-voice   45
Lpc-frame-rms2   38       Plucked string   19       Score-write-smf   46
LPP (Adagio dynamic)   34 Plusp   63                Scratch sound   11
Lpp   3                   Poisson distribution   43 Sd   3
LPPP (Adagio dynamic)   34Poisson-dist   43         Search path   1
Lppp   3                  Poke   67                 Second   62
Lpreson   38              Polyrhythm   36           Sections, Adagio   35
                          Pop   39                  Self   61
M (Adagio control)   35   Portamento switch   35    Semicolon, Adagio   35
Macroexpand   61          Power   39                Seq   24
Macroexpand-1   61        PP (Adagio dynamic)   34  Seqrep   24
Macrolet   63             PPP (Adagio dynamic)   34 Sequences   3, 33
Make-accumulate   41      Pprint   66               Sequence_example.htm   3
Make-array   62           Prcrev   22               Sequential behavior   6
Make-copier   41          Predicate Functions   63  Set   61
Make-cycle   40           Preset   34               Set intersection   47
Make-eval   41            Prin1   66                Set statement, sal   15
Make-heap   41            Princ   66                Set union   47
Make-length   41          Print   66                Set-control-srate   7, 17
Make-line   40            Print midi file   49      Set-difference   47
Make-lpanal-iterator   38 Print statement, sal   15 Set-logical-stop   24
Make-lpc-file-iterator    Probability  distributionsSet-pitch-names   17
        38                        42                Set-sound-srate   7, 17
Make-markov   41          Prod   18                 Setdir   66
Make-palindrome   40      Product   24              Setf   61
Make-product   41         Product pattern   41      Seti commnad   37
Make-random   40          Profile   64              Setq   61
Make-string-input-stream  Profiling   61            Setup nyquist   1
        67                Prog   64                 Setup-console   67
Make-string-output-stream Prog*   64                Setv command   37
        67                Prog1   64                Sf-granulate   49
Make-sum   41             Prog2   64                Sf-info   26
Make-symbol   61          Progn   64                Shape   21
Make-window   41          Program   35              Sharp   33
Maketable   18            Program change   33       Shepard tones   4, 21
Mandolin   22             Progv   64                Shift-time   18
Manipulation   of   scoresPrologic   49             Show midi file   49
        45                Property  List   FunctionsShow-lpc-data   38
Mapc   62                         62                Signal composition   27
Mapcar   62               Psetq   61                Signal multiplication   27
Mapl   62                 Pulse oscillator   19     Signal-start   16
Maplist   62              Pulse-width     modulationSignal-stop   16
Markov analysis   41              19                Sim   2, 24
Markov pattern   41       Push   39                 Simrep   24
Markov-create-rules   41  Putprop   62              Simultaneous Behavior   6
Max   65                  Pwe   20                  Sin   65
Maximum   23, 65          Pwe-list   20             Sine   19
Maximum amplitude   10, 27Pwer   20                 Siosc   19
Maximum of two sounds   27Pwer-list   20            Sitar   22
Member   62               Pwev   20                 Sixteenth note   3, 33
Memory usage   17         Pwev-list   20            Sixtyfourth note   33
MF (Adagio dynamic)   34  Pwevr   20                Slope   19
Middle C   33             Pwevr-list   20           Smooth   19
MIDI   33                 Pwl   20                  Snd-abs   26
MIDI Clock   36           Pwl-list   20             Snd-add   26
MIDI file   46            Pwlr   20                 Snd-allpoles   38
MIDI program   34         Pwlr-list   20            Snd-alpass   28
Midi-show   49            Pwlv   20                 Snd-alpasscv   28
Midi-show-file   49       Pwlv-list   20            Snd-alpassvv   28
Mikrokosmos   35          Pwlvr   20                Snd-amosc   29
Min   64                  Pwlvr-list   20           Snd-areson   28
Minimoog   50                                       Snd-aresoncv   28
Minimum   23, 64          Q  (Adagio  Quarter  note)Snd-aresonvc   28
Minusp   63                       33                Snd-aresonvv   28
Mix   24                  Q   3                     Snd-atone   28
Mix to file   25          Qd   3                    Snd-atonev   28
Snd-avg   26              Stringp   63
Snd-bandedwg   29         Sublis   62
Snd-biquad   28           Subseq   65
Snd-bowed   29            Subset   47
Snd-bowed-freq   29       Subsetp   47
Snd-buzz   29             Subst   62
Snd-chase   28            Suggestions   iii
Snd-clarinet   29         Sum pattern   41
Snd-clarinet-all   29     Sum   24
Snd-clarinet-freq   29    Surround Sound   49
Snd-clip   26             Sustain   24
Snd-compose   27          Sustain-abs   24
Snd-congen   28           Swap channels   49
Snd-const   26            Swapchannels   49
Snd-convolve   28         Symbol Functions   61
Snd-copy   27             Symbol-function   62
Snd-coterm   26           Symbol-name   62
Snd-delay   28            Symbol-plist   62
Snd-delaycv   28          Symbol-value   62
Snd-down   27             Symbolp   63
Snd-exp   27              Symbols   61
Snd-extent   16           Synchronization   36
Snd-fetch   16            System Functions   67
Snd-fetch-array   16      SystemRoot   1
Snd-fft   32
Snd-flatten   16          T (Adagio Triplet)   33
Snd-flute   29            T   33
Snd-flute-all   29        Table   21
Snd-flute-freq   29       Table memory   17
Snd-fmfb   29             Tagbody   64
Snd-fmosc   29            Tan   65
Snd-follow   27           Tap   27
Snd-from-array   16       Tapped delay   22
Snd-fromarraystream   16  Tapv   22
Snd-fromobject   16       Temp file   66
Snd-gate   27             Tempo   33, 34
Snd-ifft   32             Temporary files   66
Snd-inverse   27          Temporary    sound   files
Snd-length   16                   directory   24
Snd-log   27              Terpri   66
Snd-lpanal   38           The Format Function   66
Snd-lpreson   38          The Program Feature   64
Snd-mandolin   30         Third   62
Snd-max   27              Thirtysecond note   33
Snd-maxsamp   16          Threshold   27
Snd-maxv   27             Throw   64
Snd-modalbar   30         Time   33, 34
Snd-multiseq   30         Time shift, sal   13
Snd-normalize   27        Time Structure   24
Snd-offset   26           Time units   35
Snd-oneshot   27          Timed-seq   24
Snd-osc   29              Tone   21
Snd-overwrite   26        Top-level   64
Snd-partial   29          Touch tone   49
Snd-play   17             Trace   64
Snd-pluck   29            Transformation environment
Snd-print   17                    6
Snd-print-tree   17, 26   Transformations   6, 23
Snd-prod   27             Transpose   24
Snd-pwl   27              Transpose-abs   24
Snd-quantize   27         Triangle oscillator   19
Snd-read   26             Triangle wave   2
Snd-recip   27            Trigger   24
Snd-resample   27         Trill   37
Snd-resamplev   27        Triplet   33
Snd-reson   28            Triplet durations   3
Snd-resoncv   28          Truncate   64
Snd-resonvc   28          Tuba   4
Snd-resonvv   28          Tuning   17
Snd-samples   17          Tutorial, FM   11
Snd-save   26             Type-of   67
Snd-sax   30
Snd-sax-all   30          U   33
Snd-sax-freq   30         Uniform random   39, 65
Snd-scale   28            Union   47
Snd-seq   30              Unless   63
Snd-set-latency   18      Untrace   64
Snd-set-logical-stop   17 Unwind-protect   64
Snd-shape   28            Upper-case-p   65
Snd-sine   29             User name   66
Snd-siosc   29
Snd-sitar   30            V (Adagio Voice)   34
Snd-slider   26           Variable delay   22, 27
Snd-sqrt   26             Variable-resample function
Snd-srate   17                    27
Snd-sref   17             Vector   62
Snd-stkchorus   28        Velocity   34
Snd-stkpitshift   28      Vinal scratch   11
Snd-stkrev   29           Vocal sound   4
Snd-stop-time   17        Voice   33, 34
Snd-t0   17               Voice synthesis   21
Snd-tapf   27             Volume   35
Snd-tapv   27
Snd-time   17             W (Adagio Whole note)   33
Snd-tone   29             W   3
Snd-tonev   29            Warble   11
Snd-trigger   30          Warp   24
Snd-up   28               Warp-abs   24
Snd-white   26            Waveforms   2, 18
Snd-xform   28            Waveshaping   21
Snd-yin   28              Wavetables   2, 18
Snd-zero   26             Wd   3
Soften-clipping   48      Wg-glass-harm   22
Sort   63                 Wg-tibetan-bowl   22
Sound   18                Wg-tuned-bar   22
   accessing point   16   Wg-uniform-bar   22
   creating   from   arrayWhen   39, 63
        16                While   39
Sound    file    directoryWhole note   3, 33
        default   24      Widen   49
Sound file I/O   24       Wind sound   11
Sound file info   26      Window initialization   67
Sound from Lisp data   16 Window pattern   41
Sound-off   25            Wind_tutorial.htm   11
Sound-on   25             With statement, sal   15
Sound-srate-abs   24      Wood drum sound   4
Sound-warp   18           Workspace   46
Soundfilename   26        Write samples to file   25
Soundp   17               Write-byte   67
Sounds   16               Write-char   66
Sounds vs. Behaviors   6  Write-float   67
Span   49                 Write-int   66
Spatialization   49       Wt   3
Special command   33
Spectral     interpolationX (Adagio control)   35
        19                XLISP Command Loop   59
Speed-dial   49           XLISP Data Types   59
Splines   20              XLISP evaluator   59
Sqrt   65                 XLISP Lexical  Conventions
Square oscillator   19            59
Square root   23, 26      XLISPPATH   1
Srate   16                Xmusic   40
Sref   16
Sref-inverse   16         Y (Adagio control)   35
St   3                    Yin   23
Stacatto   24
Staccato   34             Z  (Adagio  program)   34,
Stack trace   64                  35
Standard MIDI File   46   Zerop   63
Statements, sal   13
Stats   17                ^   (Adagio    sixtyfourth
Step-to-hz   17                   note)   33
Stereo   49               ^   13
Stereo pan   49           ^=   15
Stereo panning   18
Stereo-chorus   48        |   13
Stereoize   49
STK banded waveguide   29 ~ (Adagio)   35
Stk bowed   29            ~   13
STK bowed string   22     ~=   13
STK bowed-freq   22       ~~   13
STK chorus   22, 28
Stk clarinet   22, 29
STK flute   22, 29
STK glass harmonica   22
STK jcreverb   22
STK mandolin   30
STK mandolon   22
STK modal bar   22, 30
STK nreverb   22
STK pitch shift   22, 28
STK prcreverb   22
STK reverb   29
Stk sax   22, 30
STK sitar   22, 30
STK tibetan bowl   22
STK tuned bar   22
STK uniform bar   22
Stkchorus   22
Stochastic functions   42
Strcat   65
Streamp   63
Stretch   3, 24
Stretch, sal   13
Stretch-abs   24
Stretching  Sampled Sounds
        10
String   65
String Functions   65
String  Stream   Functions
        67
String synthesis   19
String-downcase   65
String-equalp   65
String-greaterp   65
String-left-trim   65
String-lessp   65
String-not-equalp   65
String-not-greaterp   65
String-not-lessp   65
String-right-trim   65
String-search   65
String-trim   65
String-upcase   65
String/=   65
String<   65
String<=   65
String=   65
String>   65
String>=   65
                               Table of Contents

Preface                                                                     iii

1. Introduction and Overview                                                  1

   1.1. Installation                                                          1
       1.1.1. Unix Installation                                               1
       1.1.2. Win32 Installation                                              1
           1.1.2.1. What if Nyquist functions are undefined?                  1
           1.1.2.2. SystemRoot                                                1
       1.1.3. MacOS X Installation                                            2
   1.2. Using jNyqIDE                                                         2
   1.3. Using SAL                                                             2
   1.4. Helpful Hints                                                         2
   1.5. Using Lisp                                                            2
   1.6. Examples                                                              2
       1.6.1. Waveforms                                                       2
       1.6.2. Wavetables                                                      2
       1.6.3. Sequences                                                       3
       1.6.4. Envelopes                                                       3
       1.6.5. Piece-wise Linear Functions                                     3
   1.7. Predefined Constants                                                  3
   1.8. More Examples                                                         3

2. The jNyqIDE Program                                                        5

   2.1. jNyqIDE Overview                                                      5
   2.2. Command Completion                                                    5
   2.3. Browser                                                               5
   2.4. Envelope Editor                                                       5
   2.5. Equalizer Editor                                                      5

3. Behavioral Abstraction                                                     6

   3.1. The Environment                                                       6
   3.2. Sequential Behavior                                                   6
   3.3. Simultaneous Behavior                                                 6
   3.4. Sounds vs. Behaviors                                                  6
   3.5. The At Transformation                                                 7
   3.6. Nested Transformations                                                7
   3.7. Defining Behaviors                                                    7
   3.8. Sample Rates                                                          7

4. Continuous Transformations and Time Warps                                  8

   4.1. Simple Transformations                                                8
   4.2. Time Warps                                                            8
   4.3. Abstract Time Warps                                                   8
   4.4. Nested Transformations                                                9

5. More Examples                                                             10

   5.1. Stretching Sampled Sounds                                            10
   5.2. Saving Sound Files                                                   10
   5.3. Memory Space and Normalization                                       10
   5.4. Frequency Modulation                                                 10
   5.5. Building a Wavetable                                                 11
   5.6. Filter Examples                                                      11
   5.7. DSP in Lisp                                                          11

6. SAL                                                                       13

   6.1. SAL Syntax and Semantics                                             13
       6.1.1. Expressions                                                    13
           6.1.1.1. Simple Expressions                                       13
           6.1.1.2. Operators                                                13
           6.1.1.3. Function Calls                                           13
           6.1.1.4. Array Notation                                           13
           6.1.1.5. Conditional Values                                       13
       6.1.2. SAL Statements                                                 13
           6.1.2.1. begin and end                                            13
           6.1.2.2. chdir                                                    13
           6.1.2.3. define variable                                          13
           6.1.2.4. define function                                          14
           6.1.2.5. display                                                  14
           6.1.2.6. exec                                                     14
           6.1.2.7. if                                                       14
           6.1.2.8. when                                                     14
           6.1.2.9. unless                                                   14
           6.1.2.10. load                                                    14
           6.1.2.11. loop                                                    14
           6.1.2.12. print                                                   15
           6.1.2.13. return                                                  15
           6.1.2.14. set                                                     15
           6.1.2.15. with                                                    15
           6.1.2.16. exit                                                    15
   6.2. Interoperability of SAL and XLISP                                    15
       6.2.1. Function Calls                                                 15
       6.2.2. Playing Tricks On the SAL Compiler                             15

7. Nyquist Functions                                                         16

   7.1. Sounds                                                               16
       7.1.1. What is a Sound?                                               16
       7.1.2. Multichannel Sounds                                            16
       7.1.3. Accessing and Creating Sound                                   16
       7.1.4. Miscellaneous Functions                                        17
   7.2. Behaviors                                                            18
       7.2.1. Using Previously Created Sounds                                18
       7.2.2. Sound Synthesis                                                18
           7.2.2.1. Oscillators                                              19
           7.2.2.2. Piece-wise Approximations                                20
           7.2.2.3. Filter Behaviors                                         20
           7.2.2.4. Effects                                                  22
           7.2.2.5. Physical Models                                          22
           7.2.2.6. More Behaviors                                           23
   7.3. Transformations                                                      23
   7.4. Combination and Time Structure                                       24
   7.5. Sound File Input and Output                                          24
   7.6. Low-level Functions                                                  26
       7.6.1. Creating Sounds                                                26
       7.6.2. Signal Operations                                              26
       7.6.3. Filters                                                        28
       7.6.4. Table-Lookup Oscillator Functions                              29
       7.6.5. Physical Model Functions                                       29
       7.6.6. Sequence Support Functions                                     30

8. Nyquist Globals                                                           31

9. Time/Frequency Transformation                                             32

10. MIDI, Adagio, and Sequences                                              33

   10.1. Specifying Attributes                                               33
       10.1.1. Time                                                          33
       10.1.2. Pitch                                                         33
       10.1.3. Duration                                                      33
       10.1.4. Next Time                                                     33
       10.1.5. Rest                                                          33
       10.1.6. Articulation                                                  34
       10.1.7. Loudness                                                      34
       10.1.8. Voice                                                         34
       10.1.9. Timbre (MIDI Program)                                         34
       10.1.10. Tempo                                                        34
       10.1.11. Rate                                                         34
   10.2. Default Attributes                                                  34
   10.3. Examples                                                            34
   10.4. Advanced Features                                                   35
       10.4.1. Time Units and Resolution                                     35
       10.4.2. Multiple Notes Per Line                                       35
       10.4.3. Control Change Commands                                       35
       10.4.4. Multiple Tempi                                                36
       10.4.5. MIDI Synchronization                                          36
       10.4.6. System Exclusive Messages                                     36
       10.4.7. Control Ramps                                                 36
       10.4.8. The !End Command                                              37
       10.4.9. Calling C Routines                                            37
       10.4.10. Setting C Variables                                          37

11. Linear Prediction Analysis and Synthesis                                 38

   11.1. LPC Classes and Functions                                           38
   11.2. Low-level LPC Functions                                             38

12. Developing and Debugging in Nyquist                                      39

   12.1. Debugging                                                           39
   12.2. Useful Functions                                                    39

13. Xmusic and Algorithmic Composition                                       40

   13.1. Xmusic Basics                                                       40
   13.2. Pattern Classes                                                     40
       13.2.1. cycle                                                         40
       13.2.2. line                                                          40
       13.2.3. random                                                        40
       13.2.4. palindrome                                                    40
       13.2.5. heap                                                          41
       13.2.6. copier                                                        41
       13.2.7. accumulate                                                    41
       13.2.8. sum                                                           41
       13.2.9. product                                                       41
       13.2.10. eval                                                         41
       13.2.11. length                                                       41
       13.2.12. window                                                       41
       13.2.13. markov                                                       41
   13.3. Random Number Generators                                            42
   13.4. Score Generation and Manipulation                                   43
       13.4.1. Keyword Parameters                                            44
       13.4.2. Using score-gen                                               44
       13.4.3. Score Manipulation                                            45
       13.4.4. Xmusic and Standard MIDI Files                                46
       13.4.5. Workspaces                                                    46
       13.4.6. Utility Functions                                             46

14. Nyquist Libraries                                                        48

   14.1. Piano Synthesizer                                                   48
   14.2. Dymanics Compression                                                48
   14.3. Clipping Softener                                                   48
   14.4. Graphical Equalizer                                                 48
   14.5. Sound Reversal                                                      48
   14.6. Time Delay Functions                                                48
   14.7. Multiple Band Effects                                               48
   14.8. Granular Synthesis                                                  49
   14.9. MIDI Utilities                                                      49
   14.10. Reverberation                                                      49
   14.11. DTMF Encoding                                                      49
   14.12. Dolby Surround(R), Stereo and Spatialization Effects               49
   14.13. Drum Machine                                                       49
   14.14. Minimoog-inspired Synthesis                                        50
       14.14.1. Oscillator Parameters                                        50
       14.14.2. Noise Parameters                                             50
       14.14.3. Filter Parameters                                            50
       14.14.4. Amplitude Parameters                                         50
       14.14.5. Other Parameters                                             50
       14.14.6. Input Format                                                 50
       14.14.7. Sample Code/Sounds                                           51

I. Extending Nyquist                                                         52

   I.1. Translating Descriptions to C Code                                   52
   I.2. Rebuilding Nyquist                                                   52
   I.3. Accessing the New Function                                           52
   I.4. Why Translation?                                                     52
   I.5. Writing a .alg File                                                  52
   I.6. Attributes                                                           52
   I.7. Generated Names                                                      54
   I.8. Scalar Arguments                                                     54

II. Open Sound Control and Nyquist                                           55

   II.1. Sending Open Sound Control Messages                                 55
   II.2. The ser-to-osc Program                                              55

III. Intgen                                                                  56

       III.0.1. Extending Xlisp                                              56
   III.1. Header file format                                                 56
   III.2. Using #define'd macros                                             56
   III.3. Lisp Include Files                                                 57
   III.4. Example                                                            57
   III.5. More Details                                                       57

IV. XLISP: An Object-oriented Lisp                                           58

   IV.1. Introduction                                                        59
   IV.2. A Note From The Author                                              59
   IV.3. XLISP Command Loop                                                  59
   IV.4. Special Characters                                                  59
   IV.5. Break Command Loop                                                  59
   IV.6. Data Types                                                          59
   IV.7. The Evaluator                                                       59
   IV.8. Lexical Conventions                                                 59
   IV.9. Readtables                                                          60
   IV.10. Lambda Lists                                                       60
   IV.11. Objects                                                            60
   IV.12. The ``Object'' Class                                               61
   IV.13. The ``Class'' Class                                                61
   IV.14. Profiling                                                          61
   IV.15. Symbols                                                            61
   IV.16. Evaluation Functions                                               61
   IV.17. Symbol Functions                                                   61
   IV.18. Property List Functions                                            62
   IV.19. Array Functions                                                    62
   IV.20. List Functions                                                     62
   IV.21. Destructive List Functions                                         62
   IV.22. Predicate Functions                                                63
   IV.23. Control Constructs                                                 63
   IV.24. Looping Constructs                                                 64
   IV.25. The Program Feature                                                64
   IV.26. Debugging and Error Handling                                       64
   IV.27. Arithmetic Functions                                               64
   IV.28. Bitwise Logical Functions                                          65
   IV.29. String Functions                                                   65
   IV.30. Character Functions                                                65
   IV.31. Input/Output Functions                                             66
   IV.32. The Format Function                                                66
   IV.33. File I/O Functions                                                 66
   IV.34. String Stream Functions                                            67
   IV.35. System Functions                                                   67
   IV.36. File I/O Functions                                                 67
       IV.36.1. Input from a File                                            67
       IV.36.2. Output to a File                                             68
       IV.36.3. A Slightly More Complicated File Example                     68

Index                                                                        70
                                List of Figures
   Figure 1:   An envelope generated by the env function.                     3
   Figure 2:   The result of (warp4), intended to map 4 seconds of score      8
               time into 4 seconds of real time.  The function extends
               beyond 4 seconds (the dashed lines) to make sure the
               function is well-defined at location (4, 4).  Nyquist
               sounds are ordinarily open on the right.
   Figure 3:   When (warp4) is applied to (tone-seq-2), the note onsets       8
               and durations are warped.
   Figure 4:   When (warp4) is applied to (tone-seq-3), the note onsets       9
               are warped, but not the duration, which remains a constant
               0.25 seconds.  In the fast middle section, this causes
               notes to overlap.  Nyquist will sum (mix) them.
   Figure 5:   The shift-time function shifts a sound in time according to   19
               its shift argument.
   Figure 6:   Ramps generated by pwl and ramp functions.  The pwl version   23
               ramps toward the breakpoint (1, 1), but in order to ramp
               back to zero at breakpoint (1, 0), the function never
               reaches an amplitude of 1.  If used at the beginning of a
               seq construct, the next sound will begin at time 1.  The
               ramp version actually reaches breakpoint (1, 1); notice
               that it is one sample longer than the pwl version.  If used
               in a sequence, the next sound after ramp would start at
               time 1 + P, where P is the sample period.
   Figure 7:   The Linear Distribution, g = 1.                               42
   Figure 8:   The Exponential Distribution, delta = 1.                      42
   Figure 9:   The Gamma Distribution, nu = 4.                               42
   Figure 10:   The Bilateral Exponential Distribution.                      42
   Figure 11:   The Cauchy Distribution, tau = 1.                            42
   Figure 12:   The Hyperbolic Cosine Distribution.                          43
   Figure 13:   The Logistic Distribution, alpha = 1, beta = 2.              43
   Figure 14:   The Arc Sine Distribution.                                   43
   Figure 15:   The Gauss-Laplace (Gaussian) Distribution, xmu = 0, sigma    43
                = 1.
   Figure 16:   The Beta Distribution, alpha = .5, beta = .25.               43
   Figure 17:   The Bernoulli Distribution, px1 = .75.                       43
   Figure 18:   The Binomial Distribution, n = 5, p = .5.                    43
   Figure 19:   The Geometric Distribution, p = .4.                          44
   Figure 20:   The Poisson Distribution, delta = 3.                         44
   Figure 21:   System diagram for Minimoog emulator.                        50
