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<h1 id="firstHeading" class="firstHeading" lang="en">Programming in Nyquist</h1>
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<div id="siteSub">From Audacity Development Manual</div>
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<div id="jump-to-nav" class="mw-jump">Jump to: <a href="#column-one">navigation</a>, <a href="https://alphamanual.audacityteam.org/man/Programming_in_Nyquist#searchInput">search</a></div>
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<div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div id="toc" class="toc"><div id="toctitle"><h2>Contents</h2></div>
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<ul>
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<li class="toclevel-1 tocsection-1"><a href="#Programming_in_Nyquist"><span class="tocnumber">1</span> <span class="toctext">Programming in Nyquist</span></a>
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<ul>
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<li class="toclevel-2 tocsection-2"><a href="#Synthesizing"><span class="tocnumber">1.1</span> <span class="toctext">Synthesizing</span></a></li>
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<li class="toclevel-2 tocsection-3"><a href="#Combining_sounds"><span class="tocnumber">1.2</span> <span class="toctext">Combining sounds</span></a></li>
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<li class="toclevel-2 tocsection-4"><a href="#Filters"><span class="tocnumber">1.3</span> <span class="toctext">Filters</span></a></li>
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<li class="toclevel-2 tocsection-5"><a href="#Transforming_and_combining_sounds"><span class="tocnumber">1.4</span> <span class="toctext">Transforming and combining sounds</span></a></li>
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<li class="toclevel-1 tocsection-6"><a href="#Links"><span class="tocnumber">2</span> <span class="toctext">Links</span></a></li>
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<h2><span class="mw-headline" id="Programming_in_Nyquist">Programming in Nyquist</span></h2>
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<p>What makes Nyquist distinct from Lisp is that it is designed to work with sound, and has lots of built-in primitives and functions that synthesize, analyze, and manipulate sounds. Within Audacity, this makes it relatively easy to build complicated effects out of Nyquist's palette of built-in functions.
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</p><p>In Nyquist, a variable can hold a sound just as easily as it can hold a number or a string. There are a lot of functions provided that allow you to stretch, distort, and combine sounds very efficiently. It is even possible to "rip apart" a sound and access its individual samples, but that is beyond the scope of this tutorial.
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</p><p>To try out a Nyquist expression in Audacity, you can use <a href="nyquist_prompt.html" title="Nyquist Prompt">Nyquist Prompt</a> in the Effect menu. Whatever audio you have selected will be in the variable <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">*track*</span>, and the selection will be replaced with the result of the Nyquist expression you enter. In Part 3: <a href="creating_nyquist_plug_ins.html" title="Creating Nyquist Plug-ins">Creating Nyquist Plugins</a>, you will learn how to create a plugin effect using Nyquist.
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</p>
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<h3><span class="mw-headline" id="Synthesizing">Synthesizing</span></h3>
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<p>The following functions all create new sounds. You can use them to create "generate" plugin effects, or you can combine these synthesized sounds with selected audio to produce interesting effects.
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</p><p><br />
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</p>
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<table style="border-spacing:0; width: 50em;">
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<td style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(noise)</b>
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</td>
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<td style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Generates white noise
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(const value [duration])</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Generates a constant (silent) signal
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(sine pitch [duration])</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Generates a sine wave at an indicated pitch and duration.The pitch is a MIDI note number, with 60 for middle C.
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(hzosc hz)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Generates a sine wave at a particular frequency in Hz.
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(osc-saw hz)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Generates a sawtooth wave at a particular frequency in Hz.
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(osc-tri hz)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Generates a triangle wave at a particular frequency in Hz.
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(osc-pulse hz bias)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;">
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</td></tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(pluck pitch)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;">
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</td></tr></table>
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<p><b>Envelopes</b>
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</p><p>Nyquist has support for envelopes. By applying an envelope to a sound, you can control the overall shape of its amplitude. One of the easiest ways to construct an envelope is with the <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">env</span> function, which takes 7 parameters that are commonly used for shaping synthesized musical notes: attack time, decay time, release time, attack level, decay level, sustain level, and overall duration.See the figure below:
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</p><p><a href="https://alphamanual.audacityteam.org/man/File:Nyquist-envelope.gif" class="image"><img alt="Nyquist-envelope.gif" src="../m/images/d/d9/nyquist_envelope.gif" width="467" height="200" /></a>
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</p><p>To apply an envelope to a sound, just use the <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">mult</span> function. So if <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">*track*</span> is the sound, then this is the sound with a simple envelope applied to it:
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</p>
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<pre> (mult *track* (env 0.1 0.1 0.2 1.0 0.5 0.3 1.0))
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</pre>
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<p>One of the most general type of envelope is a piece-wise linear function, which can be constructed with the <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">pwl</span> function. 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 time is not implicit. For example:
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</p>
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<pre> ; symmetric rise to 0.7 (at time 1) and fall back to 0 (at time 2):
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(pwl 1.0 0.7 2.0)
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</pre>
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<h3><span class="mw-headline" id="Combining_sounds">Combining sounds</span></h3>
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<p>Besides multiplying two sounds with the <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">mult</span> function, you can add two sounds (or envelopes) with the <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">add</span> function.
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</p>
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<h3><span class="mw-headline" id="Filters">Filters</span></h3>
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<p>Nyquist comes with a number of common filters built-in. Here are some of the more common ones:
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</p><p><br />
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</p>
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<table style="border-spacing:0; width: 50em;">
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<td style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(lp sound cut-off)</b>
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</td>
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<td style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;">
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(hp sound cut-off)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> High-pass filter (first-order Butterworth). Cut-off may be a float or a signal (for time-varying filtering) and expresses hertz.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(comb sound hz decay)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Applies a comb filter to sound, which emphasizes (resonates at) frequencies that are multiples of a Hz.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(alpass sound decay hz)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> All-pass filter, creating a delay effect without the resonances of a comb filter.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(notch2 sound hz)</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;">
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</td></tr></table>
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<h3><span class="mw-headline" id="Transforming_and_combining_sounds">Transforming and combining sounds</span></h3>
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<p>It is beyond the scope of this introductory tutorial to explain all of the ways that a sound can be transformed in Nyquist. These functions do not modify sounds directly, but instead modify the Nyquist <i>environment</i>. In order for these changes to affect sounds, you must use the <span style="line-height:1.1em;letter-spacing:-0.04em;background-color:#FDEEF4;padding:3px;font-family:monospace;font-size:1.1em;border:1px dashed black">cue</span> function.
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</p><p><br />
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</p>
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<table style="border-spacing:0; width: 50em;">
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<tr>
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<td style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(stretch factor (cue sound))</b>
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</td>
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<td style="border-top:0.05pt solid #000000;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Changes the length of the sound being cued by the given factor.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(scale factor (cue sound))</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Scales the amplitude of the sound being cued by the given factor.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(loud dB (cue sound))</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Increases or decreases the volume of the sound being cued by the given number of decibels.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(at t (cue sound))</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Starts the given sound at a particular time in seconds. This cannot be used to add silence at the beginning or end, but it can be used when combining two or more sounds.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(seq (cue s1) (cue s2))</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Creates a sequence of sound s1 followed by sound s2.
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</td></tr>
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<tr>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:0.05pt solid #000000;border-right:none;padding:0.049cm;"> <b>(sim (cue s1) (cue s2))</b>
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</td>
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<td style="border-top:none;border-bottom:0.05pt solid #000000;border-left:none;border-right:0.05pt solid #000000;padding:0.049cm;"> Combines two sounds so that they are played simultaneously.
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</td></tr></table>
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<h2><span class="mw-headline" id="Links">Links</span></h2>
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<p><a href="creating_nyquist_plug_ins.html" title="Creating Nyquist Plug-ins"><b>></b>  Creating Nyquist Plugins</a> <br />
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</p><p><a href="introduction_to_nyquist_and_lisp_programming.html" title="Introduction to Nyquist and Lisp Programming"><b><</b>  Introduction to Nyquist and Lisp Programming</a> <br />
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</p><p><a href="nyquist.html" title="Nyquist"><b>|<</b> Nyquist</a>
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</p>
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<div align="center"><ul id="f_list"><li>This version created on 2025-12-04 - <a href="https://alphamanual.audacityteam.org/man/Programming_in_Nyquist">Check current version of this page (development Manual)</a></li></ul></div>
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