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<h2>
<span class="refentrytitle">GEN21</span>
</h2>
<p>GEN21 —
Generates tables of different random distributions.
</p>
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<div class="refsect1">
<a id="idm281472819090600"></a>
<h2>Description</h2>
<p>
This generates tables of different random distributions. (See also <a class="link" href="betarand.html" title="betarand"><em class="citetitle">betarand</em></a>, <a class="link" href="bexprnd.html" title="bexprnd"><em class="citetitle">bexprnd</em></a>, <a class="link" href="cauchy.html" title="cauchy"><em class="citetitle">cauchy</em></a>, <a class="link" href="exprand.html" title="exprand"><em class="citetitle">exprand</em></a>, <a class="link" href="gauss.html" title="gauss"><em class="citetitle">gauss</em></a>, <a class="link" href="linrand.html" title="linrand"><em class="citetitle">linrand</em></a>, <a class="link" href="pcauchy.html" title="pcauchy"><em class="citetitle">pcauchy</em></a>, <a class="link" href="poisson.html" title="poisson"><em class="citetitle">poisson</em></a>, <a class="link" href="trirand.html" title="trirand"><em class="citetitle">trirand</em></a>, <a class="link" href="unirand.html" title="unirand"><em class="citetitle">unirand</em></a>, and <a class="link" href="weibull.html" title="weibull"><em class="citetitle">weibull</em></a>)
</p>
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<div class="refsect1">
<a id="idm281472819036744"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 21 type level [arg1 [arg2]]</pre>
</div>
<div class="refsect1">
<a id="idm281472819034696"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>time</em></span> and <span class="emphasis"><em>size</em></span> are the usual GEN function arguments. <span class="emphasis"><em>level</em></span> defines the amplitude. Note that GEN21 is not self-normalizing as are most other GEN functions. <span class="emphasis"><em>type</em></span> defines the distribution to be used as follow:
</p>
<div class="itemizedlist">
<ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<p>1 = Uniform (positive numbers only)</p>
</li>
<li class="listitem">
<p>2 = Linear (positive numbers only)</p>
</li>
<li class="listitem">
<p>3 = Triangular (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>4 = Exponential (positive numbers only)</p>
</li>
<li class="listitem">
<p>5 = Biexponential (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>6 = Gaussian (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>7 = Cauchy (positive and negative numbers)</p>
</li>
<li class="listitem">
<p>8 = Positive Cauchy (positive numbers only)</p>
</li>
<li class="listitem">
<p>9 = Beta (positive numbers only)</p>
</li>
<li class="listitem">
<p>10 = Weibull (positive numbers only)</p>
</li>
<li class="listitem">
<p>11 = Poisson (positive numbers only)</p>
</li>
</ul>
</div>
<p>
Of all these cases only 9 (Beta) and 10 (Weibull) need extra arguments. Beta needs two arguments and Weibull one.
</p>
<p>
If <span class="emphasis"><em>type</em></span> = 6, the random numbers in the ftable follow a normal distribution centered
around 0.0 (mu = 0.0) with a variance (sigma) of <span class="emphasis"><em>level</em></span> / 3.83. Thus more than 99.99%
of the random values generated are in the range -<span class="emphasis"><em>level</em></span> to +<span class="emphasis"><em>level</em></span>.
The default value for <span class="emphasis"><em>level</em></span> is 1 (sigma = 0.261).
If a mean value different of 0.0 is desired, this mean value has to be added to the generated numbers.
</p>
</div>
<div class="refsect1">
<a id="idm281472819019032"></a>
<h2>Examples</h2>
<p>
</p>
<div class="informalexample">
<pre class="programlisting">
<span class="stamnt">f</span>1 0 1024 21 1 <span class="comment">; Uniform (white noise)</span>
<span class="stamnt">f</span>1 0 1024 21 6 <span class="comment">; Gaussian (mu=0.0, sigma=1/3.83=0.261)</span>
<span class="stamnt">f</span>1 0 1024 21 6 5.745 <span class="comment">; Gaussian (mu=0.0, sigma=5.745/3.83=1.5)</span>
<span class="stamnt">f</span>1 0 1024 21 9 1 1 2 <span class="comment">; Beta (note that level precedes arguments)</span>
<span class="stamnt">f</span>1 0 1024 21 10 1 2 <span class="comment">; Weibull</span></pre>
</div>
<p>
All of the above additions were designed by the author between May and December 1994, under the supervision of Dr. Richard Boulanger.
</p>
<p>
Here is a complete example of the GEN21 routine. It uses the file <a class="ulink" href="examples/gen21.csd" target="_top"><em class="citetitle">gen21.csd</em></a>.
</p>
<div class="example">
<a id="idm281472819008744"></a>
<p class="title">
<strong>Example 1202. Example of the GEN21 routine.</strong>
</p>
<div class="example-contents">
<p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
<div class="refsect1">
<a id="idm281472680447560"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
<span class="c1">; Select audio/midi flags here according to platform</span>
-odac <span class="c1">;;;realtime audio out</span>
<span class="c1">;-iadc ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="c1">; For Non-realtime ouput leave only the line below:</span>
<span class="c1">; -o gen21.wav -W ;;; for file output any platform</span>
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="vg">sr</span> <span class="o">=</span> <span class="mi">44100</span>
<span class="vg">ksmps</span> <span class="o">=</span> <span class="mi">32</span>
<span class="vg">nchnls</span> <span class="o">=</span> <span class="mi">2</span>
<span class="vg">0dbfs</span> <span class="o">=</span> <span class="mi">1</span>
<span class="kd">instr</span> <span class="nf">1</span>
i<span class="n">fn</span> <span class="o">=</span> <span class="nb">p4</span>
i<span class="n">size</span> <span class="o">=</span> <span class="nb">ftlen</span><span class="p">(</span>i<span class="n">fn</span><span class="p">)</span>
<span class="nb">prints</span> <span class="s">"TABLE NUMBER: </span><span class="si">%d</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> i<span class="n">fn</span>
<span class="nb">prints</span> <span class="s">"Index</span><span class="se">\t</span><span class="s">Value</span><span class="se">\n</span><span class="s">"</span>
i<span class="n">index</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1">;start loop</span>
<span class="nl">begin_loop</span><span class="p">:</span>
i<span class="n">value</span> <span class="nb">tab_i</span> i<span class="n">index</span><span class="p">,</span> i<span class="n">fn</span>
<span class="nb">prints</span> <span class="s">"</span><span class="si">%d</span><span class="s">:</span><span class="se">\t</span><span class="s">%f</span><span class="se">\n</span><span class="s">"</span><span class="p">,</span> i<span class="n">index</span><span class="p">,</span> i<span class="n">value</span>
i<span class="n">index</span> <span class="o">=</span> i<span class="n">index</span> <span class="o">+</span> <span class="mi">1</span>
<span class="k">if</span> <span class="p">(</span>i<span class="n">index</span> <span class="o"><</span> i<span class="n">size</span><span class="p">)</span> <span class="k">igoto</span> <span class="nl">begin_loop</span>
<span class="c1">;produce sound - and repeat it 10 times so you can hear the patterns: </span>
a<span class="n">phase</span> <span class="nb">phasor</span> <span class="mi">10</span><span class="o">/</span><span class="mi">10</span> <span class="c1">;play all 32 values 10x over 10 seconds</span>
a<span class="n">phase</span> <span class="o">=</span> a<span class="n">phase</span><span class="o">*</span>i<span class="n">size</span> <span class="c1">;step through table</span>
a<span class="n">frq</span> <span class="nb">table</span> a<span class="n">phase</span><span class="p">,</span> <span class="nb">p4</span> <span class="c1">;read table number</span>
a<span class="n">sig</span> <span class="nb">poscil</span> <span class="mf">.5</span><span class="p">,</span> <span class="p">(</span>a<span class="n">frq</span><span class="o">*</span><span class="mi">500</span><span class="p">)</span><span class="o">+</span><span class="mi">1000</span><span class="p">,</span><span class="mi">10</span> <span class="c1">;scale values of table 500 times, add 1000 Hz</span>
<span class="nb">outs</span> a<span class="n">sig</span> <span class="p">,</span> a<span class="n">sig</span> <span class="c1">;so we can distinguish the different tables </span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="nb">f</span><span class="mi">1</span> <span class="mi">0</span> <span class="mi">32</span> <span class="mi">21</span> <span class="mi">1</span> <span class="c1">;Uniform (white noise)</span>
<span class="nb">f</span><span class="mi">2</span> <span class="mi">0</span> <span class="mi">32</span> <span class="mi">21</span> <span class="mi">6</span> <span class="c1">;Gaussian (mu=0.0, sigma=1/3.83=0.261)</span>
<span class="nb">f</span><span class="mi">3</span> <span class="mi">0</span> <span class="mi">32</span> <span class="mi">21</span> <span class="mi">6</span> <span class="mf">5.745</span> <span class="c1">;Gaussian (mu=0.0, sigma=5.745/3.83=1.5)</span>
<span class="nb">f</span><span class="mi">4</span> <span class="mi">0</span> <span class="mi">32</span> <span class="mi">21</span> <span class="mi">9</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">2</span> <span class="c1">;Beta (note that level precedes arguments)</span>
<span class="nb">f</span><span class="mi">5</span> <span class="mi">0</span> <span class="mi">32</span> <span class="mi">21</span> <span class="mi">10</span> <span class="mi">1</span> <span class="mi">2</span> <span class="c1">;Weibull</span>
<span class="nb">f</span><span class="mi">10</span> <span class="mi">0</span> <span class="mi">8192</span> <span class="mi">10</span> <span class="mi">1</span> <span class="c1">;Sine wave</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">10</span> <span class="mi">1</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">11</span> <span class="mi">10</span> <span class="mi">2</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">22</span> <span class="mi">10</span> <span class="mi">3</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">33</span> <span class="mi">10</span> <span class="mi">4</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">44</span> <span class="mi">10</span> <span class="mi">5</span>
<span class="nb">e</span>
<span class="nt"></CsScore></span>
<span class="nt"></CsoundSynthesizer></span>
</pre>
</div>
</div>
</div>
<p><br class="example-break" />
<span class="phrase">These are the diagrams of the waveforms of the GEN21 routines, as used in the example:</span>
</p>
<div class="mediaobject">
<img src="images/gen21_1.png" alt="f 1 0 32 21 1 - positive numbers only" />
<div class="caption">
<p>f 1 0 32 21 1 - positive numbers only</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_2.png" alt="f 2 0 32 21 6" />
<div class="caption">
<p>f 2 0 32 21 6</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_3.png" alt="f 3 0 32 21 6 5.745" />
<div class="caption">
<p>f 3 0 32 21 6 5.745</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_4.png" alt="f 4 0 32 21 9 1 1 2 - positive numbers only" />
<div class="caption">
<p>f 4 0 32 21 9 1 1 2 - positive numbers only</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen21_5.png" alt="f 5 0 32 21 10 1 2 - positive numbers only" />
<div class="caption">
<p>f 5 0 32 21 10 1 2 - positive numbers only</p>
</div>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472818987816"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Paris Smaragdis</td>
</tr>
<tr>
<td>MIT, Cambridge</td>
</tr>
<tr>
<td>1995</td>
</tr>
</table>
<p>
</p>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: John ffitch</td>
</tr>
<tr>
<td>University of Bath/Codemist Ltd.</td>
</tr>
<tr>
<td>Bath, UK</td>
</tr>
</table>
<p>
</p>
<p>Precisions about mu and sigma added by François Pinot after a discussion with
Joachim Heintz on the Csound List, December 2010.</p>
<p>New in Csound version 3.2</p>
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