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<h2>
<span class="refentrytitle">GEN09</span>
</h2>
<p>GEN09 —
Generate composite waveforms made up of weighted sums of simple sinusoids.
</p>
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<div class="refsect1">
<a id="idm281472820138248"></a>
<h2>Description</h2>
<p>
These subroutines generate composite waveforms made up of weighted sums of simple sinusoids. The specification of each contributing partial requires 3 p-fields using <span class="emphasis"><em>GEN09</em></span>.
</p>
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<div class="refsect1">
<a id="idm281472820063800"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 9 pna stra phsa pnb strb phsb ...</pre>
</div>
<div class="refsect1">
<a id="idm281472820061720"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>size</em></span> -- number of points in the table. Must be a power of 2 or power-of-2 plus 1 (see <a class="link" href="f.html" title="f Statement (or Function Table Statement)"><em class="citetitle">f statement</em></a>).
</p>
<p>
<span class="emphasis"><em>pna, pnb</em></span>, etc. -- partial no. (relative to a fundamental that would occupy <span class="emphasis"><em>size</em></span> locations per cycle) of sinusoid a, sinusoid b, etc. Must be positive, but need not be a whole number, i.e., non-harmonic partials are permitted. Partials may be in any order.
</p>
<p>
<span class="emphasis"><em>stra, strb</em></span>, etc. -- strength of partials <span class="emphasis"><em>pna, pnb</em></span>, etc. These are relative strengths, since the composite waveform may be rescaled later. Negative values are permitted and imply a 180 degree phase shift.
</p>
<p>
<span class="emphasis"><em>phsa, phsb</em></span>, etc. -- initial phase of partials <span class="emphasis"><em>pna, pnb,</em></span> etc., expressed in degrees (0-360).
</p>
<div class="note" style="margin-left: 0.5in; margin-right: 0.5in;">
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<th align="left">Note</th>
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<p>
</p>
<div class="itemizedlist">
<ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<p>
These subroutines generate stored functions as sums of sinusoids of different frequencies. The two major restrictions on <span class="emphasis"><em>GEN10</em></span> that the partials be harmonic and in phase do not apply to <span class="emphasis"><em>GEN09</em></span> or <span class="emphasis"><em>GEN19</em></span>.
</p>
<p>
In each case the composite wave, once drawn, is then rescaled to unity if p4 was positive. A negative p4 will cause rescaling to be skipped.
</p>
</li>
</ul>
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</p>
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<div class="refsect1">
<a id="idm281472820049800"></a>
<h2>Examples</h2>
<p>
Here is an example of the GEN09 routine. It uses the files <a class="ulink" href="examples/gen09.csd" target="_top"><em class="citetitle">gen09.csd</em></a>.
</p>
<div class="example">
<a id="idm281472820047944"></a>
<p class="title">
<strong>Example 1190. Example of the GEN09 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="idm281472682579736"></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 gen09.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>
gi<span class="n">1</span> <span class="nb">ftgen</span> <span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="o">^</span><span class="mi">10</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span><span class="mf">0.333</span><span class="p">,</span><span class="mi">180</span> <span class="c1">;an approximation of a square wave</span>
gi<span class="n">2</span> <span class="nb">ftgen</span> <span class="mi">2</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="o">^</span><span class="mi">10</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">180</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span><span class="mf">0.333</span><span class="p">,</span><span class="mi">0</span> <span class="c1">;same values as gi1, except some phase values</span>
gi<span class="n">3</span> <span class="nb">ftgen</span> <span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="o">^</span><span class="mi">10</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">2.2</span><span class="p">,</span> <span class="mf">.5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">3.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span> <span class="c1">;inharmonic, but does not sound well --> wave does not end at same point as where it begins --> artefacts</span>
gi<span class="n">4</span> <span class="nb">ftgen</span> <span class="mi">4</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="o">^</span><span class="mi">10</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mf">.4</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">22</span><span class="p">,</span> <span class="mf">.5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">38</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span> <span class="c1">;the same proportions, but value of partial number is multiplied 10 times -->the sound is much clearer,</span>
<span class="c1">;because the sudden "jump" like the one in gi3 will pop up only once in 10 repetitions</span>
<span class="kd">instr</span> <span class="nf">1</span>
k<span class="n">amp</span> <span class="o">=</span> <span class="mf">.6</span>
k<span class="n">cps</span> <span class="o">=</span> <span class="mi">220</span>
i<span class="n">fn</span> <span class="o">=</span> <span class="nb">p4</span>
a<span class="n">sig</span> <span class="nb">poscil</span> k<span class="n">amp</span><span class="p">,</span> k<span class="n">cps</span><span class="o">*</span><span class="nb">p5</span><span class="p">,</span> i<span class="n">fn</span>
<span class="nb">outs</span> a<span class="n">sig</span><span class="p">,</span>a<span class="n">sig</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">1</span> <span class="c1">;subtle difference between table 1 and 2</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">2</span> <span class="mi">1</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">7</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span> <span class="c1">;big difference between table 3 and 4</span>
<span class="nb">i</span> <span class="mi">1</span> <span class="mi">10</span> <span class="mi">2</span> <span class="mi">4</span> <span class="mf">.1</span> <span class="c1">;p5 has to compensate for the 10 repetitions of gi4 as opposed to gi3 to get the same pitch</span>
<span class="nb">e</span>
<span class="nt"></CsScore></span>
<span class="nt"></CsoundSynthesizer></span>
</pre>
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<p><br class="example-break" />
<span class="phrase">These are the diagrams of the waveforms of the GEN09 routines, as used in the example:</span>
</p>
<div class="mediaobject">
<img src="images/gen09_1.png" alt="gi1 ftgen 1,0,2^10,9, 1,3,0, 3,1,0, 9,0.333,180 - approximation of a square wave" />
<div class="caption">
<p>gi1 ftgen 1,0,2^10,9, 1,3,0, 3,1,0, 9,0.333,180 - approximation of a square wave</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen09_2.png" alt="gi2 ftgen 2,0,2^10,9, 1,3,180, 3,1,0, 9,0.333,0 - same values as gi1, except phase value" />
<div class="caption">
<p>gi2 ftgen 2,0,2^10,9, 1,3,180, 3,1,0, 9,0.333,0 - same values as gi1, except phase value</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen09_3.png" alt="gi3 ftgen 3,0,2^10,9, 1,2,0, 3,2,0, 9,0.333,180 - inharmonic partials, but with distortion due to the sudden jump in ending and beginning of the wave" />
<div class="caption">
<p>gi3 ftgen 3,0,2^10,9, 1,2,0, 3,2,0, 9,0.333,180 - inharmonic partials, but with distortion due to the sudden jump in ending and beginning of the wave</p>
</div>
</div>
<p>
</p>
<div class="mediaobject">
<img src="images/gen09_4.png" alt="gi4 ftgen 4,0,2^10,9, 1,2,180, 3,2,0, 9,0.333,0 - same ratio as gi3, except with less artefacts" />
<div class="caption">
<p>gi4 ftgen 4,0,2^10,9, 1,2,180, 3,2,0, 9,0.333,0 - same ratio as gi3, except with less artefacts</p>
</div>
</div>
<p>
</p>
</div>
<div class="refsect1">
<a id="idm281472820029096"></a>
<h2>See Also</h2>
<p>
<a class="link" href="GEN10.html" title="GEN10"><em class="citetitle">GEN10</em></a>,
<a class="link" href="GEN19.html" title="GEN19"><em class="citetitle">GEN19</em></a>
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