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<div class="refentry" title="GEN12">
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<h2>
<span class="refentrytitle">GEN12</span>
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<p>GEN12 —
Generates the log of a modified Bessel function of the second kind.
</p>
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<div class="refsect1" title="Description">
<a id="id3734729"></a>
<h2>Description</h2>
<p>
This generates the log of a modified Bessel function of the second kind, order 0, suitable for use in amplitude-modulated FM.
</p>
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<div class="refsect1" title="Syntax">
<a id="id3734744"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 12 xint</pre>
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<div class="refsect1" title="Initialization">
<a id="id3735598"></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 a 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>). The normal value is power-of-2 plus 1.
</p>
<p>
<span class="emphasis"><em>xint</em></span> -- specifies the <span class="emphasis"><em>x</em></span> interval [0 to <span class="emphasis"><em>+xint</em></span>] over which the function is defined.
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<th align="left">Note</th>
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<p>
</p>
<div class="itemizedlist">
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<p>
This subroutine draws the natural log of a modified Bessel function of the second kind, order 0 (commonly written as <span class="emphasis"><em>I</em></span> subscript 0), over the x-interval requested. The call should have rescaling inhibited.
</p>
</li>
<li class="listitem">
<p>
The function is useful as an amplitude scaling factor in cycle-synchronous amplitude-modulated FM. (See Palamin & Palamin, <span class="emphasis"><em>J. Audio Eng. Soc., 36/9</em></span>, Sept. 1988, pp.671-684.) The algorithm is interesting because it permits the normally symmetric FM spectrum to be made asymmetric around a frequency other than the carrier, and is thereby useful for formant positioning. By using a table lookup index of <span class="emphasis"><em>I</em></span>(r - 1/r), where <span class="emphasis"><em>I</em></span> is the FM modulation index and <span class="emphasis"><em>r</em></span> is an exponential parameter affecting partial strengths, the Palamin algorithm becomes relatively efficient, requiring only oscil's, table lookups, and a single <span class="emphasis"><em>exp</em></span> call.
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<div class="refsect1" title="Examples">
<a id="id3735704"></a>
<h2>Examples</h2>
<p>
Here is a simple example of the GEN12 routine. It uses the file <a class="ulink" href="examples/gen12.csd" target="_top"><em class="citetitle">gen12.csd</em></a>. It generates the function <span class="emphasis"><em>ln</em></span>(<span class="emphasis"><em>I<sub>0</sub></em></span>(<span class="emphasis"><em>x</em></span>)) from 0 to 20. Here is its diagram:
</p>
<div class="mediaobject">
<img src="images/gen12.png" alt="Diagram of the waveform generated by GEN12." />
<div class="caption">
<p>Diagram of the waveform generated by GEN12.</p>
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<p>
</p>
<div class="example">
<a id="id3735763"></a>
<p class="title">
<b>Example 744. A simple example of the GEN12 routine.</b>
</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>
<pre class="programlisting">
<span class="csdtag"><CsoundSynthesizer></span>
<span class="csdtag"><CsOptions></span>
<span class="comment">; Select audio/midi flags here according to platform</span>
<span class="comment">; Audio out Audio in</span>
-odac -iadc <span class="comment">;;;RT audio I/O</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o gen12.wav -W ;;; for file output any platform</span>
<span class="csdtag"></CsOptions></span>
<span class="csdtag"><CsInstruments></span>
<span class="comment">; Initialize the global variables.</span>
<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">kr</span> <span class="op">=</span> 4410
<span class="ohdr">ksmps</span> <span class="op">=</span> 10
<span class="ohdr">nchnls</span> <span class="op">=</span> 1
<span class="comment">; Instrument #1.</span>
<span class="oblock">instr</span> 1
<span class="comment">; Create an index over the length of our entire note.</span>
kcps <span class="opc">init</span> 1<span class="op">/</span>p3
kndx <span class="opc">phasor</span> kcps
<span class="comment">; Read Table #1 with our index.</span>
ifn <span class="op">=</span> 1
ixmode <span class="op">=</span> 1
kamp <span class="opc">tablei</span> kndx, ifn, ixmode
<span class="comment">; Create a sine wave, use the Table #1 values to control</span>
<span class="comment">; the amplitude. This creates a sound with a long attack.</span>
a1 <span class="opc">oscil</span> kamp<span class="op">*</span>30000, 440, 2
<span class="opc">out</span> a1
<span class="oblock">endin</span>
<span class="csdtag"></CsInstruments></span>
<span class="csdtag"><CsScore></span>
<span class="comment">; Table #1: a modified Bessel function (using GEN12).</span>
<span class="stamnt">f</span> 1 0 2049 12 20
<span class="comment">; Table #2, a sine wave.</span>
<span class="stamnt">f</span> 2 0 16384 10 1
<span class="comment">; Play Instrument #1 for 2 seconds.</span>
<span class="stamnt">i</span> 1 0 2
<span class="stamnt">e</span>
<span class="csdtag"></CsScore></span>
<span class="csdtag"></CsoundSynthesizer></span>
</pre>
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<p><br class="example-break" />
</p>
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<div class="refsect1" title="Credits">
<a id="id3735802"></a>
<h2>Credits</h2>
<p>Example written by Kevin Conder</p>
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