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<div class="refentry" title="GEN06">
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<h2>
<span class="refentrytitle">GEN06</span>
</h2>
<p>GEN06 —
Generates a function comprised of segments of cubic polynomials.
</p>
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<div class="refsect1" title="Description">
<a id="id3730904"></a>
<h2>Description</h2>
<p>
This subroutine will generate a function comprised of segments of cubic polynomials, spanning specified points just three at a time.
</p>
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<div class="refsect1" title="Syntax">
<a id="id3730919"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # time size 6 a n1 b n2 c n3 d ...</pre>
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<div class="refsect1" title="Initialization">
<a id="id3731128"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>size</em></span> -- number of points in the table. Must be a power off 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>a, c, e, ...</em></span> -- local maxima or minima of successive segments, depending on the relation of these points to adjacent inflexions. May be either positive or negative.
</p>
<p>
<span class="emphasis"><em>b, d, f, ...</em></span> -- ordinate values of points of inflexion at the ends of successive curved segments. May be positive or negative.
</p>
<p>
<span class="emphasis"><em>n1, n2, n3 ...</em></span> -- number of stored values between specified points. Cannot be negative, but a zero is meaningful for specifying discontinuities. The sum <span class="emphasis"><em>n1</em></span> + <span class="emphasis"><em>n2</em></span> + ... will normally equal size for fully specified functions. (for details, see <a class="link" href="GEN05.html" title="GEN05"><em class="citetitle">GEN05</em></a>).
</p>
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<th align="left">Note</th>
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<p>
<span class="emphasis"><em>GEN06</em></span> constructs a stored function from segments of cubic polynomial functions. Segments link ordinate values in groups of 3: point of inflexion, maximum/minimum, point of inflexion. The first complete segment encompasses <span class="emphasis"><em>b</em></span>, <span class="emphasis"><em>c</em></span>, <span class="emphasis"><em>d</em></span> and has length <span class="emphasis"><em>n2</em></span> + <span class="emphasis"><em>n3</em></span>, the next encompasses <span class="emphasis"><em>d</em></span>, <span class="emphasis"><em>e</em></span>, <span class="emphasis"><em>f</em></span> and has length <span class="emphasis"><em>n4</em></span> + <span class="emphasis"><em>n5</em></span>, etc. The first segment (<span class="emphasis"><em>a</em></span>, <span class="emphasis"><em>b</em></span> with length <span class="emphasis"><em>n1</em></span>) is partial with only one inflexion; the last segment may be partial too. Although the inflexion points <span class="emphasis"><em>b</em></span>, <span class="emphasis"><em>d</em></span>, <span class="emphasis"><em>f</em></span> ... each figure in two segments (to the left and right), the slope of the two segments remains independent at that common point (i.e. the 1st derivative will likely be discontinuous). When <span class="emphasis"><em>a</em></span>, <span class="emphasis"><em>c</em></span>, <span class="emphasis"><em>e</em></span>... are alternately maximum and minimum, the inflexion joins will be relatively smooth; for successive maxima or successive minima the inflexions will be comb-like.
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<div class="refsect1" title="Examples">
<a id="id3731904"></a>
<h2>Examples</h2>
<p>
Here is a simple example of the GEN06 routine. It uses the files <a class="ulink" href="examples/gen06.csd" target="_top"><em class="citetitle">gen06.csd</em></a>. It creates a curve running 0 to 1 to -1, with a minimum, maximum and minimum at these values respectively. Inflexions are at .5 and 0 and are relatively smooth. Here is its diagram:
</p>
<div class="mediaobject">
<img src="images/gen06.png" alt="Diagram of the waveform generated by GEN06." />
<div class="caption">
<p>Diagram of the waveform generated by GEN06.</p>
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</div>
<p>
</p>
<div class="example">
<a id="id3731955"></a>
<p class="title">
<b>Example 737. A simple example of the GEN06 routine.</b>
</p>
<div class="example-contents">
<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 gen06.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
kval <span class="opc">table</span> kndx, ifn, ixmode
<span class="comment">; Generate a sine waveform, use our Table #1 value to </span>
<span class="comment">; vary its frequency by 100 Hz from its base frequency.</span>
ibasefreq <span class="op">=</span> 440
kfreq <span class="op">=</span> kval <span class="op">*</span> 100
a1 <span class="opc">oscil</span> 20000, ibasefreq <span class="op">+</span> kfreq, 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 curve (using GEN06).</span>
<span class="stamnt">f</span> 1 0 65 6 0 16 0.5 16 1 16 0 16 -1
<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="See Also">
<a id="id3731972"></a>
<h2>See Also</h2>
<p>
<a class="link" href="GEN05.html" title="GEN05"><em class="citetitle">GEN05</em></a>,
<a class="link" href="GEN07.html" title="GEN07"><em class="citetitle">GEN07</em></a>, and
<a class="link" href="GEN08.html" title="GEN08"><em class="citetitle">GEN08</em></a>
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