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<div class="refentry">
<a id="squinewave"></a>
<div class="titlepage"></div>
<a id="IndexSquinewave" class="indexterm"></a>
<div class="refnamediv">
<h2>
<span class="refentrytitle">squinewave</span>
</h2>
<p>squinewave —
A mostly bandlimited shape-shifting square-pulse-saw-sinewave oscillator with hardsync.
</p>
</div>
<div class="refsect1">
<a id="idm281472885809528"></a>
<h2>Description</h2>
<p>
This oscillator generates a variable shape waveform that can morph freely between classical shapes sine, square, pulse and saw.
The shape is controlled by two interacting values: clip (squareness) and "skew" (symmetry).
All shapes use a minimum number of samples per transition (ie, the sharp end of a saw or a pulse uses minimum N samples), this makes output bandlimited.
At higher frequency, the minimum sweep rate takes over, so over a certain pitch all shapes "degrade" to sinewave. The minimum sweep rate is i-time configurable.
Hardsync (a very quick sweep to phase=0) is supported, and a sync signal is output once per cycle.
</p>
</div>
<div class="refsect1">
<a id="idm281472885806232"></a>
<h2>Syntax</h2>
<pre class="synopsis">aout [, asyncout] <span class="command"><strong>squinewave</strong></span> acps, aClip, aSkew [, asyncin] [, iMinSweep] [, iphase]</pre>
</div>
<div class="refsect1">
<a id="idm281472885804056"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>iMinSweep</em></span> (optional) -- Range 4 and up. Sample count of the shortest square/pulse edges. Default: sr/3000 (mostly alias-free).
</p>
<p>
<span class="emphasis"><em>iphase</em></span> (optional, default=-1) -- initial phase, range 0-2, proportional to the segments of the waveform (see notes). If negative value is given, skip setting phase
</p>
</div>
<div class="refsect1">
<a id="idm281472885801336"></a>
<h2>Performance</h2>
<p>
<span class="emphasis"><em>aout</em></span> -- audio output, normalized +/-1
</p>
<p>
<span class="emphasis"><em>asyncout</em></span> -- (optional) - Sync signal: 1 at endpoint of each cycle, else 0.
</p>
<p>
<span class="emphasis"><em>acps</em></span> -- frequency. Range 0-anything; negative freq not implemented.
</p>
<p>
<span class="emphasis"><em>aClip</em></span> -- "squareness" of waveform shape. Range 0-1. Clip 0 is sinewave (or saw), clip 1 is squarewave (or pulse).
</p>
<p>
<span class="emphasis"><em>aSkew</em></span> -- symmetry of waveform shape. Range -1 to +1. Skew = 0 is symmetric like sine or square. Skew +1 or -1 is right/left-facing saw or pulse.
</p>
<p>
<span class="emphasis"><em>asyncin</em></span> -- (optional, ignored if not a-rate) - when >= 1, waveform quickly sweeps to phase 0. Sweep length is 0 to about 1.5*iMinSweep samples depending on current phase.
</p>
<p>
The <span class="emphasis"><em>squinewave</em></span> opcode is a variable shape oscillator with internally generated waveform.
The waveform has two parts:
</p>
<div class="orderedlist">
<ol class="orderedlist" type="1">
<li class="listitem">
<p>cosine sweep down, followed by flat part at -1</p>
</li>
<li class="listitem">
<p>cosine sweep up, followed by flat part at +1</p>
</li>
</ol>
</div>
<p>
At the end of (2), sync signal is output.
</p>
<div class="informaltable">
<table class="informaltable" border="0">
<colgroup>
<col />
<col />
</colgroup>
<tbody>
<tr>
<td>Clip (0-1)</td>
<td>controls the proportion of flatness to sweep length in each segment.</td>
</tr>
<tr>
<td>Skew (-1 to +1)</td>
<td>controls the proportions of segments (1) and (2) in the waveform cycle.</td>
</tr>
</tbody>
</table>
</div>
<p>
If skew < 0, part (1) is shorter, if skew > 0, (1) is longer than (2)
</p>
<p>
Classic waveforms have simple values:
</p>
<div class="itemizedlist">
<ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<p>sine: clip=0, skew=0</p>
</li>
<li class="listitem">
<p>saw(like): clip=0, skew=+1 or -1 (left- or right-facing)</p>
</li>
<li class="listitem">
<p>square: clip=1, skew=0</p>
</li>
<li class="listitem">
<p>pulse: clip=1, skew=+1 or -1</p>
</li>
</ul>
</div>
<p>
Fractional values generate intermediate waveforms.
</p>
<span class="emphasis">
<em>asyncin</em>
</span>
<p>
Hardsync input (asyncin >= 1) makes the waveform quickly sweep to end by raising frequency to 2 * sr/iMinSweep.
Sync pulses are thus sharper than the pulse waveform.
</p>
<span class="emphasis">
<em>iMinSweep</em>
</span>
<p>
The waveform is bandlimited by always using a minimum number of samples for cosine sweeps, even when clip/skew are at extreme values. This is controlled by <span class="emphasis"><em>iMinSweep</em></span>.
Since <span class="emphasis"><em>iMinSweep</em></span> is counted in samples, the waveform output is dependent on samplerate, but the spectrum will be very similiar independent of sr.
Default sr/3000 is fairly "soft", the actual values are 14 samples at 44.1K, 16 at 48K, 32 at 96K etc. <span class="emphasis"><em>iMinSweep</em></span> is counted in integers, although not strictly necessary.
</p>
<p>
If several units of <span class="emphasis"><em>squinewave</em></span> are run in unison, it is recommend to use different <span class="emphasis"><em>iMinSweep</em></span> values.
The min sweep value creates "dips" or quieter areas in the overtone series.
By using slightly different min sweep settings, spectrum is filled, rather than emphasizing the spectral profile.
</p>
</div>
<div class="refsect1">
<a id="idm281472885716680"></a>
<h2>Notes</h2>
<p>
<span class="emphasis"><em>squinewave</em></span> is based on cosine instead of sine to generate the waveform. (This simplifies the controlling logic.)
The difference is that cosine cos(0) = 1, whereas sin(0) = 0.
This means that hardsync occurs when waveform is at peak, just about to enter its down sweep. (Sinewave hardsync would occur at a zero-crossing)
</p>
<span class="emphasis">
<em>Tip</em>
</span>
<p>
The length of hardsync sweeps allows chain syncing several <span class="emphasis"><em>squinewave</em></span> units, creating staggered hardsync pulses.
</p>
<span class="emphasis">
<em>Pitch stability</em>
</span>
<p>
Note that <span class="emphasis"><em>iMinSweep</em></span> and shape limits the ability of squinewave to match frequency exactly.
When skew or clip is active, and FM is applied, the <span class="emphasis"><em>squinewave</em></span> waveform will be longer or shorter than the exact period.
The differences even out however, so with symmetric FM, <span class="emphasis"><em>squinewave</em></span> drifts back to match average frequency.
Sinewave unshaped signal (clip=skew=0) matches poscil output to 7-8 significant digits (also under FM).
</p>
<span class="emphasis">
<em>Initial phase</em>
</span>
<p>
Setting initial phase is useful if squinewave is used as a shaped LFO.
Init phase is split into 4 segments with symbolic values range 0-2, so it will start at the expected place regardless of skew/clip values.
0-1 represents the first part, 1-2 the second. Some interesting <span class="emphasis"><em>iphase</em></span> segment values are:
</p>
<div class="itemizedlist">
<ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<p>0 - start of 1st sweep down.</p>
</li>
<li class="listitem">
<p>0.5 - end of down sweep (start of "low" flat section).</p>
</li>
<li class="listitem">
<p>1 - midpoint, end of 1st flat section, start 2nd, "up" sweep</p>
</li>
<li class="listitem">
<p>1.5 - end of up sweep, (start of "high" flat section)</p>
</li>
<li class="listitem">
<p>0.25 and 1.25 are 0-crossings at middle of down/up sweep sections.</p>
</li>
<li class="listitem">
<p>0.75 and 1.75 are middle of low/high flat sections.</p>
</li>
</ul>
</div>
<p>
If <span class="emphasis"><em>iphase</em></span> < 0 (skip) at first use, initial phase is set to 1.25, ie 0-crossing of the "up" sweep. This makes output look like a sinewave.
</p>
</div>
<div class="refsect1">
<a id="idm281472885704712"></a>
<h2>Examples</h2>
<p>
Here is an example of the <span class="emphasis"><em>squinewave</em></span> opcode. It uses the file <a class="ulink" href="examples/squinewave.csd" target="_top"><em class="citetitle">squinewave.csd</em></a>.
</p>
<div class="example">
<a id="idm281472885702424"></a>
<p class="title">
<strong>Example 918. Example of the squinewave opcode.</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="idm281472707637032"></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 sqrt.wav -W ;;; for file output any platform</span>
<span class="nt"></CsOptions></span>
<span class="nt"><CsInstruments></span>
<span class="c1">;#################################################</span>
<span class="vg">0dbfs</span> <span class="o">=</span> <span class="mf">1.1</span>
<span class="vg">nchnls</span> <span class="o">=</span> <span class="mi">2</span>
<span class="vg">ksmps</span> <span class="o">=</span> <span class="mi">100</span>
<span class="c1">; aSyncin, FMod for instr 2</span>
ga<span class="n">fmod</span> <span class="nb">init</span> <span class="mi">0</span>
ga<span class="n">sync</span> <span class="nb">init</span> <span class="mi">0</span>
<span class="c1">; Modulator squinewave</span>
<span class="kd">instr</span> <span class="nf">1</span>
<span class="c1">; freq start, end</span>
a<span class="n">cps</span> <span class="nb">line</span> <span class="nb">p4</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p5</span>
<span class="c1">; shape start, end</span>
a<span class="n">clip</span> <span class="nb">line</span> <span class="nb">p6</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p7</span>
a<span class="n">skew</span> <span class="nb">line</span> <span class="nb">p8</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p9</span>
<span class="c1">; ar, async squinewave aFreq , aclip, askew [, asyncin, iMinSweep, iphase]</span>
a<span class="n">out1</span><span class="p">,</span> ga<span class="n">sync</span> <span class="n">squinewave</span> <span class="nb">cpsoct</span><span class="p">(</span>a<span class="n">cps</span><span class="p">),</span> a<span class="n">clip</span><span class="p">,</span> a<span class="n">skew</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">17</span>
<span class="nb">outs1</span> a<span class="n">out1</span>
ga<span class="n">FMod</span> <span class="o">=</span> a<span class="n">out1</span>
<span class="kd">endin</span>
<span class="c1">; squinewave using gaFMod and gasync input from i1</span>
<span class="kd">instr</span> <span class="nf">2</span>
<span class="c1">; freq & shape start, end</span>
a<span class="n">cps</span> <span class="nb">line</span> <span class="nb">p4</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p5</span>
a<span class="n">clip</span> <span class="nb">line</span> <span class="nb">p6</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p7</span>
a<span class="n">skew</span> <span class="nb">line</span> <span class="nb">p8</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p9</span>
a<span class="n">FMindex</span> <span class="nb">line</span> <span class="nb">p10</span><span class="p">,</span> <span class="nb">p3</span><span class="p">,</span> <span class="nb">p11</span>
a<span class="n">syncin</span> <span class="o">=</span> ga<span class="n">sync</span> <span class="o">*</span> <span class="nb">p12</span>
a<span class="n">freq</span> <span class="o">=</span> <span class="nb">cpsoct</span><span class="p">(</span>a<span class="n">cps</span> <span class="o">+</span> a<span class="n">FMindex</span> <span class="o">*</span> ga<span class="n">FMod</span><span class="p">)</span>
<span class="c1">; ar squinewave aFreq, aclip, askew [, asyncin, iMinSweep, iphase]</span>
a<span class="n">out2</span> <span class="n">squinewave</span> a<span class="n">freq</span> <span class="p">,</span> a<span class="n">clip</span><span class="p">,</span> a<span class="n">skew</span><span class="p">,</span> a<span class="n">syncin</span>
<span class="nb">outs2</span> a<span class="n">out2</span>
<span class="kd">endin</span>
<span class="nt"></CsInstruments></span>
<span class="nt"><CsScore></span>
<span class="c1">; First part instr 1 hardsyncs instr 2 (p12)</span>
<span class="c1">; p4=fund clip skew </span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">0</span> <span class="mf">1.</span> <span class="mf">6.11</span> <span class="mf">6.06</span> <span class="mi">0</span> <span class="mi">1</span> <span class="o">-</span><span class="mi">1</span> <span class="o">+</span><span class="mi">1</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">1.</span> <span class="cp">pp5</span> <span class="mf">2.03</span> <span class="cp">pp7</span> <span class="mi">0</span> <span class="cp">pp9</span> <span class="mi">0</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">1.</span> <span class="cp">pp5</span> <span class="mf">7.11</span> <span class="cp">pp7</span> <span class="mf">.8</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.8</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">2.</span> <span class="cp">pp5</span> <span class="mf">8.11</span> <span class="cp">pp7</span> <span class="mf">.2</span> <span class="cp">pp9</span> <span class="mi">1</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">6.05</span> <span class="cp">pp7</span> <span class="mf">.5</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.6</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">2.5</span> <span class="cp">pp5</span> <span class="mf">6.05</span> <span class="cp">pp7</span> <span class="mi">1</span> <span class="cp">pp9</span> <span class="mi">1</span>
<span class="c1">; p4=fund clip skew p10=FM p12=sync</span>
<span class="nb">i</span><span class="mi">2</span> <span class="mi">0</span> <span class="mf">.5</span> <span class="mf">1.08</span> <span class="mf">2.06</span> <span class="mi">0</span> <span class="mf">.3</span> <span class="o">-</span><span class="mf">.5</span> <span class="o">+</span><span class="mf">.5</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">4.03</span> <span class="cp">pp7</span> <span class="mf">.5</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.6</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">5.11</span> <span class="cp">pp7</span> <span class="mi">1</span> <span class="cp">pp9</span> <span class="mf">.5</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">6.01</span> <span class="cp">pp7</span> <span class="mf">.8</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.5</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">2.11</span> <span class="cp">pp7</span> <span class="mf">.1</span> <span class="cp">pp9</span> <span class="mf">.3</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">3.11</span> <span class="cp">pp7</span> <span class="mf">.8</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.8</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">2.</span> <span class="cp">pp5</span> <span class="mf">4.00</span> <span class="cp">pp7</span> <span class="mi">0</span> <span class="cp">pp9</span> <span class="mi">0</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">3.</span> <span class="cp">pp5</span> <span class="mf">3.00</span> <span class="cp">pp7</span> <span class="mf">.3</span> <span class="cp">pp9</span> <span class="mi">1</span> <span class="cp">pp11</span> <span class="o">.</span> <span class="o">.</span>
<span class="nb">s</span> <span class="c1">; End section, reset clock</span>
<span class="c1">; Second part instr 1 outputs FM for instr 2 (p10, p11)</span>
<span class="c1">; p4=fund clip skew </span>
<span class="nb">i</span><span class="mi">1</span> <span class="mi">0</span> <span class="mf">1.</span> <span class="mf">6.11</span> <span class="mf">6.06</span> <span class="mi">0</span> <span class="mi">1</span> <span class="o">-</span><span class="mf">.3</span> <span class="o">+</span><span class="mf">.3</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">1.</span> <span class="cp">pp5</span> <span class="mf">2.03</span> <span class="cp">pp7</span> <span class="mi">0</span> <span class="cp">pp9</span> <span class="mi">0</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">1.</span> <span class="cp">pp5</span> <span class="mf">7.11</span> <span class="cp">pp7</span> <span class="mf">.8</span> <span class="cp">pp9</span> <span class="mf">.8</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">2.</span> <span class="cp">pp5</span> <span class="mf">8.11</span> <span class="cp">pp7</span> <span class="mi">0</span> <span class="cp">pp9</span> <span class="mf">.4</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">6.05</span> <span class="cp">pp7</span> <span class="mf">.5</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.6</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mf">2.5</span> <span class="cp">pp5</span> <span class="mf">6.05</span> <span class="cp">pp7</span> <span class="mf">.4</span> <span class="cp">pp9</span> <span class="mf">.8</span>
<span class="c1">; p4=fund clip skew p10=FM p12=sync</span>
<span class="nb">i</span><span class="mi">2</span> <span class="mi">0</span> <span class="mf">.5</span> <span class="mf">8.08</span> <span class="mf">6.06</span> <span class="mi">0</span> <span class="mf">.3</span> <span class="o">-</span><span class="mf">.5</span> <span class="o">+</span><span class="mf">.5</span> <span class="mi">0</span> <span class="mi">3</span> <span class="mi">0</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">6.03</span> <span class="cp">pp7</span> <span class="mf">.5</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.6</span> <span class="cp">pp11</span> <span class="mi">2</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">5.11</span> <span class="cp">pp7</span> <span class="mi">1</span> <span class="cp">pp9</span> <span class="mf">.5</span> <span class="cp">pp11</span> <span class="o"><</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">6.01</span> <span class="cp">pp7</span> <span class="mf">.8</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.5</span> <span class="cp">pp11</span> <span class="mi">1</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">5.11</span> <span class="cp">pp7</span> <span class="mf">.5</span> <span class="cp">pp9</span> <span class="mf">.3</span> <span class="cp">pp11</span> <span class="o"><</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">.5</span> <span class="cp">pp5</span> <span class="mf">9.04</span> <span class="cp">pp7</span> <span class="mf">.1</span> <span class="cp">pp9</span> <span class="o">-</span><span class="mf">.3</span> <span class="cp">pp11</span> <span class="mf">.5</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">2.</span> <span class="cp">pp5</span> <span class="mf">8.11</span> <span class="cp">pp7</span> <span class="mf">.4</span> <span class="cp">pp9</span> <span class="mf">.4</span> <span class="cp">pp11</span> <span class="mi">2</span> <span class="o">.</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">3.</span> <span class="cp">pp5</span> <span class="mf">8.11</span> <span class="cp">pp7</span> <span class="mi">0</span> <span class="cp">pp9</span> <span class="mi">0</span> <span class="cp">pp11</span> <span class="mi">3</span> <span class="o">.</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" />
</p>
</div>
<div class="refsect1">
<a id="idm281472885698232"></a>
<h2>Credits</h2>
<p>
</p>
<table border="0" summary="Simple list" class="simplelist">
<tr>
<td>Author: Rasmus Ekman</td>
</tr>
<tr>
<td>November 2017</td>
</tr>
</table>
<p>
</p>
<p>New in version 6.10</p>
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