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<div class="refentry">
<a id="GENpadsynth"></a>
<div class="titlepage"></div>
<a id="IndexGENpadsynth" class="indexterm"></a>
<div class="refnamediv">
<h2>
<span class="refentrytitle">GENpadsynth</span>
</h2>
<p>"padsynth" —
Generate a sample table using the padsynth algorithm.
</p>
</div>
<div class="refsect1">
<a id="idm281472817457400"></a>
<h2>Description</h2>
<p>
Paul Octavian Nasca's "padsynth algorithm" adds bandwidth to each partial of a
periodic weaveform. This bandwidth is heard as color, movement, and additional
richness of sound.
</p>
<p>
First, the waveform is defined by the user as a series of harmonic partials.
Then, bandwidth is added by independently spreading each partial of the
original waveform from a single frequency across neighboring frequencies,
according to a "profile" function: a Gaussian curve, a square, or a rising
and then falling expontential.
</p>
<p>
The partials of the original waveform may be considered to be samples in a
discrete Fourier transform of the waveform. Normally there is not an exact
one-to-one correspondence between the frequencies of the samples (frequency
bins) of the discrete Fourier transform with the frequencies of the partials
of the original waveform, because any frequency in the inverse of the discrete
Fourier transform might be synthesized by interference between any number of
bins. However, the padsynth algorithm uses a simple trick to create this
correspondence. The discrete Fourier transform is simply made so large that
the frequency of any partial of the original waveform will be very close to
the frequency of the corresponding bin in the Fourier transform. Once this
correspondence has been created, the bandwidth profile can be applied by
centering it over the frequency bin of the original partial, scaling the
profile by the bandwidth, and simply multiplying the original partial by each
sample of the profile and adding the product to the corresponding bin of the
Fourier transform.
</p>
<p>
As the frequencies of the partials increase, their bandwidth may optionally
become wider or (less often) narrower.
</p>
<p>
Once each partial has been spread out in this way, the discrete Fourier
transform may be given random phases, and is then simply inverted to
synthesize the desired waveform, which may be used as the wavetable for
a digital oscillator.
</p>
<p>
N.B.: The size of the function table does NOT necessarily reflect one periodic
cycle of the waveform that it contains. The fundamental frequency must be used
to generate the desired pitch from an oscillator using the function table, e.g.
</p>
<code class="code">
oscillator_hz = desired_hz * (sr / padsynth_size / fundamental_hz)
</code>
</div>
<div class="refsect1">
<a id="idm281472817381704"></a>
<h2>Syntax</h2>
<pre class="synopsis"><span class="command"><strong>f</strong></span> # score_time table_size "padsynth" fundamental_frequency
partial_bandwidth partial_scale harmonic_stretch profile_shape profile_shape_parameter
partial1_amplitude [partial2_amplitude ...]</pre>
</div>
<div class="refsect1">
<a id="idm281472817379608"></a>
<h2>Initialization</h2>
<p>
<span class="emphasis"><em>table_size</em></span> -- Function table size. Should be large,
e.g. 2^18 == 262144. 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>fundamental_frequency</em></span> -- Fundamental frequency for
the generated table.
</p>
<p>
<span class="emphasis"><em>partial_bandwidth</em></span> -- Bandwidth of each partial in cents.
</p>
<p>
<span class="emphasis"><em>partial_scale</em></span> -- Scaling factor for bandwidth of each partial (log of increase/decrease
with partial frequency, 0 is no stretch or shrink).
</p>
<p>
<span class="emphasis"><em>harmonic_stretch</em></span> -- Harmonic stretch/shrink for all partials (1 is harmonic).
</p>
<p>
<span class="emphasis"><em>profile_shape</em></span> -- Number specifying the shape of the bandwidth profile:
1 = Gaussian, 2 = square, and 3 = exponential
</p>
<p>
<span class="emphasis"><em>profile_shape_parameter</em></span> -- Parameter passed to the function generating the profile shape, e.g. exponent.
</p>
<p>
<span class="emphasis"><em>partial1_amplitude, partial2_amplitude, ...</em></span> -- Amplitudes for each partial (may be zero).
</p>
</div>
<div class="refsect1">
<a id="idm281472817370824"></a>
<h2>Examples</h2>
<p>
Here is an example of the GENpadsynth routine. It uses the files <a class="ulink" href="examples/padsynth_gen.csd" target="_top"><em class="citetitle">padsynth_gen.csd</em></a>.
</p>
<div class="example">
<a id="idm281472817368952"></a>
<p class="title">
<strong>Example 1226. An example of the GENpadsynth routine.</strong>
</p>
<div class="example-contents">
<div class="refsect1">
<a id="idm281472677707304"></a>
<pre class="programlisting">
<span class="nt"><CsoundSynthesizer></span>
<span class="nt"><CsOptions></span>
-odac
<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">1</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">2000</span>
gi<span class="n">spec_len</span> <span class="nb">init</span> <span class="mi">2</span><span class="o">^</span><span class="mi">18</span>
<span class="kd">instr</span> <span class="nf">1</span>
<span class="nb">prints</span> <span class="s">"Plain sine for frequency/amplitude/distortion comparison.</span><span class="se">\n</span><span class="s">"</span>
gi<span class="n">_padsynth_1</span> <span class="nb">ftgenonce</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> gi<span class="n">spec_len</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">1</span>
i<span class="n">attack</span> <span class="o">=</span> <span class="mf">0.08</span>
i<span class="n">decay</span> <span class="o">=</span> <span class="mf">0.1</span>
i<span class="n">sustain</span> <span class="o">=</span> <span class="mf">0.25</span>
i<span class="n">release</span> <span class="o">=</span> <span class="mf">0.2</span>
a<span class="n">env</span> <span class="nb">madsr</span> i<span class="n">attack</span><span class="p">,</span> i<span class="n">decay</span><span class="p">,</span> i<span class="n">sustain</span><span class="p">,</span> i<span class="n">release</span>
i<span class="n">freq</span> <span class="nb">cpsmidinn</span> <span class="nb">p4</span>
i<span class="n">amp</span> <span class="nb">ampdb</span> <span class="nb">p5</span>
i<span class="n">basefreq</span> <span class="o">=</span> <span class="mi">440</span> <span class="c1">; can be lower or higher frequency; close to played frequency is said to be best</span>
i<span class="n">bw_cents</span> <span class="o">=</span> <span class="mf">56.96943</span> <span class="c1">; width of the peaks, 100 is semitone</span>
a<span class="n">sig</span> <span class="nb">poscil</span> i<span class="n">amp</span><span class="p">,</span> i<span class="n">freq</span><span class="p">,</span> gi<span class="n">_padsynth_1</span>
a<span class="n">sig</span> <span class="o">=</span> a<span class="n">env</span> <span class="o">*</span> a<span class="n">sig</span>
a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span> <span class="nb">pan2</span> a<span class="n">sig</span><span class="p">,</span> <span class="mf">0.5</span>
<span class="nb">outs</span> a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">2</span>
<span class="nb">prints</span> <span class="s">"PadSynth with sine tone.</span><span class="se">\n</span><span class="s">"</span>
i<span class="n">basehz</span> <span class="o">=</span> <span class="mf">261.625565</span>
<span class="c1">; p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11</span>
gi<span class="n">_padsynth_1</span> <span class="nb">ftgenonce</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> gi<span class="n">spec_len</span><span class="p">,</span> <span class="s">"padsynth"</span><span class="p">,</span> i<span class="n">basehz</span><span class="p">,</span> <span class="nb">p6</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mi">1</span>
i<span class="n">attack</span> <span class="o">=</span> <span class="mf">0.08</span>
i<span class="n">decay</span> <span class="o">=</span> <span class="mf">0.1</span>
i<span class="n">sustain</span> <span class="o">=</span> <span class="mf">0.25</span>
i<span class="n">release</span> <span class="o">=</span> <span class="mf">0.2</span>
a<span class="n">env</span> <span class="nb">madsr</span> i<span class="n">attack</span><span class="p">,</span> i<span class="n">decay</span><span class="p">,</span> i<span class="n">sustain</span><span class="p">,</span> i<span class="n">release</span>
i<span class="n">freq</span> <span class="nb">cpsmidinn</span> <span class="nb">p4</span>
i<span class="n">amp</span> <span class="nb">ampdb</span> <span class="nb">p5</span>
a<span class="n">sig</span> <span class="nb">poscil</span> i<span class="n">amp</span><span class="p">,</span> i<span class="n">freq</span><span class="o">*</span><span class="p">(</span><span class="vg">sr</span><span class="o">/</span>gi<span class="n">spec_len</span><span class="o">/</span>i<span class="n">basehz</span><span class="p">),</span> gi<span class="n">_padsynth_1</span>
a<span class="n">sig</span> <span class="o">=</span> a<span class="n">env</span> <span class="o">*</span> a<span class="n">sig</span>
a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span> <span class="nb">pan2</span> a<span class="n">sig</span><span class="p">,</span> <span class="mf">0.5</span>
<span class="nb">outs</span> a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">3</span>
<span class="nb">prints</span> <span class="s">"PadSynth with harmonics.</span><span class="se">\n</span><span class="s">"</span>
i<span class="n">basehz</span> <span class="o">=</span> <span class="mf">261.625565</span>
<span class="c1">; p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11</span>
gi<span class="n">_padsynth_1</span> <span class="nb">ftgenonce</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> gi<span class="n">spec_len</span><span class="p">,</span> <span class="s">"padsynth"</span><span class="p">,</span> i<span class="n">basehz</span><span class="p">,</span> <span class="nb">p6</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.7600046992</span><span class="p">,</span> <span class="mf">0.6199994683</span><span class="p">,</span> <span class="mf">0.9399998784</span><span class="p">,</span> <span class="mf">0.4400023818</span><span class="p">,</span> <span class="mf">0.0600003302</span><span class="p">,</span> <span class="mf">0.8499968648</span><span class="p">,</span> <span class="mf">0.0899999291</span><span class="p">,</span> <span class="mf">0.8199964762</span><span class="p">,</span> <span class="mf">0.3199984133</span><span class="p">,</span> <span class="mf">0.9400014281</span><span class="p">,</span> <span class="mf">0.3000001907</span><span class="p">,</span> <span class="mf">0.120003365</span><span class="p">,</span> <span class="mf">0.1799997687</span><span class="p">,</span> <span class="mf">0.5200006366</span><span class="p">,</span> <span class="mf">0.9300042987</span>
i<span class="n">attack</span> <span class="o">=</span> <span class="mf">0.08</span>
i<span class="n">decay</span> <span class="o">=</span> <span class="mf">0.1</span>
i<span class="n">sustain</span> <span class="o">=</span> <span class="mf">0.25</span>
i<span class="n">release</span> <span class="o">=</span> <span class="mf">0.2</span>
a<span class="n">env</span> <span class="nb">madsr</span> i<span class="n">attack</span><span class="p">,</span> i<span class="n">decay</span><span class="p">,</span> i<span class="n">sustain</span><span class="p">,</span> i<span class="n">release</span>
i<span class="n">freq</span> <span class="nb">cpsmidinn</span> <span class="nb">p4</span>
i<span class="n">amp</span> <span class="nb">ampdb</span> <span class="nb">p5</span>
a<span class="n">sig</span> <span class="nb">poscil</span> i<span class="n">amp</span><span class="p">,</span> i<span class="n">freq</span><span class="o">*</span><span class="p">(</span><span class="vg">sr</span><span class="o">/</span>gi<span class="n">spec_len</span><span class="o">/</span>i<span class="n">basehz</span><span class="p">),</span> gi<span class="n">_padsynth_1</span>
a<span class="n">sig</span> <span class="o">=</span> a<span class="n">env</span> <span class="o">*</span> a<span class="n">sig</span>
a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span> <span class="nb">pan2</span> a<span class="n">sig</span><span class="p">,</span> <span class="mf">0.5</span>
<span class="nb">outs</span> a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span>
<span class="kd">endin</span>
<span class="kd">instr</span> <span class="nf">4</span>
<span class="nb">prints</span> <span class="s">"PadSynth with inharmonic partials.</span><span class="se">\n</span><span class="s">"</span>
i<span class="n">basehz</span> <span class="o">=</span> <span class="mf">261.625565</span>
<span class="c1">; p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11</span>
gi<span class="n">_padsynth_1</span> <span class="nb">ftgenonce</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> gi<span class="n">spec_len</span><span class="p">,</span> <span class="s">"padsynth"</span><span class="p">,</span> i<span class="n">basehz</span><span class="p">,</span> <span class="nb">p6</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</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="mf">0.7600046992</span><span class="p">,</span> <span class="mf">0.6199994683</span><span class="p">,</span> <span class="mf">0.9399998784</span><span class="p">,</span> <span class="mf">0.4400023818</span><span class="p">,</span> <span class="mf">0.0600003302</span><span class="p">,</span> <span class="mf">0.8499968648</span><span class="p">,</span> <span class="mf">0.0899999291</span><span class="p">,</span> <span class="mf">0.8199964762</span><span class="p">,</span> <span class="mf">0.3199984133</span><span class="p">,</span> <span class="mf">0.9400014281</span><span class="p">,</span> <span class="mf">0.3000001907</span><span class="p">,</span> <span class="mf">0.120003365</span><span class="p">,</span> <span class="mf">0.1799997687</span><span class="p">,</span> <span class="mf">0.5200006366</span><span class="p">,</span> <span class="mf">0.9300042987</span>
i<span class="n">attack</span> <span class="o">=</span> <span class="mf">0.08</span>
i<span class="n">decay</span> <span class="o">=</span> <span class="mf">0.1</span>
i<span class="n">sustain</span> <span class="o">=</span> <span class="mf">0.25</span>
i<span class="n">release</span> <span class="o">=</span> <span class="mf">0.2</span>
a<span class="n">env</span> <span class="nb">madsr</span> i<span class="n">attack</span><span class="p">,</span> i<span class="n">decay</span><span class="p">,</span> i<span class="n">sustain</span><span class="p">,</span> i<span class="n">release</span>
i<span class="n">freq</span> <span class="nb">cpsmidinn</span> <span class="nb">p4</span>
i<span class="n">amp</span> <span class="nb">ampdb</span> <span class="nb">p5</span>
a<span class="n">sig</span> <span class="nb">poscil</span> i<span class="n">amp</span><span class="p">,</span> i<span class="n">freq</span><span class="o">*</span><span class="p">(</span><span class="vg">sr</span><span class="o">/</span>gi<span class="n">spec_len</span><span class="o">/</span>i<span class="n">basehz</span><span class="p">),</span> gi<span class="n">_padsynth_1</span>
a<span class="n">sig</span> <span class="o">=</span> a<span class="n">env</span> <span class="o">*</span> a<span class="n">sig</span>
a<span class="n">left</span><span class="p">,</span> a<span class="n">right</span> <span class="nb">pan2</span> a<span class="n">sig</span><span class="p">,</span> <span class="mf">0.5</span>
<span class="nb">outs</span> a<span class="n">left</span><span class="p">,</span> a<span class="n">right</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="mf">60.00</span> <span class="mi">60</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span>
<span class="nb">i</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span>
<span class="nb">i</span><span class="mi">2</span> <span class="mi">7</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">2</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">3</span> <span class="mi">26</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">4</span> <span class="mi">45</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mf">0.3</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mi">25</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">60.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">72.00</span> <span class="mi">60</span> <span class="mi">55</span>
<span class="nb">i</span><span class="mi">4</span> <span class="o">+</span> <span class="mi">2</span> <span class="mf">84.00</span> <span class="mi">60</span> <span class="mi">55</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="idm281472817367032"></a>
<h2>See Also</h2>
<p> More information on Padsynth: <a class="ulink" href="www.paulnasca.com/algorithms-created-by-me" target="_top"><em class="citetitle">www.paulnasca.com/algorithms-created-by-me</em></a></p>
</div>
<div class="refsect1">
<a id="idm281472817365080"></a>
<h2>Credits</h2>
<p>Written by Michael Gogins</p>
<p>New in version 6.05</p>
</div>
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