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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta http-equiv="content-type" content="text/html;
charset=windows-1252">
<meta name="GENERATOR" content="Microsoft FrontPage 3.0">
<title>Warble Tutorial</title>
<style>body {max-width: 40em}</style>
</head>
<body>
<h1>Warble Tutorial</h1>
<p>The warble function by Alex illustrates the use of AM and FM
oscillators to create an "analog" electronic synthesizer sound.</p>
<p><i>Note: all examples use SAL syntax followed by Lisp syntax in a
smaller font. Since SAL does not support optional parameters,
keyword parameters are used instead, so these implementations
are not exactly equivalent.</i><br>
</p>
<pre>function warble(dur: 1, pch: 60)
return (env(0.017, 0.1, 0.004, 1, 0.7, 0.8, 1) *
amosc(pch, fmosc(hz-to-step(8),
pwl(0, 4, 0.2, -4, 0.56, 9, 0.7, <br> 0, 1, -8, 1))) +
env(0.2, 0.09, 0.07, 0.92, 0.8, 0.6, 1) ~ 0.96 *
amosc(pch, fmosc(pch * 1.414,
pwl(0.2, 80, 0.5, 4, 0.9,<br> 1120, 1, 200, 1)))) ~ dur<br><br><small><small>(defun warble (&optional (dur 1) (pch 60))
(stretch dur
(sum (mult
(env 0.017 0.1 0.004 1 0.7 0.8 1)
(amosc pch (fmosc (hz-to-step 8)
(pwl 0 4 0.2 -4 0.56 9 0.7 0 1 -8 1))))
(mult (stretch 0.96 (env 0.2 0.09 0.07 0.92 0.8 0.6 1))
(amosc pch (fmosc (* pch 1.414)
(pwl 0.2 80 0.5 4 0.9 1120 1 200 1)))))))</small></small></pre><small><small>
</small></small><p>This sound is the sum of two components. Each of these components is the product of an
envelope (<tt>env</tt>) and an AM oscillator (<tt>amosc</tt>).
The first one modulates the AM oscillator with a low frequency
(about 8 Hz) sinusoid
produced by an FM oscillator. The modulator varies in frequency
according to a piece-wise
linear envelope.</p>
<p>The second component is similar, but uses a much higher
modulating frequency in the
audio range, producing a ring-modulation effect. Another
piece-wise linear envelope sweeps
the modulator frequency by as much as 1120 Hz.</p>
<h2>Thicker Texture</h2>
<p>A thicker texture can be obtained by playing copies of warble
together with slight
parameter changes. Here is an example:</p>
<pre>function thicker()
return sim(0.5 * warble(dur: 8, pch: 48) @ 0.0,
0.3 * warble(dur: 8.05, pch: 47.9) @ 0.05)
<br><small><small>(defun thicker ()
(sim (scale 0.5 (at 0.00 (warble 8 48)))
(scale 0.3 (at 0.05 (warble 8.05 47.9)))))</small></small></pre>
<h2>Another FM Sound</h2>
<p>The following produces another analog-sounding FM texture:</p>
<pre>function mod(dur)
return (pwl(0, 1000, 0.2, 200, 0.5, 8000, 1, 100, 1) *
fmosc(c4, pwl(0, 1, 0.5, 3.25, 1, 0.74, 1)) ~ dur
function blurp(dur)
return fmosc(c3, osc(7, dur) * mod(dur))
<br><small><small>(defun mod (dur)
(stretch dur
(mult (pwl 0 1000 .2 200 .5 8000 1 100 1)
(fmosc c4 (pwl 0 1 .5 3.25 1 .74 1)))))
(defun blurp (dur)
(fmosc c3 (mult (osc 07 dur) (mod dur))))</small></small></pre><small><small>
</small></small><p>This example relies on a combination of AM and FM: the output is
from an FM oscillator,
but its modulator is formed by multiplying (AM) two oscillators.
The first is low
frequency (about 12 Hz), giving a warbling sound, and the second,
generated by <code>(mod
dur)</code>, is another FM oscillator. It appears that the
modulation generated by the
piece-wise linear function is almost insignificant. You might try
scaling the expression
(pwl 0 1 .5 3.25 1 .74 1) in <code>mod</code> by varying amounts
to see what happens.</p>
<p>The original duration of <code>blurp</code> was 3.1 (seconds),
but longer versions are
interesting and reveal more detail.</p>
<h2>Yet Another Sound</h2>
<p>See <a href="scratch_tutorial.htm#ring">Other Sounds Using Ring
in Vinal Scratch
Tutorial</a> for another example.</p>
</body></html>
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