-
Notifications
You must be signed in to change notification settings - Fork 0
/
ch03s02.html
377 lines (377 loc) · 11.8 KB
/
ch03s02.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>3.2 Additive Synthesis</title>
<link rel="stylesheet" type="text/css" href="style.css" />
<!--[if lt IE 8]>
<link rel="stylesheet" type="text/css"
href="style_ie55.css" />
<![endif]-->
<meta name="generator" content="DocBook XSL Stylesheets V1.73.1">
<link rel="start" href="index.html"
title="Programming Electronic Music in Pd">
<link rel="up" href="ch03.html" title="Chapter 3. Audio">
<link rel="prev" href="ch03.html" title="Chapter 3. Audio">
<link rel="next" href="ch03s03.html" title="3.3 Subtractive synthesis">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"
alink="#0000FF">
<div class="navheader">
<table width="100%" summary="Navigation header">
<tr>
<th colspan="3" align="center">3.2 Additive Synthesis</th>
</tr>
<tr>
<td width="20%" align="left"><a accesskey="p" href="ch03.html"><img
src="images/prev.png" width="41" height="20" title="previous"
alt="Prev"></a> </td>
<th width="60%" align="center">Chapter 3. Audio</th>
<td width="20%" align="right"> <a accesskey="p"
href="ch03s03.html"><img src="images/next.png" width="41"
height="20" title="next" alt="Next"></a></td>
</tr>
</table>
<hr>
</div>
<div class="sect1" lang="en">
<div class="titlepage">
<div>
<div>
<h2 class="title" style="clear: both">
<a name="chapt3.2"></a>3.2 Additive Synthesis
</h2>
</div>
</div>
</div>
<div class="sect2" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title">
<a name="id422752"></a>3.2.1 Theory
</h3>
</div>
</div>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id422758"></a>3.2.1.1 The harmonic series
</h4>
</div>
</div>
</div>
<p>The additive series of frequencies (i.e., the series that
results from simply adding the same Hertz value repeatedly), which
results in a string of intervals of decreasing size, is called the
harmonic series:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-1-1-1p.jpg">
</div>
</div>
<p>You can also derive the series by repeating an experiment
devised by Pythagoras (ca. 570-510 BCE) in which a string is
divided into various proportions:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2a.jpg">
</div>
</div>
<p>The ratios describe the length of the two parts of the string
in relation to each other.</p>
<p>When a string is bowed, it doesn't just vibrate as a whole,
but also in every whole number proportion:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2b.jpg">
<div class="caption">Here the ratios describe the length of
the vibrating section in relation to the length of the entire
string.</div>
</div>
</div>
<p>All of these partial vibrations (called 'partials' or
'harmonics') result in sound as well, so every sound made on a
string is in fact already a chord!</p>
<p>The special thing about this chord is that all of its pitches
melt together, at least when their relative volumes decrease as the
pitches get higher. Every natural sound has overtones. Due to
characteristics inherent to the human ear, we hear all of these
pitches as just one tone. </p>
<p>In contrast, the upper partials themselves (i.e., the
partials above the fundamental) do not have any overtones. An
isolated sound without overtones does not exist in nature, but such
a thing can be created using electronic means. These are called
sine tones, a name that stems from the shape of their waveform:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2c.jpg">
</div>
</div>
<p>Physicist Jean Baptiste Joseph Fourier (1768-1830) discovered
that every periodic sound can be represented using only sine tones
(of different frequency, amplitude, and phase), the sum of which is
then identical with the original. Such an analysis and the
corresponding mathematical process is called a Fourier analysis and
Fourier transformation.</p>
<p>Using this principle, it is possible to create every periodic
sound by layering many sine tones, a process called "additive
synthesis".</p>
<p>In Pd, as already mentioned, "osc~" can be used to generate a
sine tone. Sine tones are a very characteristic sound of electronic
music, as they are produced and can only be produced using
electronic means.</p>
<p>Using a number of "osc~" objects, whose frequencies form an
additive series, you can create a chord based on the overtone
series:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2d.jpg">
</div>
</div>
<p>
Typically, amplitudes become smaller as the frequencies get larger
in order for the chord to blend better (though for some
instruments, it is characteristic for certain partials to be louder
than those on either side of them, e.g., the clarinet). The
arrangement and relative volumes of overtones determine a sound's <span
class="emphasis"><em>color</em></span>. You can also speak of its
<span class="emphasis"><em>spectrum</em></span>.
</p>
<p>The fact that our ears blend the overtones together becomes
clear when you change the fundamental frequency:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2e.jpg">
<div class="caption">We'll just use the first eight partials
here. (N.B. The term 'partial' includes the fundamental whereas
the term 'overtone' does not. In other words, the 1st partial =
the fundamental frequency, 2nd partial = 1st overtone, 3rd
partial = 2nd overtone, etc.)</div>
</div>
</div>
<p>Even if you leave out the lower partials, you hear the
fundamental frequency as the fundamental when you change it:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2f.jpg">
</div>
</div>
<p>
Our brain calculates the fundamental based on the remaining
spectrum. This non-existent tone is called a <span class="emphasis"><em>residual
tone</em></span>.
</p>
<p></p>
<p></p>
<hr>
</div>
</div>
<div class="sect2" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title">
<a name="id423178"></a>3.2.2 Applications
</h3>
</div>
</div>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id423184"></a>3.2.2.1 A random klangfarbe (German:
sound color)
</h4>
</div>
</div>
</div>
<p>
<a class="ulink" href="patches/3-2-2-1-random-color.pd"
target="_top">patches/3-2-2-1-random-color.pd</a>
</p>
<p>For the sake of space, this example has been limited to just
the first seven partials:</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2g.jpg">
</div>
</div>
<p></p>
<hr>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id423249"></a>3.2.2.2 Changing one klangfarbe into
another
</h4>
</div>
</div>
</div>
<p>
<a class="ulink" href="patches/3-2-2-2-colorchange.pd"
target="_top">patches/3-2-2-2-colorchange.pd</a>
</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2h.jpg">
</div>
</div>
<p></p>
<hr>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id423309"></a>3.2.2.3 Natural vs. equal-tempered
</h4>
</div>
</div>
</div>
<p>Let's look at the difference between natural and
equal-tempered intervals (first enter the fundamental frequency!):</p>
<p>
<a class="ulink" href="patches/3-2-2-3-natural-tempered.pd"
target="_top">patches/3-2-2-3-natural-tempered.pd</a>
</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2i.jpg">
</div>
</div>
<p>Showing the difference between natural and equal-tempered
tuning in cents (hundredths of a half-step):</p>
<div class="informalfigure">
<div class="mediaobject">
<img src="images/kap3/3-2j.jpg">
<div class="caption">You can see here: the 7th partial is 31
cents flatter than the equal-tempered seventh.</div>
</div>
</div>
<p></p>
<hr>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id423425"></a>3.2.2.4 More exercises
</h4>
</div>
</div>
</div>
<p>Create an overtone chord with manipulated overtones, i.e.,
with imprecise overtones.</p>
<p></p>
<p></p>
<hr>
</div>
</div>
<div class="sect2" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title">
<a name="id423446"></a>3.2.3 Appendix
</h3>
</div>
</div>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="chapt3.2.3.1"></a>3.2.3.1 Pd's limitations
</h4>
</div>
</div>
</div>
<p>The previous example of random klangfarbe reveals one of Pd's
limitations: you can't randomly determine the number of
oscillators. You have to at least determine the maximum first.</p>
<p></p>
<hr>
</div>
</div>
<div class="sect2" lang="en">
<div class="titlepage">
<div>
<div>
<h3 class="title">
<a name="id423470"></a>3.2.4 For those especially interested
</h3>
</div>
</div>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id423477"></a>3.2.4.1 Studie II
</h4>
</div>
</div>
</div>
<p>One of the pioneering pieces in the history of electronic
music is 'Studie II' by Karlheinz Stockhausen, written in 1954.
This work uses only sine tones and mixtures thereof in non-tempered
intervals. The author strongly recommends you analyze this piece!</p>
<p></p>
<hr>
</div>
<div class="sect3" lang="en">
<div class="titlepage">
<div>
<div>
<h4 class="title">
<a name="id423497"></a>3.2.4.2 Composing with spectra
</h4>
</div>
</div>
</div>
<p>In the fourth chapter of his book "Audible Design", composer
and theorist Trevor Wishart describes many possibilities for
composing with spectra.</p>
<p></p>
<p></p>
<hr>
</div>
</div>
</div>
<div class="navfooter">
</p>
<p>
<table width="100%" summary="Navigation footer">
<tr>
<td width="40%" align="left"><a accesskey="p" href="ch03.html"><img
src="images/prev.png" width="41" height="20" title="previous"
alt="Prev"></a> </td>
<td width="20%" align="center"><a accesskey="u"
href="ch03.html">Up</a></td>
<td width="40%" align="right"> <a accesskey="p"
href="ch03s03.html"><img src="images/next.png" width="41"
height="20" title="next" alt="Next"></a></td>
</tr>
<tr>
<td width="40%" align="left" valign="top">Chapter 3. Audio </td>
<td width="20%" align="center"><a accesskey="h"
href="index.html">Home</a></td>
<td width="40%" align="right" valign="top"> 3.3 Subtractive
synthesis</td>
</tr>
</table>
</div>
</body>
</html>