programming with max/msp - Virtual Sound

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Chapter 3T - Noise generators, filters, and subtractive synthesis In digital systems, white noise is generally produced using random number generators: the resulting waveform contains all of the reproducible frequencies for the digital system being used. In practice, random number generators use mathematical procedures that are not precisely random: they generate series that repeat after some number of events. For this reason, such generators are called pseudo-random generators. By modifying some of their parameters, these generators can produce different kinds of noise. A white noise generator, for example, generates random samples at the sampling rate. (If the sampling rate is 48,000 Hz, for example, it will generate 48,000 samples per second.) It is possible, however, to modify the frequency at which numbers are generated – a generating frequency equal to 5,000 numbers a second, for example, we would no longer produce white noise, but rather a noise with strongly attenuated high frequencies. When the frequency at which samples are generated is less than the sampling rate, “filling in the gaps” between one sample and the next becomes a problem, since a DSP system (defined in the glossary for Chapter 1T) must always be able to produce samples at the sampling rate. There are various ways of resolving this problem, including the following three solutions: > Simple pseudo-random sample generators These generate random values at a given frequency, maintaining a constant value until it is time to generate the next sample. This results in a waveform resembling a step function. In Figure 3.3 we see the graph of a 100 Hz noise generator; the random value is repeatedly output for a period equal to 1/100 of a second, after which a new random value is computed. If the sampling rate were 48,000 Hz, for example, each random value would be repeated as a sample 48,000 / 100 = 480 times. amplitude � �� time Fig. 3.3 Generation of pseudo-random values from “Electronic Music and Sound Design” Vol. 1 by Alessandro Cipriani and Maurizio Giri © ConTempoNet 2010 - All rights reserved 3T 297
3.1 298 Theory Paragraph 3.1 - Sound sources for subtractive synthesis > Interpolated pseudo-random sample generators These generators use interpolation between each random number and the next. (See the section on linear interpolation in Chapter 2.1.) As you can see in Figure 3.4, intermediate samples, produced during the gaps between random value computations, follow line segments that move gradually from one value to the next. amplitude Fig. 3.4 Generation of pseudo-random values with linear interpolation Interpolation between one value and the next can be linear, as shown in the figure, or polynomial, implemented using polynomial functions to connect the values using curves rather than line segments. (Polynomial interpolation is shown in Figure 3.5, however, we will not attempt to explain the details here.) The kinds of polynomial interpolation most common to computer music are quadratic (which use polynomials of the second degree) and cubic (which use polynomials of the third degree). Programming languages for synthesis and signal processing usually have efficient algorithms for using these interpolations built in to their runtimes, ready for use. amplitude � �� time � �� time Fig. 3.5 Generation of pseudo-random values with polynomial interpolation from “Electronic Music and Sound Design” Vol. 1 by Alessandro Cipriani and Maurizio Giri © ConTempoNet 2010 - All rights reserved
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Alessandro Cipriani • Maurizio Gi
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Alessandro Cipriani • Maurizio Gi
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CONTENTS Foreword by David Zicarell
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Electronic Music and Sound Design -
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LEARNING AGENDA 1T PREREQUISITES FO
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1.1 4 Theory sound or sounds that w
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1.1 6 Theory ��
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1.2 8 Theory Let’s look at a tabl
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1.2 10 Theory time (by measuring th
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1.2 12 Theory By the same reasoning
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1.2 14 Theory If the amplitude of a
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1.2 16 Theory 8 140 the threshold o
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1.2 18 Theory 1000 Hz was chosen as
Page 35 and 36: LEARNING AGENDA 1P PREREQUISITES FO
Page 37 and 38: 1.1 52 Practice Paragraph 1.1 - Fir
Page 53 and 54: 1.2 68 Practice Paragraph 1.2 - Fre
Page 55 and 56: Interlude A PROGRAMMING WITH MAX/MS
Page 57 and 58: Interlude A - Programming with Max/
Page 65 and 66: 2T ADDITIVE AND VECTOR SYNTHESIS 2.
Page 67 and 68: Chapter 2T - Additive and vector sy
Page 73 and 74: 2P ADDITIVE AND VECTOR SYNTHESIS 2.
Page 75 and 76: Chapter 2P - Additive and vector sy
Page 83 and 84: LEARNING AGENDA 3T PREREQUISITES FO
Page 85: 3.1 296 Theory dB Fig. 3.1 The spec
Page 89 and 90: 3.2 300 Theory Paragraph 3.2 - Lowp
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Page 93 and 94: 3.1 358 Practice Make sure to try s
Page 95 and 96: 3.1 360 Practice Fig. 3.6 The rand~
Page 97 and 98: 3.2 362 Practice Paragraph 3.2 - Lo
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Page 101 and 102: IB1 424 Practice defined to be the
Page 103 and 104: IB2 426 Practice From this example,
Page 105 and 106: LEARNING AGENDA 4T PREREQUISITES FO
Page 107 and 108: 4.2 474 Theory In the example, the
Page 109 and 110: 4P CONTROL SIGNALS 4.1 CONTROL SIGN
Page 111 and 112: Chapter 4P - Control signals 4.1 CO
Page 113 and 114: Chapter 4P - Control signals Under
Page 115 and 116: REFERENCES The decision was made to
Page 117 and 118: 528 constructive interference, 190,
Page 119 and 120: 530 multislider, 164, 179 multislid
Page 121 and 122: 532 switch, 434, 468 T t (see trigg
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