The theory and technique of electronic music

Description

This is the first book to develop both the theory and the practice of synthesizing musical sounds using computers. Each chapter starts with a theoretical description of one technique or problem area and ends with a series of working examples (over 100 in all), covering a wide range of applications. A unifying approach is taken throughout; chapter two, for example, treats both sampling and wavetable synthesis as special cases of one underlying technique. Although the theory is presented quantitatively, the mathematics used goes no further than trigonometry and complex numbers. The examples and supported software along with a machine-readable version of the text are available on the web and maintained by a large online community. The Theory and Techniques of Electronic Music is valuable both as a textbook and as professional reading for electronic musicians and computer music researchers. Sinusoids, amplitude and frequency (11) 1.1 Measures of Amplitude . . . . . . . . (13) 1.2 Units of Amplitude . . . . . . . . . . (14) 1.3 Controlling Amplitude . . . . . . . . (15) 1.4 Frequency . . . . . . . . . . . . . . . (16) 1.5 Synthesizing a Sinusoid . . . . . . . (17) 1.6 Superposing Signals . . . . . . . . . (20) 1.7 Periodic Signals . . . . . . . . . . . . (21) 1.8 About the Software Examples . . . . (22) Quick Introduction to Pd . . . . . . (25) How to find and run the examples . (27) 1.9 Examples . . . . . . . . . . . . . . . (27) Constant amplitude scaler . . . . . . (27) Amplitude control in decibels . . . . (29) Smoothed amplitude control with an envelope generator (31) Major triad . . . . . . . . . . . . . . (32) Conversion between frequency and pitch (32) More additive synthesis . . . . . . . (33) Exercises . . . . . . . . . . . . . . . . . . (35) Wavetables and samplers (37) 2.1 The Wavetable Oscillator . . . . . . (39) 2.2 Sampling . . . . . . . . . . . . . . . (43) 2.3 Enveloping samplers . . . . . . . . . (45) 2.4 Timbre stretching . . . . . . . . . . . (49) 2.5 Interpolation . . . . . . . . . . . . . (53) 2.6 Examples . . . . . . . . . . . . . . . (57) 2.6.1 wavetable oscillator . . . . . (57) 2.6.2 wavetable lookup in general . (58) 2.6.3 using a wavetable as a sampler (60) 2.6.4 looping samplers . . . . . . . (62) 2.6.5 Overlapping sample looper . (64) 2.6.6 Automatic read point precession (66) iii (8) Audio and control computations (69) 3.1 The sampling theorem . . . . . . (69) 3.2 Control . . . . . . . . . . . . . . (71) 3.3 Control streams . . . . . . . . . . (73) 3.4 Converting from audio signals to numeric control streams (77) 3.5 Control streams in block diagrams (78) 3.6 Event detection . . . . . . . . . . (79) 3.7 Control computation using audio signals directly (81) 3.8 Operations on control streams . . (83) 3.9 Control operations in Pd . . . . . (85) 3.10 Examples . . . . . . . . . . . . . (87) 3.10.1 Sampling and foldover . . (87) 3.10.2 Converting controls to signals (89) 3.10.3 Non-looping sample player . (90) 3.10.4 Signals to controls . . . . (92) 3.10.5 Analog-style sequencer . . (92) 3.10.6 MIDI-style synthesizer . . (94) Automation and voice management (97) 4.1 Envelope Generators . . . . . . . (97) 4.2 Linear and Curved Amplitude Shapes (100) 4.3 Continuous and discontinuous control changes . (102) 4.3.1 Muting . . . . . . . . . . (103) 4.3.2 Switch-and-ramp . . . . . (104) 4.4 Polyphony . . . . . . . . . . . . . (106) 4.5 Voice allocation . . . . . . . . . . (106) 4.6 Voice tags . . . . . . . . . . . . . (107) 4.7 Encapsulation in Pd . . . . . . . (110) 4.8 Examples . . . . . . . . . . . . . (111) 4.8.1 ADSR envelope generator (111) 4.8.2 Transfer functions for amplitude control (114) 4.8.3 Additive synthesis: Rissets bell . (115) 4.8.4 Additive synthesis: spectral envelope control (118) 4.8.5 Polyphonic synthesis: sampler . (121) Modulation (127) 5.1 Taxonomy of spectra . . . . . . . (127) 5.2 Multiplying audio signals . . . . (130) 5.3 Waveshaping . . . . . . . . . . . (134) 5.4 Frequency and phase modulation (140) 5.5 Examples . . . . . . . . . . . . . (143) 5.5.1 Ring modulation and spectra (143) 5.5.2 Octave divider and formant adder (145) 5.5.3 Waveshaping and difference tones . (146) 5.5.4 Waveshaping using Chebychev polynomials (147) 5.5.5 Waveshaping using an exponential function (148) 5.5.6 Sinusoidal waveshaping: evenness and oddness (149) 5.5.7 Phase modulation and FM . . . . . . . . . . (151) Designer spectra (155) 6.1 Carrier/modulator model . . . . . . . . . . . . . . . (156) 6.2 Pulse trains . . . . . . . . . . . . . . . . . . . . . . . (159) 6.2.1 Pulse trains via waveshaping . . . . . . . . . (159) 6.2.2 Pulse trains via wavetable stretching . . . . . (160) 6.2.3 Resulting spectra . . . . . . . . . . . . . . . . (160) 6.3 Movable ring modulation . . . . . . . . . . . . . . . (164) 6.4 Phase-aligned formant (PAF) generator . . . . . . . (166) 6.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . (171) 6.5.1 Wavetable pulse train . . . . . . . . . . . . . (171) 6.5.2 Simple formant generator . . . . . . . . . . . (174) 6.5.3 Two-cosine carrier signal . . . . . . . . . . . . (175) 6.5.4 The PAF generator . . . . . . . . . . . . . . . (176) 6.5.5 Stretched wavetables . . . . . . . . . . . . . . (180) Time shifts (181) 7.1 Complex numbers . . . . . . . . . . . . . . . . . . . (182) 7.1.1 Sinusoids as geometric series . . . . . . . . . (184) 7.2 Time shifts and phase changes . . . . . . . . . . . . (186) 7.3 Delay networks . . . . . . . . . . . . . . . . . . . . . (186) 7.4 Recirculating delay networks . . . . . . . . . . . . . (191) 7.5 Power conservation and complex delay networks . . (195) 7.6 Artificial reverberation . . . . . . . . . . . . . . . . . (200) 7.6.1 Controlling reverberators . . . . . . . . . . . (202) 7.7 Variable and fractional shifts . . . . . . . . . . . . . (204) 7.8 Accuracy and frequency response of interpolating delay lines (207) 7.9 Pitch shifting . . . . . . . . . . . . . . . . . . . . . . (208) 7.10 Examples . . . . . . . . . . . . . . . . . . . . . . . . (214) 7.10.1 Fixed, noninterpolating delay line . . . . . . (214) 7.10.2 Recirculating comb filter . . . . . . . . . . . . (215) 7.10.3 Variable delay line . . . . . . . . . . . . . . . (216) 7.10.4 Order of execution and lower limits on delay times (217) 7.10.5 Order of execution in non-recirculating delay lines (219) 7.10.6 Non-recirculating comb filter as octave doubler (221) 7.10.7 Time-varying complex comb filter: shakers . (222) 7.10.8 Reverberator . . . . . . . . . . . . . . . . . . (224) 7.10.9 Pitch shifter . . . . . . . . . . . . . . . . . . . (224) 7.10.10Exercises . . . . . . . . . . . . . . . . . . . . (227) Filters (229) 8.1 Taxonomy of filters . . (230) 8.1.1 Low-pass and high-pass filters . (230) 8.1.2 Band-pass and stop-band filters . (232) 8.1.3 Equalizing filters (232) 8.2 Designing filters . . . . (235) 8.2.1 Elementary non-recirculating filter (235) 8.2.2 Non-recirculating filter, second form (236) 8.2.3 Elementary recirculating filter . (239) 8.2.4 Compound filters (239) 8.2.5 Real outputs from complex filters . (240) 8.3 Designing filters . . . . (242) 8.3.1 One-pole low-pass filter (242) 8.3.2 One-pole, one-zero high-pass filter (243) 8.3.3 Shelving filter . (244) 8.3.4 Band-pass filter . (246) 8.3.5 Peaking and band-stop filter (246) 8.3.6 Butterworth filters (247) 8.3.7 Stretching the unit circle with rational functions (249) 8.3.8 Butterworth band-pass filter (252) 8.3.9 Time-varying coefficients (253) 8.3.10 Impulse responses of recirculating filters (255) 8.3.11 All-pass filters (255) 8.4 Applications . . . . . . (258) 8.4.1 Subtractive synthesis . (258) 8.4.2 Envelope following (258) 8.4.3 Single Sideband Modulation . (261) 8.5 Examples . . . . . . . (263) 8.5.1 Prefabricated low-, high-, and band-pass filters (263) 8.5.2 Prefabricated time-variable band-pass filter (264) 8.5.3 Envelope followers (266) 8.5.4 Single sideband modulation (266) 8.5.5 Using elementary filters directly: (269) 8.5.6 Making and using all-pass filters (269) Fourier analysis and resynthesis (273) 9.1 Fourier analysis of periodic signals (273) 9.1.1 Fourier transform as additive synthesis . (275) 9.1.2 Periodicity of the Fourier transform (275) 9.2 Properties of Fourier transforms (275) 9.2.1 Fourier transform of DC . (276) 9.2.2 Shifts and phase changes (277) 9.2.3 Fourier transform of a sinusoid (279) 9.3 Fourier analysis of non-periodic signals . (280) 9.4 Fourier analysis and reconstruction of audio signals . (283) 9.4.1 Narrow-band companding (285) 9.4.2 Timbre stamping (classical vocoder) . (287) Phase . . . . . . . . . . . . . . . . . . . . . . (289) 9.5.1 Phase relationships between channels . (293) Phase bashing . . . . . . . . . . . . . . . . . . (294) Examples . . . . . . . . . . . . . . . . . . . . (296) 10 Classical waveforms (305) Symmetries and Fourier series . . . . . . . . . (307) 10.1.1 Sawtooth waves and symmetry . . . . (308) Decomposing the classical waveforms into sawtooth and parabolic (8) waves . . . . . . . . . . . . . . . . . . . . . . (310) Fourier series of the elementary waveforms . . (312) Predicting and controlling foldover . . . . . . (317) 10.4.1 Oversampling . . . . . . . . . . . . . . (317) 10.4.2 Sneaky triangle waves . . . . . . . . . (318) 10.4.3 Transition splicing . . . . . . . . . . . (319) Examples . . . . . . . . . . . . . . . . . . . . (322)