Music and Acoustics From Instrument to Computer

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ISBN: 9781905209262 | 1905209266
Cover: Hardcover
Copyright: 10/24/2006

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This overview on the nature of musical sounds, from their production by acoustic music instruments to synthesized sounds obtained with computers, includes topics such as sound propagation, Fourier and time-frequency analysis, psychoacoustics, analogue and digital-signal processing theory, computer science, and MP3 sound compression.

Foreword

(4)

Chapter 1. Sounds

(48)

1.1. Sound propagation

(10)

1.1.1. A look at the physical models

(4)

1.1.1.1. Mass conservation

(2)

1.1.1.2. The Euler equation

(1)

1.1.1.3. The state equation

(1)

1.1.2. The wave equation

(2)

1.1.3. The Helmholtz equation

(2)

1.1.4. Sound intensity

(2)

1.2. Music theory interlude

(4)

1.2.1. Intervals, octave

(1)

1.2.2. Scientific pitch notation

(1)

1.2.3. Dividing the octave into twelve semitones

(1)

1.2.4. Diatonic scales

(2)

1.2.4.1. Major scale

(1)

1.2.4.2. Minor scales

(1)

1.3. Different types of sounds

(10)

1.3.1. Periodic sounds

(3)

1.3.1.1. Fourier series

(1)

1.3.2. Sounds with partials

(1)

1.3.3. Continuous spectrum sounds

(1)

1.3.4. Noise

(4)

1.4. Representation of sound

(8)

1.4.1. Time or frequency analysis, discrete Fourier transform

(2)

1.4.2. Time-frequency analysis, the spectrogram

(5)

1.5. Filtering

(7)

1.5.1. Discrete spectrum

(4)

1.5.1.1. Transfer function

(1)

1.5.1.2. Impulse response

(2)

1.5.2. Continuous spectrum

(1)

1.5.3. Ideal low-pass, band-pass and all-pass filters

(3)

1.6. Study problems

(2)

1.6.1. Normal reflection on a wall (*)

(1)

1.6.2. Comb filtering produced by a microphone located near a wall (**)

(1)

1.6.3. Summing intensities (***)

(1)

1.6.4. Intensity of a standing wave (**)

(1)

1.6.5. Sound of a siren (*)

(1)

1.7. Practical computer applications

(7)

1.7.1. First sound, vectors

(1)

1.7.2. Modifying the parameters: the command file

(1)

1.7.3. Creating more complex sounds: using functions

(1)

1.7.3.1. Noise and siren interlude

(1)

1.7.4. Analysis

(2)

1.7.4.1. Time analysis

(1)

1.7.4.2. Frequency analysis

(1)

1.7.4.3. Time-frequency analysis

(1)

1.7.5. Filtering

(2)

Chapter 2. Music Instruments

(50)

2.1. Strings

(6)

2.1.1. Free vibrations of a string

(3)

2.1.2. Beats, chords and consonance

(3)

2.2. Bars

(5)

2.2.1. Bar fixed at both ends

(2)

2.2.2. Bar clamped at one end

(2)

2.3. Membranes

(2)

2.4. Tubes

(10)

2.4.1. Pressure control

(4)

2.4.1.1. Response to a harmonic excitation

(1)

2.4.1.2. The resonance effect

(2)

2.4.1.3. Natural modes

(1)

2.4.1.4. The resulting sound

(1)

2.4.2. Speed control

(3)

2.4.2.1. Response to a harmonic excitation

(2)

2.4.2.2. Resonance and natural modes

(1)

2.4.2.3. Comments on phases

(1)

2.4.3. Tuning

(1)

2.5. Timbre of instruments

(9)

2.5.1. Nature of the spectrum

(6)

2.5.1.1. Harmonics or partials, the piano's inharmonicity

(1)

2.5.1.2. Richness in higher harmonics

(2)

2.5.1.3. Different harmonics distributions

(1)

2.5.1.4. The purpose of the resonator

(1)

2.5.2. Envelope of the sound

(3)

2.5.2.1. Calculation of the envelope

(1)

2.5.2.2. Using several envelopes

(1)

2.6. Study problems

(12)

2.6.1. Vibrations of a string (general case) (**)

(2)

2.6.2. Plucked string (*)

100

(1)

2.6.3. Bow drawn across a string (*)

100

(1)

2.6.4. String reduced to one degree of freedom (**)

101

(1)

2.6.5. Coupled string-bridge system and the remanence effect (***)

102

(2)

2.6.6. Calculation of the inharmonicity of a real string (***)

104

(2)

2.6.7. Coincidence frequency of a wave in a board (***)

106

(1)

2.6.8. Resonance of the bourdon (**)

107

(1)

2.6.9. Resonance of a cylindrical dual controlled tube (**)

108

(1)

2.6.10. Resonance of a conical tube (1) (**)

109

(1)

2.6.11. Resonance of a conical tube (2) (**)

110

(1)

2.7. Practical computer applications

110

(5)

2.7.1. Create your synthesizer

110

(2)

2.7.1.1. Write your instrument function

111

(1)

2.7.1.2. Add an envelope

111

(1)

2.7.1.3. And play your instrument

112

(1)

2.7.2. Modify the timbre of your instrument

112

(1)

2.7.3. Remanent sound

112

(3)

Chapter 3. Scales and Temperaments

115

(12)

3.1. The Pythagorean scale

116

(1)

3.2. The Zarlino scale

117

(1)

3.3. The tempered scales

118

(3)

3.3.1. Equal temperament

119

(1)

3.3.2. A historical temperament

119

(1)

3.3.3. Equal temperament with perfect fifth

120

(1)

3.3.4. The practice of tuners

120

(1)

3.3.5. The practice of musicians

121

(1)

3.4. A brief history of A4

121

(1)

3.5. Giving names to notes

122

(1)

3.6. Other examples of scales

123

(1)

3.7. Study problems

123

(2)

3.7.1. Frequencies of a few scales (***)

123

(1)

3.7.2. Beats of the fifths and the major thirds (*)

123

(2)

3.8. Practical computer applications

125

(2)

3.8.1. Building a few scales

125

(1)

3.8.2. Listening to beats

125

(2)

Chapter 4. Psychoacoustics

127

(14)

4.1. Sound intensity and loudness

127

(3)

4.1.1. The phon

128

(1)

4.1.2. The sone

129

(1)

4.2. The ear

130

(1)

4.3. Frequency and pitch

131

(5)

4.3.1. The mel scale

132

(1)

4.3.2. Composed sounds

133

(1)

4.3.2.1. Pitch of sounds composed of harmonics

133

(1)

4.3.2.2. Pitch of sounds composed of partials

133

(1)

4.3.3. An acoustic illusion

134

(2)

4.4. Frequency masking

136

(2)

4.5. Study problems

138

(1)

4.5.1. Equal-loudness levels (**)

138

(1)

4.5.2. Frequency masking (**)

138

(1)

4.5.3. Perpetually ascending sound (**)

138

(1)

4.6. Practical computer applications

138

(3)

4.6.1. Frequency masking

138

(1)

4.6.2. Perpetually ascending scale

138

(3)

Chapter 5. Digital Sound

141

(28)

5.1. Sampling

143

(12)

5.1.1. The Nyquist criterion and the Shannon theorem

145

(7)

5.1.1.1. Case of a sinusoidal signal

145

(2)

5.1.1.2. General case

147

(1)

5.1.1.3. Consequences

148

(1)

5.1.1.4. Theoretical impossibility

148

(1)

5.1.1.5. What happens if the Nyquist criterion is not met?

148

(4)

5.1.2. Quantization

152

(2)

5.1.2.1. Error due to quantization

153

(1)

5.1.3. Reconstruction of the sound signal

154

(1)

5.2. Audio compression

155

(5)

5.2.1. Psychoacoustic compression

155

(4)

5.2.2. Entropy compression

159

(1)

5.3. Digital filtering and the Z-transform

160

(4)

5.3.1. Digital filtering

160

(1)

5.3.2. The Z-transform

161

(3)

5.3.2.1. Definition

161

(1)

5.3.2.2. Effect of a delay

162

(1)

5.3.2.3. Filtering and Z-transform

163

(1)

5.4. Study problems

164

(3)

5.4.1. Nyquist criterion (*)

164

(1)

5.4.2. Aliasing of an ascending sound (*)

165

(1)

5.4.3. Another example of reconstruction (***)

165

(1)

5.4.4. Elementary filter bank (**)

166

(1)

5.5. Practical computer applications

167

(2)

5.5.1. Spectrum aliasing

167

(1)

5.5.2. Quantization noise

168

(1)

Chapter 6. Synthesis and Sound Effects

169

(22)

6.1. Synthesis of musical sounds

170

(5)

6.1.1. Subtractive synthesis

170

(1)

6.1.2. Additive synthesis

171

(1)

6.1.3. FM synthesis

171

(3)

6.1.4. Synthesis based on the use of sampled sounds

174

(1)

6.2. Time effects: echo and reverberation

175

(4)

6.2.1. Simple echo

175

(1)

6.2.2. Multiple echo

176

(1)

6.2.3. Reverberation

177

(2)

6.2.3.1. Using the impulse response

177

(1)

6.2.3.2. Using echoes and all-pass filters

178

(1)

6.3. Effects based on spectrum modification

179

(7)

6.3.1. The 'Wah-wah' effect

180

(2)

6.3.1.1. An example of a band-pass filter

180

(2)

6.3.2. AM or FM type sound effects

182

(4)

6.3.2.1. Vibrato

183

(1)

6.3.2.2. Leslie effect

184

(2)

6.4. Study problems

186

(2)

6.4.1. The Doppler effect (**)

186

(1)

6.4.2. FM and Chowning (***)

187

(1)

6.5. Practical computer applications

188

(3)

6.5.1. Sound synthesis

188

(1)

6.5.2. Chowning synthesis

188

(1)

6.5.3. Reverberation

189

(1)

6.5.4. Vibrato

189

(1)

6.5.5. The Leslie effect

189

(2)

Bibliography

191

(2)

Index

193

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Music and Acoustics From Instrument to Computer

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