This book contains a complete and accurate mathematical treatment of the sounds of music with an emphasis on musical timbre. The book spans the range from tutorial introduction to advanced research and application to speculative assessment of its various techniques. All the contributors use a generalized additive sine wave model for describing musical timbre which gives a conceptual unity, but is of sufficient utility to be adapted to many different tasks.
Author(s): James Beauchamp
Series: Modern Acoustics and Signal Processing
Edition: 1
Publisher: Springer
Year: 2006
Language: English
Pages: 352
Contents......Page 15
Preface......Page 7
Acknowledgments......Page 14
1. Analysis and Synthesis of Musical Instrument Sounds......Page 23
1. Analysis/Synthesis Methods......Page 24
1.1 Harmonic Filter Bank (Phase Vocoder) Analysis/Synthesis......Page 25
1.2 Spectral Frequency-Tracking Method......Page 48
2. Analysis Results Using SNDAN......Page 64
2.1 Analysis File Data Formats......Page 65
2.2 Phase-Vocoder Analysis Examples for Fixed-Pitch Harmonic Musical Sounds......Page 66
2.3 Phase-Vocoder Analysis of Sounds with Inharmonic Partials......Page 80
2.4 Frequency-Tracking Analysis of Harmonic Sounds......Page 97
3. Summary......Page 104
References......Page 108
1 Introduction to Musical Signal Analysis in the Frequency Domain......Page 112
2.2 Calculations......Page 115
2.3 Results......Page 118
3.1 Background......Page 121
3.2 Calculations......Page 122
3.3 Results......Page 123
4.1 Introduction......Page 125
4.2 Results Using the High-Resolution Frequency Tracker......Page 126
5.1 Frequency Ratios of Spectral Components of Musical Sounds......Page 127
5.2 Perceived Pitch Center of Bowed String Instrument Vibrato Tones......Page 133
Appendix A: An Efficient Algorithm for the Calculation of a Constant-Q Transform......Page 138
Appendix B: Single-Frame Approximation—Calculation of Phase Change for a Hop Size of One Sample......Page 139
References......Page 141
1. Introduction......Page 144
2. Additive Synthesis Model......Page 145
2.1 Real-Time Synthesis......Page 146
3.2 Noise-Enhanced Sinusoidal Analysis......Page 147
3.3 Spectral Reassignment......Page 150
4. Navigating Source Timbres: Timbre Control Space......Page 153
4.3 Producing Intermediate Timbres: Timbre Morphing......Page 157
4.5 Time Dilation Using Time Envelopes......Page 158
4.6 Morphed Envelopes......Page 159
4.7 Low-Amplitude Partials......Page 160
5. New Possibilities for the Performer: The Continuum Fingerboard......Page 161
5.1 Previous Work......Page 162
5.2 Mechanical Design of the Playing Surface......Page 163
References......Page 164
1. Introduction......Page 167
1.1 History of Sinusoidal Modeling......Page 168
1.2 Audio Signal Models for Data Compression and Transformation......Page 170
1.3 Chapter Overview......Page 171
2.1 Related Current Systems......Page 172
2.3 Reasons for the Different Models......Page 173
3. Multiresolution Sinusoidal Modeling......Page 174
3.1 Analysis Filter Bank......Page 176
3.2 Sinusoidal Parameters......Page 177
3.3 Switched Phase Reconstruction......Page 180
4. Transform-Coded Transients......Page 183
4.1 Transient Detection......Page 184
4.2 A Simplified Transform Coder......Page 185
5. Noise Modeling......Page 186
5.1 Bark-Band Quantization......Page 187
5.2 Line-Segment Approximation......Page 188
6. Applications......Page 189
7. Conclusions......Page 192
References......Page 193
1. Introduction......Page 197
2.1 Source–Filter Models......Page 200
2.2 Source–Filter Models Represented by Spectral Envelopes......Page 203
2.3 Spectral Envelopes and Perception......Page 206
2.4 Source and Spectrum Tilt......Page 208
2.5 Properties of Spectral Envelopes......Page 209
3. Spectral Envelope Estimation Methods......Page 210
3.2 Autoregression Spectral Envelope......Page 212
3.3 Cepstrum Spectral Envelope......Page 216
3.4 Discrete Cepstrum Spectral Envelope......Page 219
3.5 Improvements on the Discrete Cepstrum Method......Page 222
3.6 Estimation of the Spectral Envelope of the Residual Signal......Page 226
4.1 Requirements......Page 227
4.3 Frequency Domain Sampled Representation......Page 228
4.4 Geometric Representation......Page 229
4.5 Formants......Page 230
4.6 Comparison of Representations......Page 232
5.1 Transcodings......Page 233
5.3 Morphing......Page 234
6.1 Filter Synthesis......Page 238
6.3 Additive Synthesis with the FFT–1 Method......Page 239
7.1 Controlling Additive Synthesis......Page 240
7.2 Synthesis and Transformation of the Singing Voice......Page 241
9. Summary......Page 242
Appendix: List of Symbols......Page 243
References......Page 244
1. Introduction......Page 250
2. Evaluation of Wavetable and FM Methods......Page 251
3. Comparison of Wavetable and FM Methods......Page 253
3.2 Wavetable-Index Matching......Page 254
3.3 Wavetable-Interpolation Matching......Page 256
3.4 Formant-FM Matching......Page 258
3.5 Double-FM Matching......Page 259
3.6 Nested-FM Matching......Page 260
4. Results......Page 262
4.1 The Trumpet......Page 263
4.2 The Tenor Voice......Page 265
5. Conclusions......Page 267
References......Page 269
1. Introduction......Page 272
2.1 Salience of Partitioned Time Segments......Page 273
2.2 Relational Timbre Studies......Page 280
3. The Experimental Control of Acoustical Variables......Page 285
4. Conclusions and Directions for Future Research......Page 289
References......Page 290
1. Timbre: A Problematic Definition......Page 294
2.1 Continuous Perceptual Dimensions......Page 296
2.2 The Notion of Specificities......Page 307
2.3 Individual and Group Listener Differences......Page 308
2.4 Evaluating the Predictive Power of Timbre Spaces......Page 312
2.5 Verbal Attributes of Timbre......Page 318
3. Categories of Timbre......Page 319
3.1 Studies of the Perception of Causality of Sound Events......Page 321
3.2 Categorical Perception: A Speech-Specific Phenomenon......Page 323
4. Conclusions......Page 334
References......Page 335
C......Page 342
l......Page 343
S......Page 344
T......Page 346
W......Page 347
