Descript |
1 online resource (xiii, 411 pages) : digital, PDF file(s). |
Content |
text txt |
Media |
computer c |
Carrier |
online resource cr |
Note |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
Contents |
Preface -- Acknowledgements -- Introduction -- 1. Waves and harmonics -- 1.1. What is sound? -- 1.2. The human ear -- 1.3. Limitations of the ear -- 1.4. Why sine waves? -- 1.5. Harmonic motion -- 1.6. Vibrating strings -- 1.7. Sine waves and frequency spectrum -- 1.8. Trigonometric identities and beats -- 1.9. Superposition -- 1.10. Damped harmonic motion -- 1.11. Resonance -- 2. Fourier theory -- 2.1. Introduction -- 2.2. Fourier coefficients -- 2.3. Even and odd unctions -- 2.4. Conditions for convergence -- 2.5. The Gibbs phenomenon -- 2.6. Complex coefficients -- 2.7. Proof of Fejér's theorem -- 2.8. Bessel functions -- 2.9. Properties of Bessel functions -- 2.10. Bessel's equation and power series -- 1.11. Fourier series for FM feedback and planetary motion -- 2.12. Pulse streams -- 2.13. The Fourier transform -- 2.14. Proof of the inversion formula -- 2.15. Spectrum -- 2.16. The Poisson summation formula -- 2.17. The Dirac delta function -- 2.18. Convolution -- 2.19. Cepstrum -- 2.20. The Hilbert transform and instantaneous frequency -- 3. A mathematician's guide to the orchestra -- 3.1. Introduction -- 3.2. The wave equation for strings -- 3.3. Initial conditions -- 3.4. The bowed string -- 3.5. Wind instruments -- 3.6. The drum -- 3.7. Eigenvalues of the Laplace operator -- 3.8. The horn -- 3.9. Xylophones and tubular bells -- 3.10. The mbira -- 3.11. The gong -- 3.12. The bell -- 3.13. Acoustics. |
|
9. Symmetry in music -- 9.1. Symmetries -- 9.2. The harp of the Nzakara -- 9.3. Sets and groups -- 9.4. Change ringing -- 9.5. Cayley's theorem -- 9.6. Clock arithmetic and octave equivalence -- 9.7. Generators -- 9.8. Tone rows -- 9.9. Cartesian products -- 9.10. Dihedral groups -- 9.11. Orbits and cosets -- 9.12. Normal subgroups and quotients -- 9.13. Burnside's lemma -- 9.14. Pitch class sets -- 9.15. Pólya's enumeration theorem -- 9.16. The Mathieu group M₁₂ -- Appendix A : Bessel functions -- Appendix B : Equal tempered scales -- Appendix C : Frequency and MIDI chart -- Appendix D : Intervals -- Appendix E : Just, equal and meantone scales compared -- Appendix F : Music theory -- Appendix G : Recordings -- References -- Bibliography -- Index. |
|
7. Digital music -- 7.1. Digital signals -- 7.2. Dithering -- 7.3. WAV and MP3 files -- 7.4. MIDI -- 7.5. Delta functions and sampling -- 7.6. Nyquist's theorem -- 7.7. The z-transform -- 7.8. Digital filters -- 7.9. The discrete Fourier transform -- 7.10. The fast Fourier transform -- 8. Synthesis -- 8.1. Introduction -- 8.2. Envelopes and LFOs -- 8.3. Additive synthesis -- 8.4. Physical modelling -- 8.5. The Karplus-Strong algorithm -- 8.6. Filter analysis for the Karplus-Strong algorithm -- 8.7. Amplitude and frequency modulation -- 8.8. The Yamaha DX7 and FM synthesis -- 8.9. Feedback, or self-modulation -- 8.10. CSound -- 8.11. FM synthesis using CSound -- 8.12. Simple FM instruments -- 8.13. Further techniques in CSound -- 8.14. Other methods of synthesis -- 8.15. The phase vocoder -- 8.16. Chebyshev polynomials. |
|
4. Consonance and dissonance -- 4.1. Harmonics -- 4.2. Simple integer rations -- 4.3. History of consonance and dissonance -- 4.4. Critical bandwidth -- 4.5. Complex tones -- 4.6. Artificial spectra -- 4.7. Combination tones -- 4.8. Musical paradoxes -- 5. Scales and temperaments : the fivefold way -- 5.1. Introduction -- 5.2. Pythagorean scale -- 5.3. The cycle of fifths -- 5.4. Cents -- 5.5. Just intonation-- 5.6. Major and minor -- 5.7. The dominant seventh -- 5.8. Commas and schismas -- 5.9. Eitz's notation -- 5.10. Examples of just scales -- 5.11. Classical harmony -- 5.12. Meantone scale -- 5.13. Irregular temperaments -- 5.14. Equal temperament -- 5.15. Historical remarks -- 6. More scales and temperaments -- 6.1. Harry Partch's 43 tone and other just scales -- 6.2. Continued fractions -- 6.3. Fifty-three tempered scales -- 6.5. Thirty-one tone scale -- 6.6. The scales of Wendy Carlos -- 6.7. The Bohlen-Pierce scale -- 6.8. Union vectors and periodicity blocks -- 6.9. Septimal harmony. |
Note |
Unlimited number of concurrent users. UkHlHU |
ISBN |
9780511811722 (ebook) |
|
9780521853873 (hardback) |
|
9780521619998 (paperback) |
|