Start Over Please hold this item Export MARC Display Return To Browse
 
     
Limit search to available items
Record: Previous Record Next Record
Author Benson, D. J. (David J.), 1955-
Title Music : a mathematical offering / Dave Benson.
Publisher Cambridge : Cambridge University Press, 2007.


Click on the following to:
Go to eBook
Persistent link to this item
Click link and copy URL from browser navigation toolbar

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)
 Click on the terms below to find similar items in the catalogue
Author Benson, D. J. (David J.), 1955-
Subject Music -- Acoustics and physics.
Music theory -- Mathematics.
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)
Author Benson, D. J. (David J.), 1955-
Subject Music -- Acoustics and physics.
Music theory -- Mathematics.

Subject Music -- Acoustics and physics.
Music theory -- Mathematics.
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)
Persistent link to this item
Click link and copy URL from browser navigation toolbar

Links and services for this item:

Persistent link to this item
Click link and copy URL from browser navigation toolbar