Music : (Record no. 121199)
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| 000 -LEADER | |
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| fixed length control field | 06432nam a22003858i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511811722 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20201015164314.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 101021s2007||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511811722 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780521853873 (hardback) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780521619998 (paperback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | ML3805 |
| Item number | .B35 2007 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 781.2 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Benson, D. J. |
| Fuller form of name | (David J.), |
| Dates associated with a name | 1955- |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Music : |
| Remainder of title | a mathematical offering / |
| Statement of responsibility, etc. | Dave Benson. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cambridge : |
| Name of producer, publisher, distributor, manufacturer | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2007. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xiii, 411 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | Preface -- |
| -- | Acknowledgements -- |
| -- | Introduction -- |
| -- | 1. |
| Title | Waves and harmonics -- |
| Miscellaneous information | 1.1. |
| Title | What is sound? -- |
| Miscellaneous information | 1.2. |
| Title | The human ear -- |
| Miscellaneous information | 1.3. |
| Title | Limitations of the ear -- |
| Miscellaneous information | 1.4. |
| Title | Why sine waves? -- |
| Miscellaneous information | 1.5. |
| Title | Harmonic motion -- |
| Miscellaneous information | 1.6. |
| Title | Vibrating strings -- |
| Miscellaneous information | 1.7. |
| Title | Sine waves and frequency spectrum -- |
| Miscellaneous information | 1.8. |
| Title | Trigonometric identities and beats -- |
| Miscellaneous information | 1.9. |
| Title | Superposition -- |
| Miscellaneous information | 1.10. |
| Title | Damped harmonic motion -- |
| Miscellaneous information | 1.11. |
| Title | Resonance -- |
| Miscellaneous information | 2. |
| Title | Fourier theory -- |
| Miscellaneous information | 2.1. |
| Title | Introduction -- |
| Miscellaneous information | 2.2. |
| Title | Fourier coefficients -- |
| Miscellaneous information | 2.3. |
| Title | Even and odd unctions -- |
| Miscellaneous information | 2.4. |
| Title | Conditions for convergence -- |
| Miscellaneous information | 2.5. |
| Title | The Gibbs phenomenon -- |
| Miscellaneous information | 2.6. |
| Title | Complex coefficients -- |
| Miscellaneous information | 2.7. |
| Title | Proof of Fejér's theorem -- |
| Miscellaneous information | 2.8. |
| Title | Bessel functions -- |
| Miscellaneous information | 2.9. |
| Title | Properties of Bessel functions -- |
| Miscellaneous information | 2.10. |
| Title | Bessel's equation and power series -- |
| Miscellaneous information | 1.11. |
| Title | Fourier series for FM feedback and planetary motion -- |
| Miscellaneous information | 2.12. |
| Title | Pulse streams -- |
| Miscellaneous information | 2.13. |
| Title | The Fourier transform -- |
| Miscellaneous information | 2.14. |
| Title | Proof of the inversion formula -- |
| Miscellaneous information | 2.15. |
| Title | Spectrum -- |
| Miscellaneous information | 2.16. |
| Title | The Poisson summation formula -- |
| Miscellaneous information | 2.17. |
| Title | The Dirac delta function -- |
| Miscellaneous information | 2.18. |
| Title | Convolution -- |
| Miscellaneous information | 2.19. |
| Title | Cepstrum -- |
| Miscellaneous information | 2.20. |
| Title | The Hilbert transform and instantaneous frequency -- |
| Miscellaneous information | 3. |
| Title | A mathematician's guide to the orchestra -- |
| Miscellaneous information | 3.1. |
| Title | Introduction -- |
| Miscellaneous information | 3.2. |
| Title | The wave equation for strings -- |
| Miscellaneous information | 3.3. |
| Title | Initial conditions -- |
| Miscellaneous information | 3.4. |
| Title | The bowed string -- |
| Miscellaneous information | 3.5. |
| Title | Wind instruments -- |
| Miscellaneous information | 3.6. |
| Title | The drum -- |
| Miscellaneous information | 3.7. |
| Title | Eigenvalues of the Laplace operator -- |
| Miscellaneous information | 3.8. |
| Title | The horn -- |
| Miscellaneous information | 3.9. |
| Title | Xylophones and tubular bells -- |
| Miscellaneous information | 3.10. |
| Title | The mbira -- |
| Miscellaneous information | 3.11. |
| Title | The gong -- |
| Miscellaneous information | 3.12. |
| Title | The bell -- |
| Miscellaneous information | 3.13. |
| Title | Acoustics. |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | 9. |
| Title | Symmetry in music -- |
| Miscellaneous information | 9.1. |
| Title | Symmetries -- |
| Miscellaneous information | 9.2. |
| Title | The harp of the Nzakara -- |
| Miscellaneous information | 9.3. |
| Title | Sets and groups -- |
| Miscellaneous information | 9.4. |
| Title | Change ringing -- |
| Miscellaneous information | 9.5. |
| Title | Cayley's theorem -- |
| Miscellaneous information | 9.6. |
| Title | Clock arithmetic and octave equivalence -- |
| Miscellaneous information | 9.7. |
| Title | Generators -- |
| Miscellaneous information | 9.8. |
| Title | Tone rows -- |
| Miscellaneous information | 9.9. |
| Title | Cartesian products -- |
| Miscellaneous information | 9.10. |
| Title | Dihedral groups -- |
| Miscellaneous information | 9.11. |
| Title | Orbits and cosets -- |
| Miscellaneous information | 9.12. |
| Title | Normal subgroups and quotients -- |
| Miscellaneous information | 9.13. |
| Title | Burnside's lemma -- |
| Miscellaneous information | 9.14. |
| Title | Pitch class sets -- |
| Miscellaneous information | 9.15. |
| Title | Pólya's enumeration theorem -- |
| Miscellaneous information | 9.16. |
| Title | 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 -- |
| Miscellaneous information | References -- |
| -- | Bibliography -- |
| -- | Index. |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | 7. |
| Title | Digital music -- |
| Miscellaneous information | 7.1. |
| Title | Digital signals -- |
| Miscellaneous information | 7.2. |
| Title | Dithering -- |
| Miscellaneous information | 7.3. |
| Title | WAV and MP3 files -- |
| Miscellaneous information | 7.4. |
| Title | MIDI -- |
| Miscellaneous information | 7.5. |
| Title | Delta functions and sampling -- |
| Miscellaneous information | 7.6. |
| Title | Nyquist's theorem -- |
| Miscellaneous information | 7.7. |
| Title | The z-transform -- |
| Miscellaneous information | 7.8. |
| Title | Digital filters -- |
| Miscellaneous information | 7.9. |
| Title | The discrete Fourier transform -- |
| Miscellaneous information | 7.10. |
| Title | The fast Fourier transform -- |
| Miscellaneous information | 8. |
| Title | Synthesis -- |
| Miscellaneous information | 8.1. |
| Title | Introduction -- |
| Miscellaneous information | 8.2. |
| Title | Envelopes and LFOs -- |
| Miscellaneous information | 8.3. |
| Title | Additive synthesis -- |
| Miscellaneous information | 8.4. |
| Title | Physical modelling -- |
| Miscellaneous information | 8.5. |
| Title | The Karplus-Strong algorithm -- |
| Miscellaneous information | 8.6. |
| Title | Filter analysis for the Karplus-Strong algorithm -- |
| Miscellaneous information | 8.7. |
| Title | Amplitude and frequency modulation -- |
| Miscellaneous information | 8.8. |
| Title | The Yamaha DX7 and FM synthesis -- |
| Miscellaneous information | 8.9. |
| Title | Feedback, or self-modulation -- |
| Miscellaneous information | 8.10. |
| Title | CSound -- |
| Miscellaneous information | 8.11. |
| Title | FM synthesis using CSound -- |
| Miscellaneous information | 8.12. |
| Title | Simple FM instruments -- |
| Miscellaneous information | 8.13. |
| Title | Further techniques in CSound -- |
| Miscellaneous information | 8.14. |
| Title | Other methods of synthesis -- |
| Miscellaneous information | 8.15. |
| Title | The phase vocoder -- |
| Miscellaneous information | 8.16. |
| Title | Chebyshev polynomials. |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | 4. |
| Title | Consonance and dissonance -- |
| Miscellaneous information | 4.1. |
| Title | Harmonics -- |
| Miscellaneous information | 4.2. |
| Title | Simple integer rations -- |
| Miscellaneous information | 4.3. |
| Title | History of consonance and dissonance -- |
| Miscellaneous information | 4.4. |
| Title | Critical bandwidth -- |
| Miscellaneous information | 4.5. |
| Title | Complex tones -- |
| Miscellaneous information | 4.6. |
| Title | Artificial spectra -- |
| Miscellaneous information | 4.7. |
| Title | Combination tones -- |
| Miscellaneous information | 4.8. |
| Title | Musical paradoxes -- |
| Miscellaneous information | 5. |
| Title | Scales and temperaments : the fivefold way -- |
| Miscellaneous information | 5.1. |
| Title | Introduction -- |
| Miscellaneous information | 5.2. |
| Title | Pythagorean scale -- |
| Miscellaneous information | 5.3. |
| Title | The cycle of fifths -- |
| Miscellaneous information | 5.4. |
| Title | Cents -- |
| Miscellaneous information | 5.5. |
| Title | Just intonation-- |
| Miscellaneous information | 5.6. |
| Title | Major and minor -- |
| Miscellaneous information | 5.7. |
| Title | The dominant seventh -- |
| Miscellaneous information | 5.8. |
| Title | Commas and schismas -- |
| Miscellaneous information | 5.9. |
| Title | Eitz's notation -- |
| Miscellaneous information | 5.10. |
| Title | Examples of just scales -- |
| Miscellaneous information | 5.11. |
| Title | Classical harmony -- |
| Miscellaneous information | 5.12. |
| Title | Meantone scale -- |
| Miscellaneous information | 5.13. |
| Title | Irregular temperaments -- |
| Miscellaneous information | 5.14. |
| Title | Equal temperament -- |
| Miscellaneous information | 5.15. |
| Title | Historical remarks -- |
| Miscellaneous information | 6. |
| Title | More scales and temperaments -- |
| Miscellaneous information | 6.1. |
| Title | Harry Partch's 43 tone and other just scales -- |
| Miscellaneous information | 6.2. |
| Title | Continued fractions -- |
| Miscellaneous information | 6.3. |
| Title | Fifty-three tempered scales -- |
| Miscellaneous information | 6.5. |
| Title | Thirty-one tone scale -- |
| Miscellaneous information | 6.6. |
| Title | The scales of Wendy Carlos -- |
| Miscellaneous information | 6.7. |
| Title | The Bohlen-Pierce scale -- |
| Miscellaneous information | 6.8. |
| Title | Union vectors and periodicity blocks -- |
| Miscellaneous information | 6.9. |
| Title | Septimal harmony. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Music |
| General subdivision | Acoustics and physics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Music theory |
| General subdivision | Mathematics. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| International Standard Book Number | 9780521853873 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511811722">https://doi.org/10.1017/CBO9780511811722</a> |
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