Music : a mathematical offering / Dave Benson.

By: Benson, D. J. (David J.), 1955-
Language: English Publisher: Cambridge, UK ; New York : Cambridge University Press, 2013Description: 1 online resource (xiii, 411 pages) : illustrations (some color)Content type: txt Media type: rdamedia Carrier type: online resourceISBN:  46125; 0521619998 (pbk.) 9780511811722Subject(s): Music -- Acoustics and physics | Music -- Mathematics | Musical perceptionGenre/Form: Electronic books.DDC classification: 781.2 LOC classification: ML3805 | .B35 2013Online resources: Full text available from Cambridge University Press Click here to view
Contents:
Introduction: Read pp. 1-4 1 - Waves and harmonics: Read pp. 5-35 2 - Fourier theory: Read pp. 36-90 3 - A mathematician's guide to the orchestra: Read pp. 91-143 4 - Consonance and dissonance: Read pp. 144-160 5 - Scales and temperaments: the fivefold way: Read pp. 161-209 6 - More scales and temperaments: Read pp. 210-244 7 - Digital music: Read pp. 245-264 8 - Synthesis: Read pp. 265-311 9 - Symmetry in music: Read pp. 312-360 Appendix A - Bessel functions: Read pp. 361-364 Appendix B - Equal tempered scales: Read pp. 365-366 Appendix C - Frequency and MIDI chart: Read pp. 367-367 Appendix D - Intervals: Read pp. 368-371 Appendix E - Just, equal and meantone scales compared: Read pp. 372-373 Appendix F - Music theory: Read pp. 374-380 Appendix G - Recordings: Read pp. 381-385 References: Read pp. 386-388 Bibliography: Read pp. 389-392 Index: Read pp. 393-411
Summary: 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.
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COLLEGE LIBRARY
781.2 B443 2013 (Browse shelf) Available CL-46125
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May be used as an undergraduate textbook; includes exercises.

Includes bibliographical references (p. 386-392) and index.

Introduction: Read pp. 1-4
1 - Waves and harmonics: Read pp. 5-35
2 - Fourier theory: Read pp. 36-90
3 - A mathematician's guide to the orchestra: Read pp. 91-143
4 - Consonance and dissonance: Read pp. 144-160
5 - Scales and temperaments: the fivefold way: Read pp. 161-209
6 - More scales and temperaments: Read pp. 210-244
7 - Digital music: Read pp. 245-264
8 - Synthesis: Read pp. 265-311
9 - Symmetry in music: Read pp. 312-360
Appendix A - Bessel functions: Read pp. 361-364
Appendix B - Equal tempered scales: Read pp. 365-366
Appendix C - Frequency and MIDI chart: Read pp. 367-367
Appendix D - Intervals: Read pp. 368-371
Appendix E - Just, equal and meantone scales compared: Read pp. 372-373
Appendix F - Music theory: Read pp. 374-380
Appendix G - Recordings: Read pp. 381-385
References: Read pp. 386-388
Bibliography: Read pp. 389-392
Index: Read pp. 393-411

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.

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