Music: A Mathematical Offering

Music: A Mathematical Offering

3.83 (24 ratings by Goodreads)
  • Electronic book text
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Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 263 b/w illus. 17 colour illus.
  • 1139632914
  • 9781139632911

Table of contents

Preface; Introduction; Acknowledgements; 1. Waves and harmonics; 2. Fourier theory; 3. A mathematician's guide to the orchestra; 4. Consonance and dissonance; 5. Scales and temperaments: the fivefold way; 6. More scales and temperaments; 7. Digital music; 8. Synthesis; 9. Symmetry in music; 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; Bibliography; Index.show more

Review quote

'... informative and well-written ... Not only does this book cover basic material thoroughly, it also presents much of interest to those already familiar with the area of math and music. And the author provides a wealth of citations to the often scattered literature on the subject.' Zentralblatt MATH '... an excellent introduction to the interdisciplinary subject of music and mathematics (which also involves physics, biology, psycho-acoustics, and the history of science and digital technology). The book can easily be used as the text for undergraduate courses.' The Mathematical Intelligencershow more

About Dave Benson

David J. Benson is a 6th Century Professor in the Department of Mathematical Sciences at the University of Aberdeen.show more

Rating details

24 ratings
3.83 out of 5 stars
5 25% (6)
4 42% (10)
3 25% (6)
2 8% (2)
1 0% (0)
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