Music: A Mathematical Offering
Music: A Mathematical Offering
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.
- The only modern account that is comprehensive and thorough
- Lots of musical examples that make the mathematical ideas concrete; lots of illustrations
- Self-contained for the enthusiast but also usable as a course text in mathematics, physics and engineering departments
Reviews & endorsements
'… 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 Intelligencer
Product details
November 2006Paperback
9780521619998
426 pages
244 × 170 × 20 mm
0.84kg
263 b/w illus. 17 colour illus.
Available
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.
