Music: A Mathematical Offering
Cambridge University Press, 11/23/2006
EAN 9780521853873, ISBN10: 0521853877
Hardcover, 426 pages, 24.7 x 17.4 x 2.5 cm
Language: English
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.
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.
'... 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