The Math Behind the Music

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Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on • overtones, scales, and tuning systems • the musical dice game attributed to Mozart and Haydn • the several-hundred-year-old style of bell-playing known as ringing the changes • the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.

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Editorial Reviews

From the Publisher
"...a text which relates music and mathematics in a manner accessible to many individuals, and provides a bibliography of further readings on each chapter's topics, so the best use of this book may be as a jumping-off point for further examinations of whichever topic interests and individual reader.The Math Behind the Musicdoes not require advanced understanding of either mathematics or music: in fact most of the text could be easily understood by an interested high school student."
Sarah Boslaugh
MAA Reviews

"Leon Harkleroad has written a concise and accessible survey of some of the interesting mathematics of music, and he has done so in a way that requires a minimum of preparation on the reader's part in either music or mathematics."
Gareth Loy, Gareth, Inc.

"The book can be recommended as a first survey. Those who want to know more can find many suggestions for further study in the extensive bibliography. The book addresses readers who do not have much mathematical knowledge. Everything is explained clearly and at great length, and the theoretical facts are illustrated by many pictures, scores, and the tracks on the accompanying CD."
The Mathematical Intelligencer

"The material is very well presented and well explained, it comes with many (musical and mathematical) examples and illustrations (the book even comes with a CD-ROM from which the reader can listen to the musical examples of the book), and many details side aspects, anecdotes and references are provided."
Christian Krattenhaler, Mathematical Reviews

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Product Details

  • ISBN-13: 9780521009355
  • Publisher: Cambridge University Press
  • Publication date: 5/28/2006
  • Series: Outlooks Series
  • Edition description: BK&CD-ROM
  • Pages: 158
  • Sales rank: 699,438
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.55 (d)

Table of Contents

Preface; Acknowledgments; 1. Mathematics and music, a duet; 2. Pitch: the ground of music; 3. Tuning up; 4. How to vary a theme mathematically; 5. Bells and groups: music by chance; 6. Pattern, pattern, pattern ; 7. Sight meets sound; 8. How NOT to mix mathematics and music; 9. Bibliography; Contents of the CD; Illustration credits; Index.

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