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Are there any good books on musical theory from a mathematical standpoint? Is "Music theory and mathematics : chords, collections, and transformations", edited by Jack Douthett, Martha M. Hyde, and Charles J. Smith, one on them?

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I am not a big fan of "is X a good book in subject Y" questions. Whether a book is suitable for a reader depends on a lot more than just the book itself. –  Willie Wong May 3 '11 at 14:55
Seen this? –  J. M. May 3 '11 at 14:59
Can you give more objective criteria that "good"? –  Rasmus May 3 '11 at 15:45

6 Answers 6

up vote 11 down vote accepted

There's Music: a mathematical offering by Dave Benson. It can be downloaded from his website.

There's Philip Ball's the Music Instinct, although this would be more from the science point of view than the mathematical one.

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The author website you can download Music: a mathematical offering from is here. It's a really great book! –  ShreevatsaR Jun 5 '11 at 17:50
New link here. –  Cristian Garcia Aug 16 '14 at 22:08

If you like category theory and topos theory you might want to look at Mazzolas, Topos of Music: Geometric Logic of Concepts, Theory, and Performance

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This is by far the most mathematically intense book on music theory ever written. –  Matt Feb 16 '12 at 6:41

I don't know which level you mean, but Mathematics and Music seems nice. There is also Musimathics, which seems more advanced. [Disclaimer: I don't have first-hand experience with either book.]

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I've actually flipped through Musimathics a long time ago; for mathematicians/scientists/engineers who have been interested in music for a long time, there's not a lot of new stuff in there, but it's a terrific book for people with some experience/interest in math or the natural sciences who want to learn it all properly. –  Gerben May 3 '11 at 20:38

If you want to understand scales from a mathematical/dsp perspective, and why a certain scale is the most "natural" for the music of a given instrument or culture, you should check out Tuning, Timbre, Spectrum, Scale by Sethares.

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I don't think it's explicitly mathematical, but Peter Westergaard's An Introduction to Tonal Theory might be appealing (I haven't read it myself).

There is also a blog which seems to have much about it:


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