This subject relates directly to computer science and the study of patterns.

See the seminal book by Guerino Mazzola, called "The Topos of Music: Geometric Logic of Concepts, Theory, and Performance" (ISBN: 3764357312, $153.00; note, Amazon charges a special extra shipping fee due to size and weight).

Description: 
http://www.birkhauser.ch/books/math/5731.htm

See related page by prof who says "In Winter 2003 I taught a different seminar on this subject [music and mathematics], focussing on two recent books, Guerino Mazzola's The Topos of Music and Michael Leyton's A Generative Theory of Shape."
http://faculty.washington.edu/jrahn/w2002musicmath.htm
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At that price, I'm not in a hurry to run out and buy it right away.

The problem is that it clearly focuses on a formal mathematical view of music, but no matter how modern that approach may be, it cannot be other than a sterile view when it leaves out all mention of psychoacoustics, and most important of all, emotion.

A recent argument in a different forum about such topics brought up accusations that such people aren't even talking about music at all, they're talking about numbers. This criticism may be too extreme, but only slightly so.

Music is not a branch of '''pure''' mathematics, and no matter how useful math is in describing some aspects of music, that doesn't make music a branch of applied mathematics, either. It is an art, and is no closer to being adequately captured by math than are other arts such as painting (despite the undoubted power of mathematics in e.g. computer graphics).

There's a famous quote that goes something like "the reason that music cannot be accurately translated into words isn't because it's too simple, it's because it's too rich."

There have been a number of attempts to produce formal grammars of music as well, e.g. by Leonard Bernstein. None have been considered to be very successful, no matter how interesting they are in toy domains of music.

-- DougMerritt
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CategoryMath