"Scientifically, I could never be made to understand
what a note in music is, or how one note differs
from another"
          -- Charles Lamb, Essays

"Music has many resemblances to algebra"
          -- Novalis

"There is music wherever there is harmony,
order, or proportion"
          -- Sir Thomas Browne

"Check out Guitar George;
He knows all the chords."
          -- Mark Knopfler, "Sultans of Swing"

From Polychords to Polya: Adventures in Musical Combinatorics
by Mike Keith

     From the time of Pythagoras, who realized that the difficulty in constructing a musical scale is due to the fact that there are no integer solutions to the equation

(3/2)m = 2n,

until the present time, when computer algorithms are used to compose musical pieces, there has been a lively interaction between the musical arts and the mathematical sciences.

     This book explores the various connections between the basic musical building blocks - chords, scales, and rhythms - and the area of mathematics known as combinatorics, which is concerned with counting and classifying configurations of objects. We consider questions such as the following:

     In the process of examining these questions we find applications of many mathematical concepts: binomial coefficients, necklace counting, Pascal's triangle, the Fibonacci sequence, and Polya counting theory. Even the Catalan numbers make a brief appearance.

     FPTP (as we like to call it) is a quality hardcover book with 166 pages. It was first published in 1991, has recently been out of print, but is now available again. Go here to order a copy from Amazon.com.