Music and mathematics are closely linked, and musical rhythm serves as an example of the practical use of different mathematical principles. It has recently been noted in fact that the mathematical regularity of certain music, such as that of Mozart, can be a spur to clearer thinking, at least for a short period of time after listening to a piece of music. Music has a psychological effect that is partly explained by its mathematical regularity, seen in the way music is divided into regular bars, beats, and different note lengths. Psychologists have discovered the importance of patterns in music and in aspects of human behavior. Music satisfies certain human needs for order and rhythm, and mathematics both explains and empowers this process.
Edward Rothstein writes about the relationship between music and mathematics and what he calls the inner life of both. He notes that both satisfied similar cravings in him as he studied mathematics and pursued music. He notes how musicians have often invoked mathematics to describe the orderliness of their art. Chopin stated that the fugue is like pure logic in music. Bach, an exponent of the fugue, was also fond of a related form, the canon, which he often treated as a mathematical puzzle. In this century, mathematical thinking has pervaded much musical thought, such as that of Schoenberg, with his serial system for manipulating the twelve tones of the scale. John Cage sought a lack of order in his music and yet used computer-generated random numbers for composing. Rothstein says that these connections are far from incidental and that they reveal something profound about the nature of both music and mathematics (Rothstein xv-xvi).
Teachout notes that what Rothstein is talking about is known as the philosophy of music. He says that philosophers of music seek the truth about music. Rothstein's approach is to illuminate the truth about music in terms of mathematics, a method that ha...