Relationship of Music and Mathematics

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

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egan in Egypt out of the need for surveying the annual flooding of the Nile; Aristotle argued instead that Egyptian mathematics grew out of the speculations of the priestly leisure class. . . Music was, by its nature, most probably the possession of all people and existed at even the most primitive level, but its highest systematic and rational cultivation must also have been reserved for the priestly classes, among whom it became part of ritual--and so possessed a special place in early conceptions of the universe. In fact, the need for specialized knowledge in the practice of mathematics and the practice of music may have conferred on both a prestigious position (Rothstein 14). Both mathematics and music involve abstract intellectual patterns which Anthony Storr notes are satisfying to human beings and engage human feelings. He notes that an examination of pure music could lead to a description of it as abstract patterns of tones with no obvious relationship either with the external world or with mental processes, but this is not the case: "Mathematics and music have often been represented as similar, because both are concerned with linking together abstractions, with making patterns of ideas" (Storr 177-178). Storr cites

Category: Arts - R