The Dialogue between Mathematics and Music: the Mathematical Analysis of Mozart's Music and its Effect on the Listener

Author: Jui-Lin Ong(Department of Applied Chemistry,Fooyin University)

Vol.&No.：Vol. 49, No.2
Date：October 2004
Pages：85-100
DOI：10.6210/JNTNULL.2004.49(2).05

Abstract：

The roots of mathematics are closely connected with those of music. The rational structure or system of mathematics is implicitly aesthetic, given its properties of order and harmony; in this sense it is musical, even though there is no transmission of sound. By the same token, music-even though in it there are no explicit digits or other mathematical signs-is implicitly mathematical in and through its amplitude, frequency, quality, rhythm, melody, form and style. The present investigation sets out to describe Mozart's music mathematically. This structural analysis of the music and its effects on the listener therefore includes: examples of the application of mathematics to music, the measurement of the effects of Mozart's music, the application of the golden ratio to Mozart's musical structure, and an analysis of the application of mathematics to the musical structure of Mozart concertos: specifically the first movements of No. 3 (G major), 4 (D major) and 5 (A major). These analyses strongly suggest the close correlation between mathematics and music. This study thus aims to promote the integration of technology and the humanities by opening a dialogue between music and mathematics.

Keywords：mathematics, music, golden ratio, Mozart, concerto

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