An Exploration of Mathematical and Musical Connections

Authors

• Jeffrey Pair, California State University, Long BeachFollow
• Egypt Pannell, California State University, Long BeachFollow
• Dani Rodriguez, California State University, Long BeachFollow
• Jerico Sarmiento, California State University, Long BeachFollow

Abstract / Synopsis

In this paper, we present an introduction to some of the mathematical principles underlying music and mathematically develop a connection between the twelve musical notes and the group of integers modulo twelve. Our discussion touches on the simple mathematical ratios used to calculate consonant musical tones on the length of a string, the frequencies of tones and the method by which the twelfth root of two provides the foundation of equal temperament tuning, some algebraic connections to musical concepts like the euphonious circle of fifths, and a curious connection to twin primes.

Recommended Citation

Jeffrey Pair, Egypt Pannell, Dani Rodriguez & Jerico Sarmiento, "An Exploration of Mathematical and Musical Connections," Journal of Humanistic Mathematics, Volume 16 Issue 2 (July 2026), pages 176-190. . Available at: https://scholarship.claremont.edu/jhm/vol16/iss2/10

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