Menkhus, Hailey

An Exploration of Mathematical Structures within Music

As a double major in music performance and pure mathematics, Hailey has always been fascinated by the myriad ways one could connect the two subjects. On occasion, they would peruse the available writings on the subject. As the readings began piling up, the thought of a thesis project on the subject began to form. When not studying, Hailey can often be found at a coffee shop or walking the (self-proclaimed) “best math cat ever” Pi around the quad.

Major: Music Performance and Pure Mathematics

Senior, School of Music

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Abstract

This paper examines the relationships between music and mathematics specifically in the area of harmony and different tonal systems. To more closely examine this relationship it looks into four specific 12-tone tonal systems, Equal Temperament, Just Intonation, Mean-Tone, and Pythagorean Tuning, and one other system proposed by Harry Partch. The systems were examined in terms of music theory and in terms of mathematics. This paper compares these systems and points out the advantages and disadvantages of each of them. It ends with a case study of two recordings of Anaktoria by Iannis Xenakis applying the information from the previous sections.

Thesis Director: Davis Sher, Ph.D.

Department: Mathematical Sciences

Faculty Reader: Fredrick Gifford, Ph.D.

Department: School of Music

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Project Poster

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Presentation