Algebraic Structures in Microtonal Music
Abstract
We will discuss how certain group theory structures are found in music theory. Western music splits the octave into 12 equal tones called half-steps. We can take this division further and split the octave into 24 equal tones by splitting each half-step in two, called a quarter-step. By assigning each of these 24 notes a number, we can discuss musical actions mathematically. In this paper, we analyze 24-tone microtonal music and explore how musical and harmonic structures in this system can be interpreted in terms of group-theoretic structures. This work extends the study by Crans, Fiore, and Satyendra.
Cite
@article{arxiv.2506.17778,
title = {Algebraic Structures in Microtonal Music},
author = {Veronica Flynn and Carmen Rovi},
journal= {arXiv preprint arXiv:2506.17778},
year = {2025}
}
Comments
17 pages, 12 figures. The content should be accessible for students in a first course of Abstract Algebra. A musical background is not necessary. Comments welcome!