Algebraic Structures in Microtonal Music

TL;DR

This paper explores how group theory structures underpin microtonal music, specifically analyzing 24-tone systems and extending previous mathematical studies of musical structures.

Contribution

It introduces a detailed analysis of 24-tone microtonal music using group theory, extending prior work by Crans, Fiore, and Satyendra.

Findings

Identification of group-theoretic structures in 24-tone music

Mathematical interpretation of musical actions in microtonal systems

Extension of previous algebraic analyses in music theory

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.