How can group theory be used to explain symmetries in classical music?

Abstract

This project will explore what symmetries exist in classical music and how we can express them using group theory, specifically group actions. Using mathematical objects and techniques from post-tonal music theory, we can describe aspects of tonal music theory. A few examples of objects from post-tonal music theory are transformation groups, pitch classes, and pitch set classes. This paper will define group actions which are relevant to symmetries in classical music, and analyze these actions using orbits, stabilizers, actions by subgroups, etc. The paper will also provide examples from classical pieces. Instead of a twelve tone model that is used in post-tonal theory, we will attempt to define and use a diatonic model for classical music, with a corresponding diatonic symmetry group.