Group Action in Major Scale Intervals

Authors

Presenter(s)

Ava Franke

Comments

1:15-2:30, Kennedy Union Ballroom

Files

Description

This project explores the application of group theory to musical intervals within a major scale. By representing intervals as a subgroup of the integers modulo 12, we examine properties such as transitivity, faithfulness, isomorphism, homomorphism, rotations, and reflections. Our analysis reveals that musical intervals exhibit both cyclic and dihedral group structures. This establishes the integers modulo 12 as a symmetry group, allowing for understanding of note transformations in 12-tone equal temperament.

Publication Date

4-23-2025

Project Designation

Capstone Project

Primary Advisor

Atif A. Abueida, Richard Buckalew

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium, College of Arts and Sciences

Recommended Citation

"Group Action in Major Scale Intervals" (2025). Stander Symposium Projects. 4175.
https://ecommons.udayton.edu/stander_posters/4175