Group Theory With Applications to Musical Keys

Student: Faith Njuare Dickson (Project, 2025)
Department of Mathematics
Cross Rivers University of Technology, Calabar, Cross Rivers State

Abstract

This interdisciplinary project bridges the gap between mathematics and music,
leveraging Group Theory to unravel the intricate relationships between musical keys.
By employing abstract algebraic concepts, we reveal the symmetries and patterns
underlying musical structures. Our research investigates the isomorphic connections
between group theory and musical keys, shedding light on the mathematical
foundations of harmony and composition.
Through a comprehensive analysis of musical keys and their corresponding group
structures, we demonstrate how mathematical concepts such as symmetry groups,
cyclic groups, and permutation groups inform music theory. This study provides
insights into the algebraic properties of musical transformations, modulations, and
chord progressions.
The findings of this project contribute to a deeper understanding of the intersections
between mathematics and music, offering implications for music composition,
analysis, and education. By formalizing the connections between group theory and
musical keys, we pave the way for further research in mathematical music theory and
its applications.

Keywords
Group theory musical Keys transposition inversion sharps keys flat keys.
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