The Math of Music: A Look at Musical Group Theory

I will explore a distinct connection between music theory and group theory.  The focus will be on some particular sets within music theory and how to prove that these sets are groups.  My presentation will consist of a brief overview of the aspects of group theory necessary for analyzing these sets as well as some basic music theory.  I will then delve into the connection between the two.  The three different music theory sets that will be focused on in this presentation are the Transposition and Inversion Set, a modified version of the Transposition and Inversion Set and the Twelve-Tone Set.  In reality only two of these sets are groups and I will explain which ones those are and why.  These groups are typically not used intentionally during composition but can be found in many pieces of music.