Mathematics and Music: Using Group Theory to Qualify N-Note Tonal Systems

In this senior thesis we examine the relationship between math, specifically group theory, and tonal music systems. In particular, we examine the 12-note tonal system of western music and identify some of its fundamental properties. From there we establish criteria that an alternative tonal system must meet to be considered an acceptable alternative to the 12-note tonal system. We build a mathematical model for n-note tonal systems using cyclic groups of order n. Ultimately we conclude that in order for an n-note tonal system to be acceptable, the system must be composed of n notes where n is divisible by 4, but not divisible by 8.