## Mathematics and Music

From a purely computational point of view, there are several well-known applications of mathematics in music from basic arithmetic (to study such fundamental elements of music such as tempo and meter), to the golden ratio and Fibonacci numbers (to determine the number of notes in subsections of longer works), to Fourier series (to understand the nature of harmonics), and to logarithmic scales (used in some tuning systems). Indeed, problems associated with tuning also gives us an opportunity to investigate the concept of rational approximations to irrational numbers as well as provide us with an application of group theory.

However, modern dodecaphonic compositions make more profound use of theoretical mathematics, which expedites the incorporation of set theory, abstract algebra, number theory, and probability and statistics into music. In this talk, we intend to focus on some of these deeper relationships between mathematics and music.

A/V requirements: Laptop, LCD Projector