Harmony, rational and irrational numbers, and their relationships in music

Abstract

This lecture aims at introducing a general audience to the beautiful relationship between maths, physics and music. We will explore the evolution of ideas that led to the equal temperament tuning, the 12-note system which prevails in much music worldwide. The main characters in this story are the wave equation in a string and its pure solutions, which are given by waves with integral periods; the relations between them which are rational numbers; and finally, a twist in the plot where equal-tempered tuning is actually done with irrational numbers to achieve symmetry.