Los Angeles Math Circle

6/1: The mathematics of musical scales (Olga Radko)

Why do some musical intervals sound pleasant, while others do not? Why do we have exactly 12 notes in an octave of a piano? Why arenít distances between frets on a flute or a guitar equal to each other? The answers, surprisingly, involve deep mathematical analysis and topics such as continued fractions, the problem of doubling the cube, and rational approximations.