Music can be defined as the art (or science) of blending vocal and/or instrumental sounds to produce form and harmony. This paper is about the mathematics which underlies both music theory and how different instruments create sounds/notes. Consideration will be given to scales, intervals, and harmonics but not rhythm although it is a fundamental…

How should men and women be seated around a dinner table to maximize conversation between members of the opposite sex? What can be said about the distribution of points around two concentric circles? How are the white and black keys on the piano keyboard organized? What spin configuration in the Ising model minimizes energy? These four problems…