MSGSS
Music, geometry, and topology
Music theory has a long interplay with math. Usually, this connection is made either through (1) algebra, where the notes are modeled as Z/12 and explain phenomena such as the circle of fifths, or (2) PDEs, where the equations explain exactly why we appreciate the exact intervals we do. We will instead proceed via (3) topology and geometry, where the notes live instead on the circle S^1, and the spaces of other chords live in more complicated spaces called orbifolds, which for dyads is the Mobius strip. This happens because of a “Pauli exclusion principle”, which also identifies orbifolds of chords with orbifolds of electrons in 1D spacetime. The mathematical formulation leaves all sorts of questions from music to math and vice-versa, some of which we will explore this in a rather interactive way.