Musical Math or Mathematical Music?
What makes music sound good? for an intriguing answer to that question from Princeton professor Dmitri Tymoczko. Here is the abstract of his paper on Geometrical Music Theory: "Western musicians traditionally classify pitch collections by disregarding the effects of five kinds of musical transformation: octave shift, permutation, transposition, inversion, and cardinality change. Here we model these transformations mathematically, showing that they generate 32 equivalence classes of chords, 243 equivalence classes of chord sequences, and 32 families of geometrical quotient spaces, in which both chords and chord-sequences are represented. This model reveals connections between diverse music-theoretical concepts, yields new tools for analyzing music, unifies many existing geometrical representations of musical structure, and suggests an answer to a longstanding question about how to represent the similarity between chord-types."
