The Mathematics in Music

I went to a very interesting performance today: “The Mathematics in Music: a concert-conversation with Elaine Chew”, in Killian Hall at MIT. Elaine is visiting Harvard for the year from USC, where she is a professor. She has an amazingly broad background that is super-pleasing… having studied math, computer science, music performance, and operations research.

Elaine performed four piano pieces, three of which were composed just for her, that use playful tricks in math as compositional inspiration. Some of these tricks included:

Composing with a meter determined by the numbers in a row (or column) of a completed Sudoku puzzle. This piece had a different time signature for every measure… 3/8, 1/8, 7/8, 9/8, and so on, accompanied by an entirely different sequence for the other hand. I was very impressed that anyone could play a piece like that. Listening in the audience, you want desperately to tap your foot to ground yourself in some kind of beat, but it’s impossible.
A bi-tonal piece: right hand and left play in different keys. Chew likened this to patting your head and rubbing your belly at the same time.
Genetic programming: The composer applies the idea of genetic mutations and substitutions on a familiar theme at the note and phrase level, which results in some jarring effects.

Elaine and her colleague, Alexandre Francois, developed a way of visualizing tonality called MuSA.RT, which accompanied her during two of the pieces. MuSA.RT shows (as a real-time accompaniment to MIDI-enabled piano) the changing notes and key of the piece along a spiral that is kind of like a 3-D version of the Tonnetz. More on the model in Elaine’s paper (PDF).