(credit: Claire Thompson via Flickr)

The annual meeting of the American Association for the Advancement of Science wrapped up last week in Washington, DC. One particularly enjoyable and informative highlight was a session on Mathematics and Music, which presented some work in progress by three prominent researchers in this area.

Noam Elkies of Harvard University presented the first talk, titled “The Entropy of Music: How Many Possible Pieces of Music Are There?” He illustrated his points with virtuosic turns on a keyboard. His basic idea was to apply concepts similar to those used in statistical mechanics and information theory to approach the question posed in his title. Elkies addressed how much a piece of music needs to change before it is a different piece, rather than a variation on the original. He also talked about how much information remains when the redundancy of repeated themes in a piece is accounted for.

Elkies did not address the problem of musical semantics in enough depth to make a compelling case that his statistical approach could generate real insight. But his lecture ended with an impressive performance, from memory, of a piece made from a baroque-style repeating arpeggiation where the root of the chord changed from measure to measure based not on a conventional harmonic progression, but on the digits of π. The result was an intriguingly disorienting congress of order with randomness, evoking something like an inebriated Buxtehude.