During rowing this morning I was catching up on old Quirks and Quarks segments and came across a great interview of Dan Levitin of McGill. Dan is a cognitive neuroscientist with a deep interest in music (he was a recording engineer for rock bands before becoming fascinated by the brain and wandering off to take a PhD in neurology - I recommend his book Your Brain on Music).
He analyzed a pile of classical musical scores and found a power law relationship in the rhythm. (note - one has to be very careful when calling something a power law - the notion is a bit abused, but that doesn't take away from this being interesting). Here is the paper (outside the firewall) - a bit of math but worth the read if you are into this sort of thing and the interview - which is at a non-technical level (8 min mp3)
Musical rhythm spectra from Bach to Joplin obey a 1/f power law
Edited* by Dale Purves, Duke University Medical Center, Durham, NC, and approved January 10, 2012 (received for review August 31, 2011)
Much of our enjoyment of music comes from its balance of predictability and surprise. Musical pitch fluctuations follow a 1/f power law that precisely achieves this balance. Musical rhythms, especially those of Western classical music, are considered highly regular and predictable, and this predictability has been hypothesized to underlie rhythm's contribution to our enjoyment of music. Are musical rhythms indeed entirely predictable and how do they vary with genre and composer? To answer this question, we analyzed the rhythm spectra of 1,788 movements from 558 compositions of Western classical music. We found that an overwhelming majority of rhythms obeyed a 1/fβ power law across 16 subgenres and 40 composers, with β ranging from ∼0.5–1. Notably, classical composers, whose compositions are known to exhibit nearly identical 1/f pitch spectra, demonstrated distinctive 1/f rhythm spectra: Beethoven's rhythms were among the most predictable, and Mozart's among the least. Our finding of the ubiquity of 1/f rhythm spectra in compositions spanning nearly four centuries demonstrates that, as with musical pitch, musical rhythms also exhibit a balance of predictability and surprise that could contribute in a fundamental way to our aesthetic experience of music. Although music compositions are intended to be performed, the fact that the notated rhythms follow a 1/f spectrum indicates that such structure is no mere artifact of performance or perception, but rather, exists within the written composition before the music is performed. Furthermore, composers systematically manipulate (consciously or otherwise) the predictability in 1/f rhythms to give their compositions unique identities.