09 March 2012

Dum...dum..DUM-DI-dum, dumDUMdum-dum

Ray Girvan could do this topic (and many others) so much better justice than I, but...

Musical structures and conventions tend to stability within any given culture, yet nevertheless show drift over time and differ between cultures. They appear to be good examples of memes which have some roots in our neurobiology and others in convergent experiential conditioning.

Whilst looking for something else entirely, I just ran across a fascinating paper in PNAS which explores rhythm spectra across a corpus of Western classical music. Here is the abstract...

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/f β 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.

If this doesn't interest you, you've probably stopped reading already; if it does, the article reference is below

  • Daniel J. Levitina, Parag Chordiab & Vinod Menonc. "Musical rhythm spectra from Bach to Joplin obey a 1/f power law" in Proceedings of the National Academy of Sciences, March 6 2012, vol. 109 no. 10 3716-3720.


Julie Heyward said...

Why does this feel a little like sayig that a glass of Château Rieussec smells of ripe pineapple and honey because it contains ethyl butyrate and phenylethylic alcohols?

[Not that I've ever had a glass of Château Rieussec or know that they smell of ripe pineapple and honey, much less that it's because of the ethyl butyrate and phenylethylic alcohols -- I just read and repeat this stuff ... and I hope you appreciate how long it took me to type ethylyl butyrate and phenylethylic alcohol three times.]

Felix said...

I don't even know what Château Rieussec is! :-)

But, it's a fair point Julie.

I think this needs more than a reply comment ... I'll come back to it in a post of its own.