Thursday, May 9, 2013

The Golden Ratio in Improvised Music

Analysts such as Ernő Lendvai and Roy Howat have claimed to discover signs of the golden ratio in compositions by Bartók and Debussy, respectively. It has also been discussed with regard to Mozart's piano sonatas, and elsewhere. But is the golden section strictly an architectural principle, or could it be a natural, emergent property of music? If the latter is true, one might expect to find it in purely improvised music. 

This improvisation by trombonist Ben Gerstein is approximately 115 seconds long. The ostensible climax occurs on G3, the note with the highest pitch, greatest intensity, and longest duration of the entire piece, at roughly 71 seconds in. The ratio of the duration of the whole improvisation to the duration preceding the climax, then, is 115/71, or 1.6197... This is very close to the golden ratio value of 1.6180... The ratio of the duration of the piece preceding the climax to the duration following the climax is 71/44, or 1.6136... Since the ratios of the larger and smaller durations are not exactly equal, they do not precisely represent the golden proportion. Nonetheless, the climax of Gerstein's improvisation is a remarkably close approximation of the sectio aurea

Is this example a solitary coincidence, or is it often the case that a proper sense of balance in a piece of music will spontaneously approximate the golden ratio? 

A more extensive analysis of Gerstein's improvised music can be found here.

No comments:

Post a Comment