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.
Evidence from recent brain studies suggests that the pleasure in listening to music is derived at least partly from "pattern recognition and prediction," which would seem to lend support to Leonard Meyer's theory of musical expectation.
Does this have critical implications for non-developmental or non-teleological music? For music that is effectively static, or without recognizable patterns? Or for ad hoc music of the type which bears no relation to an established tradition or corpus, for which it is impossible for the listener to make any kind of prediction?
In The Aesthetics of Music, philosopher Roger Scruton points out one of the problems with thinking about music in terms of pattern recognition and prediction, expectation and frustration: "The pattern of expectations and fulfilments would change from hearing to hearing, to the point where, knowing the piece by heart, we should assign probability 1 to every event in it, and therefore cease to distinguish it from other pieces in the repertoire." (332)
"As an unfamiliar piece unfolds in time, our brains predict how it will continue to unfold," says Valorie Salimpoor, the neuroscientist who authored the study linked to above. Ostensibly it is the satisfaction of these predictions that gives us pleasure. Unfortunately, this tells us nothing about our understanding and enjoyment of a piece of music that we already know note for note, of which for musical Kenner as well as Liebhaber there are many.
Furthermore, the conclusions of this study suffers from a certain circularity. The study tells us that listening to music releases dopamine in the brain. The brain releases dopamine when we like something. So this study confirms that we like listening to music. This might strike some as less than earth-shattering news.
While Pinker's notion of music as "auditory cheesecake" may well explain its biological origins, it remains to be seen whether neuroscience will succeed in explaining our experience of music and its subjective meanings. Scruton expounds on his skepticism in this regard here.
