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The Golden Ratio
Nov. 14th, 2006 08:18 amA recent WaPo article (registration required) on the timelessness of beauty reports on someone who created a "mask" of a human face based on the Golden Ratio. It seems to predict fairly well according to the WaPo, matching up with real faces throughout the ages that have been thought to be beautiful.
And of course, the Golden Ratio has long been used in art and architecture to create a feeling of harmonious proportion. It is a ratio, after all.
So I wondered... what about music?
Music is based on ratios. A note is a particular frequency of vibration in the air, say A = 440 Hz, to use the modern standard. The A that's an octave higher is double that frequency, 880 Hz, and the one that's an octave lower is half of it, 220 Hz. That's ratios of 1:2 and 2:1. The notes in between can also be expressed as ratios, although... well, it gets complicated after that, because there are different ways of picking the ratios. That's temperment, if you've ever wondered what the hell a "Well-Tempered Clavier" was. It doesn't mean the clavier was on Prozac; it means that the ratios between the notes were selected according to a "well-tempered" scheme (as opposed to, say, an "equal tempered" scheme).
The oldest tempering scheme is "Pythagorean," and it's based on nice whole number ratios, like 1:2, 2:3, and 3:4. 1.61803... does not figure into it.
A quick Google search goes a long way to convince me that the Golden Ratio just doesn't have a large impact on music, certainly not in the relationship of notes to one another. It may be used sometimes to structure a piece, say to place a climactic passage. And some modern musicians are playing around with it and the related Fibonacci sequence. But it doesn't seem to do much at all for making things sound beautiful, either in harmony or by melodic interval.
Beauty in music goes back to its underlying physics (it seems to me), and that physics of vibration will give you those nice whole number ratios that Pythagoras liked.
Not that there's any reason the Golden Ratio should apply to sound. It appeals to our sense of sight. Its frequent appearance in natural phenomena argues that it implies some spatial optimization: the best way to arrange flower petals or nautillus chambers. But again, that's got nothing to do with sound. So perhaps it's not all that surprising after all.
Hey, the title of the journal is "Random Thoughts." They can't all be random quotes.
And of course, the Golden Ratio has long been used in art and architecture to create a feeling of harmonious proportion. It is a ratio, after all.
So I wondered... what about music?
Music is based on ratios. A note is a particular frequency of vibration in the air, say A = 440 Hz, to use the modern standard. The A that's an octave higher is double that frequency, 880 Hz, and the one that's an octave lower is half of it, 220 Hz. That's ratios of 1:2 and 2:1. The notes in between can also be expressed as ratios, although... well, it gets complicated after that, because there are different ways of picking the ratios. That's temperment, if you've ever wondered what the hell a "Well-Tempered Clavier" was. It doesn't mean the clavier was on Prozac; it means that the ratios between the notes were selected according to a "well-tempered" scheme (as opposed to, say, an "equal tempered" scheme).
The oldest tempering scheme is "Pythagorean," and it's based on nice whole number ratios, like 1:2, 2:3, and 3:4. 1.61803... does not figure into it.
A quick Google search goes a long way to convince me that the Golden Ratio just doesn't have a large impact on music, certainly not in the relationship of notes to one another. It may be used sometimes to structure a piece, say to place a climactic passage. And some modern musicians are playing around with it and the related Fibonacci sequence. But it doesn't seem to do much at all for making things sound beautiful, either in harmony or by melodic interval.
Beauty in music goes back to its underlying physics (it seems to me), and that physics of vibration will give you those nice whole number ratios that Pythagoras liked.
Not that there's any reason the Golden Ratio should apply to sound. It appeals to our sense of sight. Its frequent appearance in natural phenomena argues that it implies some spatial optimization: the best way to arrange flower petals or nautillus chambers. But again, that's got nothing to do with sound. So perhaps it's not all that surprising after all.
Hey, the title of the journal is "Random Thoughts." They can't all be random quotes.
