I've seen the golden section applied to art, but does it apply to sound/timing as well? Just curious.
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2$\begingroup$ -1. This question may be inappropriate for mathoverflow. It's certainly mis-tagged. $\endgroup$– Kim MorrisonCommented Dec 12, 2009 at 19:27
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2$\begingroup$ Mario Livio's book on the golden ratio (amazon.com/Golden-Ratio-Worlds-Astonishing-Number/dp/0767908163) does a pretty good job of debunking most golden ratio myths. You should probably read that before asking such questions. $\endgroup$– Qiaochu YuanCommented Dec 12, 2009 at 19:31
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3$\begingroup$ And that book is "debunked" in the Notices article which Scott Morrison mentions in his answer. $\endgroup$– José Figueroa-O'FarrillCommented Dec 12, 2009 at 19:44
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8$\begingroup$ I dont think reading a basic book/paper in a subject is a requirement to asking a question about it. $\endgroup$– Gil KalaiCommented Dec 12, 2009 at 19:46
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3$\begingroup$ I don't think MO is a good place for this question. Its connection to mathematics is at best extremely tenuous. It may be more appropriate at some of the math forums listed in the FAQ. $\endgroup$– Anton GeraschenkoCommented Dec 13, 2009 at 1:52
4 Answers
Almost certainly not, seeing as the golden ratio has almost nothing to do with (classical) art and architecture anyway. See for example this review in the Notices.
Here's a page on its relation to music: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html#music
My guess this is not an appropriate question for MO, but being weekend and all...
I have heard of one approach to memorization which consists in repeating something in time intervals corresponding to the Fibonacci sequence. I did not find a reference, so take this with a grain of salt, though :)
I believe so Debussy and apparently others used the Fibonacci sequence in his work. See here for more information and references. Especially see the following: Roy Howat (1983). Debussy in Proportion: A Musical Analysis. Cambridge University Press. ISBN 0-521-31145-4. There is a preview of this book on Google books.