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On Wed, Sep 2, 2009 at 11:54 AM, Alex Fink<[log in to unmask]> wrote:
> On Wed, 2 Sep 2009 09:04:10 -0700, Garth Wallace <[log in to unmask]> wrote:
>
>>I have given a bit of thought to music in my concultures in general.
>>The Kulaqil people use a just intonation tuning system based on ratios
>>between successive numbers in the Fibonacci sequence (1:1, 2:1, 3:2,
>>5:3, 8:5, 13:8).
>
> That's a little curious, esp. if the sequence continues further than you
> specified. Ratios of successive Fibonaccis converge, of course, to
> (1+sqrt(5))/2, or about 833 cents, i.e. these intervals become very close to
> each other relatively quickly as you continue (the comma between each
> successive pair is about 2.618 times smaller than the last). So the music
> would be built from a bunch of intervals mostly fairly close to each other.
Yeah, they regard the golden ratio as a sort of ideal interval (for
numerological reasons, partly), but in practice don't go past 13:8.
Their national instrument only has strings for the ratios I gave. Some
composers have experimented with 21:13, and some harps have been built
to accommodate it, but it's marginal at best. As a practical matter,
21:13 is a pain to tune, and the number of strings gets difficult to
manage.
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