It is an approximation, and gets closer and closer, and it works if you start with ANY 2 positive numbers and make a Fibonacci-esque series from them. You could start with 2 and 417, then 419, 836, 1255, etc, and gradually the ratios of consecutive members of the series start to approach the golden ratio.
The golden ratio is defined by x=1/x + 1
when you take, for instance, 13/8, that is 1 + 5/8... or 21/13 is 1 + 8/13... 34/21 is 1 + 13/21, because of the way you obtain each number. Always 1 + the reciprocal of the previous ratio. So you will never quite reach the golden ratio, but you alternately go slightly higher and slightly lower, getting gradually closer.
On 6/29/06, Federico xaero@inwind.it wrote:
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Mathieu Bouchard wrote:
On Wed, 28 Jun 2006, padawan12 wrote:
Carey and Mouerlon are both known for fibonacci based syncopations. It seems there are indeed many useful rythmnic applications contained in the fib sequence, off the top of my head I haven't a clue why, one to research. This is most definitely not "house" though. :)
The Fibonacci sequence has this peculiarity that any two consecutive numbers are coprime.
and also: if you divide any fib number by its preceeding number, you get the "magic" number (the one of Pitagora's sectio aurea)
(this works better with numbers > 100)
try it yourself. here is an old post of mine: http://lists.puredata.info/pipermail/pd-list/2005-02/025822.html
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