RE: [microsound] Fibonacci in music

[Paulo Mouat <microsound@xxxxxxxxxxxx>]

> From: Richard Zvonar
> P.S. The Fibonacci series (1, 1, 2, 3, 5, 8, 13, 21...) is 
> formed by adding two consecutive terms to derive the next 
> term in the series (therefore 13 + 21 gives the next term 
> 34). The Golden Mean (or Golden Proportion or Ratio) may be 
> approximated by dividing consecutive Fibonacci numbers (13/21 
> = 0.61905..., 21/13 = 1.61538...).

The division of two consecutive terms of a sequence with any two natural
numbers as starting points and where terms are determined through addition
of the two previous terms will eventually tend to the golden section.  This
is not intrinsic to the Fibonacci series and is probably the reason why the
golden section is widely found in nature.

> The higher up the series the closer the approximation to the 
> proportion, which is commonly represented as "phi" and equals 
> 1.6180339887499... or -0.61803398874989...  For more details 
> and an explanation of why phi has two values, see:
> 
> http://www.vashti.net/mceinc/golden.htm

A more complete description may be found at

http://mathworld.wolfram.com/GoldenRatio.html


//p
http://www.interdisciplina.org/00.0/


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