[microsound] 1.61803399

[Kim Cascone]

>
> Au contrare, mon frere...Bartok may not have had notes specific to the 
> use of the golden ratio, but there are musicologists who have analyzed 
> his works (Harry Halbreich, Erno Lendvai) and have noted its use in some 
> of his pieces - most notably the string quartets (my favorites), and the 
> sonata for 2 pianos and percussion.

true in that a couple of his pieces do make use of Fib/Phi but that was 
the exception rather than the rule in Bartok's work
actually, it was Lendvai's 'analysis' which have been discounted by 
Somfai, Tatlow and Griffiths as being dubious


0.6180340 is an *inverse* ratio and not the actual ratio of phi 
which is 1.61803399
and hence is NOT the number the fibonacci series converges to


take any two numbers 
for example: 7 and 9
sum them
then keep adding that sum to the prior number in the series

7+9=16
16+9=25
.../...
1186+1919=3105

until you get far into the series
say to about 3105
divide that number by 1919
you get 1.618030224
which as you can see starts to look a lot like phi which calculated to 20 places is


    **1.61803398874989484820...**