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How to convert a ratio to cents

Jul 6th, 2004 07:05
Fedrix Marc, Robert Walker, http://www.cpdiscount.com http://www.cpsilver.com http://www.cphandmade.com http://www.cpcustom-jewelry.com


How to convert a ratio or decimal to cents
When you add cents, you multiply ratios.
Let c be one cent as a ratio or decimal.
Since 1200 cents make one octave, we have:
c*c*...*c (1200 times) = 2.
In other words:
c^1200 = 2.
Here c works out as 1.00057778951.
Let's try to find 5/4 in cents.
Then we want x such that
c^x = 5/4.
So taking logs, we want
1200 log c =log 2
and
x log c = log (5/4)
so
x /1200 = log (5/4)/log 2
and so x = 1200 log (5/4)/log 2.
which works out at 
386.31371386483
To check this: 
c^386.31371386483 = 1.00057778951^386.31371386483 = 1.25 = 5/4
General formula is
value in cents = 1200 log(ratio)/log 2.