Entry

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.