source file: m1493.txt
Date: Tue, 4 Aug 1998 09:18:06 -0500 (CDT)

Subject: Re: cents to frequency

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Tue, 4 Aug 1998, Mark Wilkes wrote:
> I'm looking for a formula which will let me convert from cents to hertz.
> Any ideas?

First of all, cents are a measure of interval size, which is to say a
frequency _ratio_, while Hertz are a measure of absolute frequency.
While we often use intervals and notes almost interchangably on the
list, it's understood that you would multiply the interval by whatever
the frequency is of the note you're using as your 1/1 or keynote.

That said, cents are just the log, base 2, of an intervals (frequency
ratio) times 1200.  So to go the other direction, just divide by 1200
and take the antilog base 2.  Of course, most calculators don't do
logarithms in base 2, only base e and base 10 (natural and common log).
So before you take the antilog you have to multiply by the log of 2 in
the same base to get the right answer.

Example: to convert 386 cents to a frequency ratio, divide 386 by 1200,
getting 0.321666...  Multiply by the log of 2--I'll use natural logs, so
the natural log of 2 is 0.693147...; multiplying that with the previous
number gives 0.2229623...  Then taking the antilog of that (base e
again--don't switch to common log now, or it'll screw stuff up!) gives 
1.24977..., which is very close to 1.25 or the frequency ratio of 5/4
that we all know 386 cents approximates.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Churchill? Can he run a hundred balls?"
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End of TUNING Digest 1493
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