From: Pete Leigh <pete.leigh@...>

To: A list for linux audio users <linux-audio-user@...>

Date: Sunday, December 11, 2005 - 10:24 pm

On 11/12/05, Atte André Jensen wrote:

If A is 440 then the A an octave up (call it A') is 2 x 440 = 880.

To go from A to A' in 12 equal steps (we're assuming equal

temperament), we need an interval, call it I, so that multiplying

by I will give the frequency a semitone higher, and doing that

12 times will go up one octave:

A x I x I x I x I x I x I x I x I x I x I x I x I = A',

so, rearranging:

I^12 = A' / A

but A' / A = 440/880 = 2.

So I^12 = 2.

So I is the twelfth root of 2. Multiply the frequency of a note by

that and you get the frequency a semitone higher. The twelfth

root of two is approximately 1.05946309436, or, as kcalc has

it: 1.059463094359295264523454505045663154306

( http://en.wikipedia.org/wiki/Twelfth_root_of_two )

To go up one cent, the same logic indicates you'd multiply by

the 1,200th root of two, since there are 100 cents in a semitone.

kcalc tells me it's:

1.000577789506554859250142541782224725466

( http://en.wikipedia.org/wiki/Cent_%28music%29 )

- Pete.

Re: [linux-audio-user] transposing frequency, Pete Leigh, (Sun Dec 11, 10:24 pm)

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