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',
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
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: