On 11/12/05, Atte Andr? Jensen <atte.jensen@xxxxxxxxx> wrote: > Hi > > Suppose I have an A with a frequency of 440 hz. Which > formula should I use for transposing x semitones up/down? > So which frequency would the Bb a half step higher for > instance have? What about cents (1/100's of half steps)? 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.
