linuxaudio.org

On 11/12/05, Atte André Jensen  wrote:

quoted text
> 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.