11 Dec
2005
11 Dec
'05
6:13 p.m.
On Sun, 11 Dec 2005 22:37:05 +0100
Atte André Jensen <atte.jensen(a)gmail.com> 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)?
One half step in equal tempered tuning is the frequency ratio of
1:2^(1/12)
a.k.a the twelfth root of two. So, for an octave you get:
1:(2^(1/12) * 2^(1/12) * .... * 2^(1/12)) = 1:(2^(1/12))^12 = 1:2
:)
And for any interval of n semitones you get a frequency ratio of:
1:(2^(1/12))^n = 1:2^(n/12)
Sorry, i don't know about cents. It might be the 100th root of 2^(1/12)
a.k.a 1:(2^(1/12))^(1/100) = 1:2^(1/1200). So when you go 1200 cents
(1:2^(1200/1200) = 1:2) you have again the octave. No guarantee on that
though.
Regards,
Flo
--
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