[linux-audio-user] transposing frequency

[Florian Schmidt]

On Sun, 11 Dec 2005 22:37:05 +0100
Atte André Jensen <atte.jensen at 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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