Finding Frequencies

Hello everyone, I'm sure this question is really basic.(I hope :))

In the western cromatic scale there are 12 pitches in an
octave. To find a frequency by octaves divide by 2 for the lower and
multiply by 2 for the higher octave. So here is my question. How does
one find the frequencies of the pitches in between these octaves?
or if this octave was divided equally by any other number...what is
the equation? I have books on acoustics and sound but I still do not
understand this.

Thanks,
Ivan Serbulova

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--- In tuning@egroups.com, "Ivan S." <ivan_s_@h...> wrote:
> Hello everyone, I'm sure this question is really basic.(I hope :))
>
> In the western cromatic scale there are 12 pitches in an
> octave. To find a frequency by octaves divide by 2 for the lower and
> multiply by 2 for the higher octave. So here is my question. How
does
> one find the frequencies of the pitches in between these octaves?
> or if this octave was divided equally by any other number...what is
> the equation? I have books on acoustics and sound but I still do
not
> understand this.

In 12-tone equal temperament, going up n semitones means multiplying
the frequency by

2^(n/12).

Going down n semitones means multiplying by 2^(-n/12), or
equivalently, dividing by 2^(n/12).

In m-note equal temperament, the formula is 2^(n/m).