> Actually an octave contains 12 notes. The frequency of each note
> is a factor of the twelfth root of two higher than the next lower note.
> When you look at just the "white keys" you are only looking at 7
> of the notes in the octave, and they are not evenly spaced in frequency

One of my earliest commissions was to devise an equally tempered
scale generator across all keys. Unfortunately it proved to be doable
but wieldy and impractical

I was asked to have a go because the frequencies arising from the
progressions in one key do not precisely equal the frequencies in
another key, it's all relative

http://en.wikipedia.org/wiki/Equal_temperament

For example, if you have your instruments tuned to a C scale, it can
sound quite dischordant (especially to the trained ear) or not "sweet"
if a piece is played on instruments with fixed tuning in another key. eg
an F in the C scale is not the same frequency as the F in the Bb scale,
so an F played on a Bb bassoon will be off compared with a piano F

Joe


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