Ramsay
for the key of E, and is no longer F#135, but F#136 11/16; and so A# produced by 5 from F#136 11/16, as Euler has it, but A#683 7/16, A itself having been already raised a comma before it comes to be sharpened. So Euler's chromatic scale of 12 semitones is all wrong except F#, which, by accident, is right.1 [Scientific Basis and Build of Music, page 108]
Nature does give us the chromatic scale of 12 semitones, but she does so by a very different process.
We have, however, to thank Euler, perhaps, for starting the genesis of the scale from F instead of C, which he does without assigning any reason for it, and, it seems without seeing the deep significance of it; and since he does this as a mere matter of course, it would be interesting to know if he had not seen F thus used by some other, it may be some obscure genius who had insight to discern, more than push to put forth his finding - a case in which the world has doubtless sometimes been a loser. - Editor. [Scientific Basis and Build of Music, page 108]
See Also