Benquo comments on Harry Potter and the Methods of Rationality discussion thread, part 15, chapter 84 - Less Wrong Discussion
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Look up "equal temperament." There are 12 half-steps in an Octave, after each octave the frequency should double, and the simplest way to arrange it is to make each step a multiplication by h=2^(1/12) so that h^12=2.
Many people report that "natural" intervals like the 3:2 and 4:3 ratio, sound better than the equal temperament approximations, though I don't hear much of a difference myself.
It's really obvious if you expect any decent math to invoke exponents of 2.