It's an interesting exercise to look for equal divisions of the octave into n intervals that provide bettter approximations to (say) 3rd, 5th, 7th harmonics than n = 12 . WFL Continued fractions is one way to get better approximations. I think there is also a method that uses the Stern-Brocot tree but I can't find a reference. Heres some links on scales and continued fractions; http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html http://www.math.niu.edu/~rusin/uses-math/music/12 Stuart Anderson