Tuning Methods

Odd Limit O- & U-tonal Tunings

Odd-limit otonal tunings are those comprised of ratios with numerators, with all powers of 2 removed, no greater than the limit, and which have octave equivalent denominators that do not exceed the odd limit. The utonal tunings simply invert each ratio (and multiply by appropriate powers of 2). These pages address only 12-tone, octave-repeating versions. An octave-repeating, odd-limit, strictly otonal or utonal tuning will have a number of tones equal to (the limit + 1)/2.

  • 11-limit
  • 13-limit
  • 15-limit
  • 17-limit
  • 19-limit
  • 21-limit
  • 23-limit

Copyright 2004 by David J. Finnamore
All rights reserved.