Harmonic Series Tunings

Harmonic series tunings include all those that are generated in terms of subsets of the harmonic or subharmonic series. The examples offered below are made to fit on a standard 12-tone keyboard, +/-99c with reference to 12 EDO.

Simple Harmonic Fragments
- 1-24, reduced to octave equivalence. This is the only 12-tone tuning in its category, because:
  1. Any set of 12 consecutive non-equivalent tones, starting on any number 1-13, yields a transposition of the same tuning.
  2. Starting on any tone greater than 13 produces an incomplete octave.
- If you're not concerned with maintaining octave equivalence, the number of possible tunings in the Simple Harmonic Fragment category is theoretically infinite, although after about harmonic 60, adjacent tones may not be perceived as belonging separate pitch classes (because they're less than 30 cents apart).
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Modified Harmonic Fragments - Early in my tuning experiments, I explored 12-tone, and sometimes as many as 19-tone, subsets "based on" odd numbers 13 through 31. By "base" I meant simply starting on that number and counting upward. Of course, a complete set in any octave range contains the same number of tones as the "base." If you want a 12-tone subset on any base greater than 12, you have to decide how to pare it down. Choosing which tones to omit and/or add was, admittedly, a bit arbitrary. My criteria were vague, but generally tended toward preserving simpler ratios overall. I later gave up that approach in favor of more clearly defined structures. But it was not altogether unfruitful.
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- Example: 19-tone base-19, modifed, with mp3 music.
- Example: 13-tone base-14, with mp3 music.
Primes only
Composites only
Simple Skip-sets
ASPluCT Series

2005 by David J. Finnamore
tuning@elvenminstrel.com

Tuning Methods

Harmonic Series Tunings