TOH
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An n-TOH (pronounced /toʊ/, like "toe") stands for the nth tritave of odd harmonics.
TOHs reject factors of 2 in JI ratios, having a prime minimum of 3 (similar to Bohlen-Pierce).
It is similar in concept to an octave of the harmonic series, a special case of a mode of the harmonic series where the mode is a power of 2. However, here the tuning spans (and repeats at) the tritave, and includes only odds.
| step | 0 | 1 |
|---|---|---|
| Pitch | (1/1) | 3/1 |
| Reduced | (1/1) | 3/1 |
| Step | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Pitch | (3/3) | 5/3 | 7/3 | 9/3 |
| Reduced | (1/1) | 5/3 | 7/3 | 3/1 |
| Step | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| Pitch | (9/9) | 11/9 | 13/9 | 15/9 | 17/9 | 19/9 | 21/9 | 23/9 | 25/9 | 27/9 |
| Reduced | (1/1) | 11/9 | 13/9 | 5/3 | 17/9 | 19/9 | 7/3 | 23/9 | 25/9 | 3/1 |
Listening
https://soundcloud.com/cmloegcmluin/sets/third-tritave-odd-harmonics