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.
The first four tritaves of odd harmonics, on C, notated using Richie's HEJI extensions.
| 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