9edt
The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding interval for 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187. 9edt is the third no-twos zeta peak edt.
Following 4edt, this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to 7edo in diatonic music.
This scale is also related to 17edo by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1. 9edt is exactly every third step of 27edt.
| Steps | Size (in ¢) |
Comparable intervals |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 211.328 | 9/8 (204) |
| 2 | 422.657 | 9/7 (435) |
| 3 | 633.985 | 13/9 (637) |
| 4 | 845.313 | 13/8 (841), 5/3 (884), 8/5 (814) |
| 5 | 1056.642 | 9/5 (1018), 11/6 (1049) |
| 6 | 1267.970 | 27/13 (1265) |
| 7 | 1479.298 | 7/3 (1467) |
| 8 | 1690.627 | 8/3 (1698) |
| 9 | 1901.955 | 3/1 |