9edt: Difference between revisions
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The '''9 equal division of 3''', the [[tritave]], divides it into 9 equal steps of size 211.328 [[cent]]s 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 [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]]. | The '''9 equal division of 3''', the [[tritave]], divides it into 9 equal steps of size 211.328 [[cent]]s 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 [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]]. | ||
Revision as of 19:43, 5 October 2022
| ← 8edt | 9edt | 10edt → |
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.
| Steps | Size | Comparable intervals | |
|---|---|---|---|
| (in ¢) | in hekts | ||
| 0 | 1/1 | ||
| 1 | 211.328 | 144.444 | 9/8 (204) |
| 2 | 422.657 | 288.889 | 9/7 (435) |
| 3 | 633.985 | 433.333 | 13/9 (637) |
| 4 | 845.313 | 577.778 | 13/8 (841), 5/3 (884), 8/5 (814) |
| 5 | 1056.642 | 722.222 | 9/5 (1018), 11/6 (1049) |
| 6 | 1267.970 | 866.667 | 27/13 (1265) |
| 7 | 1479.298 | 1011.111 | 7/3 (1467) |
| 8 | 1690.627 | 1155.556 | 8/3 (1698) |
| 9 | 1901.955 | 1300 | 3/1 |