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 | 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]]. | ||
Following [[ | 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 [[ | 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]]. | ||
0 | {| class="wikitable" | ||
! Steps | |||
! Size <br/><small>(in [[cent|¢]])</small> | |||
! 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]] | |||
|} | |||
[[Category:Macrotonal]] | |||
[[Category:Edt]] | |||
[[ | |||
Revision as of 12:36, 2 October 2018
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 (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 |