9edt: Difference between revisions
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{| class="wikitable" | {| class="wikitable" | ||
! rowspan="2" | Steps | ! rowspan="2" | Steps | ||
! Size | ! colspan="2" | Size | ||
! Comparable intervals | ! rowspan="2" | Comparable intervals | ||
|- | |- | ||
!(in [[cent|¢]]) | !(in [[cent|¢]]) | ||
! | !in hekts | ||
|- | |- | ||
| 0 | | 0 | ||
| 0 | | colspan="2" | 0 | ||
| [[1/1]] | | [[1/1]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 211.328 | | 211.328 | ||
|144.444 | |||
| [[9/8]] (204) | | [[9/8]] (204) | ||
|- | |- | ||
| 2 | | 2 | ||
| 422.657 | | 422.657 | ||
|288.889 | |||
| [[9/7]] (435) | | [[9/7]] (435) | ||
|- | |- | ||
| 3 | | 3 | ||
| 633.985 | | 633.985 | ||
|433.333 | |||
| [[13/9]] (637) | | [[13/9]] (637) | ||
|- | |- | ||
| 4 | | 4 | ||
| 845.313 | | 845.313 | ||
|577.778 | |||
| [[13/8]] (841), [[5/3]] (884), [[8/5]] (814) | | [[13/8]] (841), [[5/3]] (884), [[8/5]] (814) | ||
|- | |- | ||
| 5 | | 5 | ||
| 1056.642 | | 1056.642 | ||
|722.222 | |||
| [[9/5]] (1018), [[11/6]] (1049) | | [[9/5]] (1018), [[11/6]] (1049) | ||
|- | |- | ||
| 6 | | 6 | ||
| 1267.970 | | 1267.970 | ||
|866.667 | |||
| [[27/13]] (1265) | | [[27/13]] (1265) | ||
|- | |- | ||
| 7 | | 7 | ||
| 1479.298 | | 1479.298 | ||
|1011.111 | |||
| [[7/3]] (1467) | | [[7/3]] (1467) | ||
|- | |- | ||
| 8 | | 8 | ||
| 1690.627 | | 1690.627 | ||
|1155.556 | |||
| [[8/3]] (1698) | | [[8/3]] (1698) | ||
|- | |- | ||
| 9 | | 9 | ||
| 1901.955 | | 1901.955 | ||
|1300 | |||
| [[3/1]] | | [[3/1]] | ||
|} | |} | ||
Revision as of 17:08, 10 April 2019
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 | 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 |