86edo: Difference between revisions
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{{Infobox ET}} | |||
'''86edo''' is the [[EDO|equal division of the octave]] into 86 parts of 13.9535 cents each. 86 = 2 * 43, and the [[patent val]] is a [[contorted]] [[43edo|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675. | '''86edo''' is the [[EDO|equal division of the octave]] into 86 parts of 13.9535 cents each. 86 = 2 * 43, and the [[patent val]] is a [[contorted]] [[43edo|43]] in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it [[support]]s mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675. | ||
Revision as of 18:42, 4 October 2022
| ← 85edo | 86edo | 87edo → |
86edo is the equal division of the octave into 86 parts of 13.9535 cents each. 86 = 2 * 43, and the patent val is a contorted 43 in the 5-limit. In the 7-limit the patent val tempers out 6144/6125, so that it supports mohajira temperament. In the 11-limit it tempers out 245/242, 540/539 and 4000/3993, and in the 13-limit 144/143, 196/195 and 676/675. It provides the optimal patent val for the 13-limit 9&86 temperament tempering out 144/143, 196/195, 245/242 and 676/675.
86edo is closely related to the delta scale, which is the equal division of the classic diatonic semitone into eight parts of 13.9664 cents each.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.28 | +4.38 | -6.04 | +5.39 | +6.82 | -3.32 | +0.10 | +6.67 | -4.49 | +3.64 | -0.37 |
| Relative (%) | -30.7 | +31.4 | -43.3 | +38.6 | +48.9 | -23.8 | +0.7 | +47.8 | -32.2 | +26.1 | -2.6 | |
| Steps (reduced) |
136 (50) |
200 (28) |
241 (69) |
273 (15) |
298 (40) |
318 (60) |
336 (78) |
352 (8) |
365 (21) |
378 (34) |
389 (45) | |