911edo
| ← 910edo | 911edo | 912edo → |
911 equal divisions of the octave (abbreviated 911edo or 911ed2), also called 911-tone equal temperament (911tet) or 911 equal temperament (911et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 911 equal parts of about 1.32 ¢ each. Each step represents a frequency ratio of 21/911, or the 911th root of 2.
911edo is consistent in the 5-odd-limit, tempering out the vulture comma, and is also a suitable 2.3.5.13.19.23 system, with a comma basis {41600/41553, 59375/59319, 186875/186624, 253125/252928, 2167425/2166784}. Though inconsistent to the 11-limit, the patent val tunes the rank-3 temperament hanuman.
Aside from the patent val, there is a number of mappings to be considered. 911c val provides an additional 282 & 911c extension to the escapade temperament, and 911cde val is a tuning for the 11-limit arch temperament of the same family.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.131 | -0.364 | +0.658 | +0.261 | +0.603 | -0.132 | -0.234 | +0.423 | +0.182 | -0.528 | +0.046 |
| Relative (%) | +9.9 | -27.6 | +50.0 | +19.8 | +45.8 | -10.1 | -17.7 | +32.1 | +13.8 | -40.1 | +3.5 | |
| Steps (reduced) |
1444 (533) |
2115 (293) |
2558 (736) |
2888 (155) |
3152 (419) |
3371 (638) |
3559 (826) |
3724 (80) |
3870 (226) |
4001 (357) |
4121 (477) | |