1131edo
| ← 1130edo | 1131edo | 1132edo → |
1131 equal divisions of the octave (abbreviated 1131edo or 1131ed2), also called 1131-tone equal temperament (1131tet) or 1131 equal temperament (1131et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1131 equal parts of about 1.06 ¢ each. Each step represents a frequency ratio of 21/1131, or the 1131st root of 2.
1131edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps. Otherwise, it has good approximations to harmonics 5, 7, 9, 13, making it suitable for a 2.9.5.7.13 subgroup interpretation.
Meanwhile using the patent val, the equal temperament tempers out 1600000/1594323 (amity comma) in the 5-limit, 2401/2400 (breedsma) and 4802000/4782969 (canousma) in the 7-limit, 3025/3024, 41503/41472, and 151262/151250 in the 11-limit. It provides the optimal patent val for amicable temperament, the rank-2 temperament that tempers out 2401/2400 and 1600000/1594323, and for canou temperament, the rank-3 temperament that tempers out 4802000/4782969.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.432 | -0.107 | -0.126 | -0.196 | +0.406 | -0.209 | +0.325 | +0.084 | -0.431 | +0.307 | -0.158 |
| Relative (%) | +40.7 | -10.1 | -11.8 | -18.5 | +38.3 | -19.7 | +30.7 | +8.0 | -40.6 | +28.9 | -14.9 | |
| Steps (reduced) |
1793 (662) |
2626 (364) |
3175 (913) |
3585 (192) |
3913 (520) |
4185 (792) |
4419 (1026) |
4623 (99) |
4804 (280) |
4968 (444) |
5116 (592) | |
Subsets and supersets
Since 1131 factors into 3 × 13 × 29, 1131edo has subset edos 3, 13, 29, 39, 87 and 377, and it shares the excellent approximation to harmonic 5 with 87edo.