1092edo
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Prime factorization
22 × 3 × 7 × 13
Step size
1.0989¢
Fifth
639\1092 (702.198¢) (→213\364)
Semitones (A1:m2)
105:81 (115.4¢ : 89.01¢)
Consistency limit
13
Distinct consistency limit
13
| ← 1091edo | 1092edo | 1093edo → |
1092 equal divisions of the octave (1092edo), or 1092-tone equal temperament (1092tet), 1092 equal temperament (1092et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1092 equal parts of about 1.1 ¢ each.
1092edo is related to 364edo, but it differs in mapping for 5 and 11. Despite having large errors on harmonics, it is consistent in the 13-odd-limit. It is not consistent higher than that because its mapping for 15/8 is off by one step of a stack of 3/2 and 5/4. It provides the optimal patent val for the sextile temperament and the rank-3 loki temperament.
In higher limits, 1092edo is good at the 2.13.29.31.53.59 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.243 | +0.499 | +0.405 | +0.486 | +0.330 | +0.132 | -0.357 | +0.539 | +0.289 | -0.451 | +0.297 |
| relative (%) | +22 | +45 | +37 | +44 | +30 | +12 | -32 | +49 | +26 | -41 | +27 | |
| Steps (reduced) |
1731 (639) |
2536 (352) |
3066 (882) |
3462 (186) |
3778 (502) |
4041 (765) |
4266 (990) |
4464 (96) |
4639 (271) |
4796 (428) |
4940 (572) | |