# 1092edo

 ← 1091edo 1092edo 1093edo →
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

1092 equal divisions of the octave (abbreviated 1092edo or 1092ed2), also called 1092-tone equal temperament (1092tet) or 1092 equal temperament (1092et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1092 equal parts of about 1.1 ¢ each. Each step represents a frequency ratio of 21/1092, or the 1092nd root of 2.

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 as 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

Approximation of odd harmonics in 1092edo
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 (%) +22.1 +45.5 +36.8 +44.2 +30.1 +12.0 -32.5 +49.1 +26.3 -41.1 +27.0
Steps
(reduced)
1731
(639)
2536
(352)
3066
(882)
3462
(186)
3778
(502)
4041
(765)
4266
(990)
4464
(96)
4639
(271)
4796
(428)
4940
(572)

### Subsets and supersets

Since 1092 factors into 22 × 3 × 7 × 13, 1092edo has subset edos 2, 3, 4, 6, 7, 12, 13, 14, 21, 26, 28, 39, 42, 52, 78, 84, 91, 156, 182, 273, 364, and 546.