1092edo

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← 1091edo1092edo1093edo →
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.