1342edo

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← 1341edo1342edo1343edo →
Prime factorization 2 × 11 × 61
Step size 0.894188¢ 
Fifth 785\1342 (701.937¢)
Semitones (A1:m2) 127:101 (113.6¢ : 90.31¢)
Consistency limit 9
Distinct consistency limit 9

1342 equal divisions of the octave (abbreviated 1342edo or 1342ed2), also called 1342-tone equal temperament (1342tet) or 1342 equal temperament (1342et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1342 equal parts of about 0.894 ¢ each. Each step represents a frequency ratio of 21/1342, or the 1342nd root of 2.

1342edo is consistent to the 9-odd-limit, but there is a large relative delta for harmonics 7 and 11. Its notability lies in the utility as every other step of the full 13-limit monster – 2684edo, so it probably makes more sense as a 2.3.5.13 subgroup temperament. In the 5-limit it tempers out kwazy, [-53 10 16, senior [-17 62 -35, and egads, [-36 52 51; in the 2.3.5.13 subgroup it tempers out 140625/140608.

Prime harmonics

Approximation of prime harmonics in 1342edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.018 -0.025 -0.421 +0.396 +0.009 -0.335 +0.252 +0.340 -0.367 +0.419
Relative (%) +0.0 -2.0 -2.8 -47.0 +44.3 +1.0 -37.5 +28.1 +38.0 -41.0 +46.9
Steps
(reduced)
1342
(0)
2127
(785)
3116
(432)
3767
(1083)
4643
(617)
4966
(940)
5485
(117)
5701
(333)
6071
(703)
6519
(1151)
6649
(1281)

Subsets and supersets

Since 1342 factors as 2 × 11 × 61, 1342edo has subset edos 2, 11, 22, 61, 122, and 671. 2684edo, which doubles it, corrects the harmonics 7 and 11 to near-just qualities.