# 1342edo

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 ← 1341edo 1342edo 1343edo →
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.