# 1337edo

 ← 1336edo 1337edo 1338edo →
Prime factorization 7 × 191
Step size 0.897532¢
Fifth 782\1337 (701.87¢)
Semitones (A1:m2) 126:101 (113.1¢ : 90.65¢)
Consistency limit 13
Distinct consistency limit 13

1337 equal divisions of the octave (abbreviated 1337edo or 1337ed2), also called 1337-tone equal temperament (1337tet) or 1337 equal temperament (1337et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1337 equal parts of about 0.898 ¢ each. Each step represents a frequency ratio of 21/1337, or the 1337th root of 2.

1337edo is consistent to the 13-odd-limit, although the errors of harmonics 5, 7, and 13 are quite large. The equal temperament tempers out 2401/2400 (breedsma), 65625/65536 (horwell comma) and 703125/702464 (meter) in the 7-limit, so that it supports tertiaseptal. In the 11-limit it tempers out 3025/3024 and 41503/41472, so that it supports hemitert.

### Odd harmonics

Approximation of odd harmonics in 1337edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.085 -0.375 -0.389 -0.170 -0.233 -0.438 +0.437 +0.056 -0.430 +0.423 -0.002
Relative (%) -9.5 -41.8 -43.4 -19.0 -26.0 -48.8 +48.7 +6.2 -47.9 +47.2 -0.2
Steps
(reduced)
2119
(782)
3104
(430)
3753
(1079)
4238
(227)
4625
(614)
4947
(936)
5224
(1213)
5465
(117)
5679
(331)
5873
(525)
6048
(700)

### Subsets and supersets

Since 1337 factors into 7 × 191, 1337edo contains 7edo and 191edo as subsets.