# 437edo

 ← 436edo 437edo 438edo →
Prime factorization 19 × 23
Step size 2.746¢
Fifth 256\437 (702.975¢)
Semitones (A1:m2) 44:31 (120.8¢ : 85.13¢)
Dual sharp fifth 256\437 (702.975¢)
Dual flat fifth 255\437 (700.229¢)
Dual major 2nd 74\437 (203.204¢)
Consistency limit 7
Distinct consistency limit 7

437 equal divisions of the octave (abbreviated 437edo or 437ed2), also called 437-tone equal temperament (437tet) or 437 equal temperament (437et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 437 equal parts of about 2.75 ¢ each. Each step represents a frequency ratio of 21/437, or the 437th root of 2.

## Theory

437edo is consistent to the 7-odd-limit, but the errors of harmonics 3 and 5 are quite large, giving us the option of treating it as either a full 11-limit temperament, or a 2.9.15.21.13.17 subgroup temperament.

Using the patent val, the equal temperament tempers out 2401/2400 and 4096000/4084101 in the 7-limit; 3025/3024, 41503/41472, 16384/16335, and 151263/151250 in the 11-limit.

### Odd harmonics

Approximation of odd harmonics in 437edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.02 +0.87 +0.51 -0.71 +0.63 -0.25 -0.85 -0.61 -0.95 -1.22 +0.56
Relative (%) +37.1 +31.7 +18.6 -25.7 +22.8 -9.2 -31.1 -22.1 -34.4 -44.3 +20.3
Steps
(reduced)
693
(256)
1015
(141)
1227
(353)
1385
(74)
1512
(201)
1617
(306)
1707
(396)
1786
(38)
1856
(108)
1919
(171)
1977
(229)

### Subsets and supersets

Since 437 factors into 19 × 23, 437edo contains 19edo and 23edo as subsets. 874edo, which doubles it, gives a good correction to the harmonic 3.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [-1385 437 [437 1385]] 0.1114 0.1114 4.06