437edo

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← 436edo437edo438edo →
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 2.746 ¢ 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 +32 +19 -26 +23 -9 -31 -22 -34 -44 +20
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

Scales