# 374edo

 ← 373edo 374edo 375edo →
Prime factorization 2 × 11 × 17
Step size 3.20856¢
Fifth 219\374 (702.674¢)
Semitones (A1:m2) 37:27 (118.7¢ : 86.63¢)
Consistency limit 3
Distinct consistency limit 3

374 equal divisions of the octave (abbreviated 374edo or 374ed2), also called 374-tone equal temperament (374tet) or 374 equal temperament (374et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 374 equal parts of about 3.21 ¢ each. Each step represents a frequency ratio of 21/374, or the 374th root of 2.

## Theory

374et is inconsistent to the 5-odd-limit since harmonic 5 is about halfway between its steps. Omitting the harmonic 5, it is consistent to the 31-odd-limit.

Using the patent val, the equal temperament tempers out 5120/5103, 1071875/1062882, 1500625/1492992, 2100875/2097152, and 9765625/9680832 in the 7-limit; 1375/1372, 4375/4356, 12005/11979, and 41503/41472 in the 11-limit. It supports quintakwai and quartemka.

### Prime harmonics

Approximation of prime harmonics in 374edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.72 -1.29 +0.16 +0.55 +0.11 +0.93 +0.88 +0.60 +0.37 +0.42
Relative (%) +0.0 +22.4 -40.1 +4.9 +17.3 +3.6 +28.9 +27.5 +18.8 +11.5 +13.1
Steps
(reduced)
374
(0)
593
(219)
868
(120)
1050
(302)
1294
(172)
1384
(262)
1529
(33)
1589
(93)
1692
(196)
1817
(321)
1853
(357)

### Subsets and supersets

Since 374 factors into 2 × 11 × 17, 374edo has subset edos 2, 11, 17, 22, 34, and 187. 748edo, which doubles it, gives a good correction to the harmonic 5, but its approximation of harmonic 3 has drifted too far to render it inconsistent in the 9-odd-limit.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [593 -374 [374 593]] -0.2268 0.2267 7.07
2.3.7 [4 -22 11, [51 -18 -8 [374 593 1050]] -0.1699 0.2018 6.29
2.3.7.11 41503/41472, 1362944/1361367, 70493667328/70027449129 [374 593 1050 1294]] -0.1675 0.1748 5.45
2.3.7.11.13 10648/10647, 20449/20412, 41503/41472, 652288/649539 [374 593 1050 1294 138 4]] -0.1401 0.1656 5.16
2.3.7.11.13.17 2058/2057, 8281/8262, 8624/8619, 22528/22491, 34816/34749 [374 593 1050 1294 1384 1529]] -0.1546 0.1546 4.82
2.3.7.11.13.17.19 1729/1728, 2058/2057, 2912/2907, 5929/5928, 22528/22491, 34816/34749 [374 593 1050 1294 1384 1529 1589]] -0.1622 0.1444 4.50