374edo

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← 373edo374edo375edo →
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 374-tone equal temperament (374tet), 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 of 374edo 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 +22 -40 +5 +17 +4 +29 +28 +19 +12 +13
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