374edo
Theory
374et is only consistent to the 3-odd-limit. Omitting the harmonic 5, it is consistent to the 31-odd-limit. Using the patent val, it tempers out 40500000/40353607, 184528125/184473632, 5120/5103 and 2100875/2097152 in the 7-limit; 1073741824/1071794405, 161280/161051, 820125/819896, 2097152/2096325, 12005/11979, 2621440/2614689, 496125/495616, 1296000/1294139, 1265625/1261568, 200704/200475, 5767168/5764801, 1375/1372, 184549376/184528125, 1479016/1476225, 275653125/275365888, 41503/41472, 1362944/1361367, 166375/165888, 3294225/3294172 and 322102/321489 in the 11-limit. It supports quintakwai and quartemka.
Prime harmonics
| 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
374 factors into 2 × 11 × 17, with subset edos 2, 11, 17, 22, 34, and 187. 748edo, which doubles it, gives a good correction to the harmonic 5.
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 | 41503/41472, 20449/20412, 652288/649539, 10648/10647 | [⟨374 593 1050 1294 1384]] | -0.1401 | 0.1656 | 5.16 |
| 2.3.7.11.13.17 | 22528/22491, 2058/2057, 34816/34749, 8624/8619, 8281/8262 | [⟨374 593 1050 1294 1384 1529]] | -0.1546 | 0.1546 | 4.82 |
| 2.3.7.11.13.17.19 | 1729/1728, 2912/2907, 22528/22491, 2058/2057, 5929/5928, 34816/34749 | [⟨374 593 1050 1294 1384 1529 1589]] | -0.1622 | 0.1444 | 4.50 |