574edo
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Theory
574et tempers out 67108864/66976875, 78125000/78121827 and 2100875/2097152 in the 7-limit; 161280/161051, 1019215872/1019046875, 166698/166375, 131072/130977, 107495424/107421875, 5632/5625, 1890625/1889568, 160083/160000, 532400/531441 and 391314/390625 in the 11-limit.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.484 | +0.446 | -0.882 | +0.598 | -0.110 | -0.426 | -0.649 | +0.994 | -1.006 | +0.609 |
| Relative (%) | +0.0 | +23.2 | +21.3 | -42.2 | +28.6 | -5.2 | -20.4 | -31.0 | +47.5 | -48.1 | +29.1 | |
| Steps (reduced) |
574 (0) |
910 (336) |
1333 (185) |
1611 (463) |
1986 (264) |
2124 (402) |
2346 (50) |
2438 (142) |
2597 (301) |
2788 (492) |
2844 (548) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [65 -41⟩ | ⟨574 910] | -0.1527 | 0.1527 | 7.30 |
| 2.3.5 | [23 6 -14⟩, [42 -47 14⟩ | ⟨574 910 1333] | -0.1658 | 0.1260 | 6.03 |
| 2.3.5.7 | 10976/10935, 2100875/2097152, 78125000/78121827 | ⟨574 910 1333 1611] | -0.0459 | 0.2347 | 11.23 |
| 2.3.5.7.11 | 5632/5625, 10976/10935, 160083/160000, 166698/166375 | ⟨574 910 1333 1611 1986] | -0.0713 | 0.2160 | 10.33 |
| 2.3.5.7.11.13 | 2080/2079, 1001/1000, 4096/4095, 10976/10935, 166698/166375 | ⟨574 910 1333 1611 1986 2124] | -0.0544 | 0.2007 | 9.60 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 2 | 34\571 | 71.454 | 25/24 | Vishnu |