574edo
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Prime factorization
2 × 7 × 41
Step size
2.09059¢
Fifth
336\574 (702.439¢) (→24\41)
Semitones (A1:m2)
56:42 (117.1¢ : 87.8¢)
Consistency limit
5
Distinct consistency limit
5
← 573edo | 574edo | 575edo → |
574 equal divisions of the octave (574edo), or 574-tone equal temperament (574tet), 574 equal temperament (574et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 574 equal parts of about 2.09 ¢ each.
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 | +23 | +21 | -42 | +29 | -5 | -20 | -31 | +48 | -48 | +29 | |
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 |