574edo

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← 573edo574edo575edo →
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

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.

Approximation of prime harmonics in 574edo
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

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
2 34\571 71.454 25/24 Vishnu