574edo

← 573edo

574edo

575edo →

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