653edo

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653edo

654edo →

Prime factorization	653 (prime)
Step size	1.83767 ¢
Fifth	382\653 (701.991 ¢)
Semitones (A1:m2)	62:49 (113.9 ¢ : 90.05 ¢)
Consistency limit	21
Distinct consistency limit	21

Theory

653edo is distinctly consistent to the 21-odd-limit, tempering out 68719476736000/68630377364883 (tricot comma) and [-20 -24 25⟩ (counterhanson comma) in the 5-limit; 2401/2400, 65625/65536, and 7656250000000/7625597484987 in the 7-limit; 3025/3024, 41503/41472, 496125/495616, and 1953125/1948617 in the 11-limit; 2080/2079, 4459/4455, 6656/6655, 10985/10976, and 170625/170368 in the 13-limit; 1225/1224, 2058/2057, 2431/2430, 2500/2499, 4914/4913, and 11271/11264 in the 17-limit; 1445/1444, 1521/1520, 1540/1539, 1729/1728, 3136/3135, 4200/4199, and 4394/4389 in the 19-limit.

Prime harmonics

Approximation of prime harmonics in 653edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.036	-0.403	-0.373	-0.016	-0.711	-0.208	+0.190	+0.210	-0.481	-0.166
	Relative (%)	+0.0	+1.9	-21.9	-20.3	-0.9	-38.7	-11.3	+10.3	+11.4	-26.2	-9.0
Steps (reduced)		653 (0)	1035 (382)	1516 (210)	1833 (527)	2259 (300)	2416 (457)	2669 (57)	2774 (162)	2954 (342)	3172 (560)	3235 (623)

Subsets and supersets

653edo is the 119th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[1035 -653⟩	[⟨653 1035]]	-0.0113	0.0113	0.61
2.3.5	[39 -29 3⟩, [-20 -24 25⟩	[⟨653 1035 1516]]	+0.0503	0.0875	4.76
2.3.5.7	2401/2400, 65625/65536, [7 -27 13 2⟩	[⟨653 1035 1516 1833]]	+0.0709	0.0838	4.56
2.3.5.7.11	2401/2400, 3025/3024, 65625/65536, 1953125/1948617	[⟨653 1035 1516 1833 2259]]	+0.0576	0.0795	4.33
2.3.5.7.11.13	2080/2079, 2401/2400, 3025/3024, 10985/10976, 65625/65536	[⟨653 1035 1516 1833 2259 2416]]	+0.0801	0.0882	4.80
2.3.5.7.11.13.17	1225/1224, 2058/2057, 2080/2079, 2401/2400, 4914/4913, 10985/10976	[⟨653 1035 1516 1833 2259 2416 2669]]	+0.0759	0.0823	4.48
2.3.5.7.11.13.17.19	1225/1224, 1445/1444, 1521/1520, 1540/1539, 2058/2057, 2080/2079, 2401/2400	[⟨653 1035 1516 1833 2259 2416 2669 2774]]	+0.0608	0.0867	4.72

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	21\653	38.59	45/44	Hemitert
1	42\653	77.18	256/245	Tertiaseptal
1	172/653	316.08	6/5	Counterhanson
1	308/653	566.00	81920/59049	Tricot