362edo

← 361edo

362edo

363edo →

Prime factorization	2 × 181
Step size	3.31492 ¢
Fifth	212\362 (702.762 ¢) (→ 106\181)
Semitones (A1:m2)	36:26 (119.3 ¢ : 86.19 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

362edo is enfactored in the 3-limit and is only consistent to the 5-odd-limit, with two mappings possible for the 7-limit:

• ⟨362 574 841 1016] (patent val),
• ⟨362 574 841 1017] (362d).

Using the patent val, it tempers out 393216/390625 and [25 -48 22⟩ in the 5-limit; 4375/4374, 458752/455625 and 11529602/11390625 in the 7-limit, supporting barbados.

Using the 362d val, it tempers out 393216/390625 and [25 -48 22⟩ in the 5-limit; 5120/5103, 118098/117649 and 1959552/1953125 in the 7-limit.

Odd harmonics

Approximation of odd harmonics in 362edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.81	+1.53	-0.87	+1.61	-1.04	+1.46	-0.98	+1.12	+0.83	-0.06	+1.56
	Relative (%)	+24.4	+46.2	-26.2	+48.7	-31.4	+44.1	-29.4	+33.8	+25.0	-1.9	+47.1
Steps (reduced)		574 (212)	841 (117)	1016 (292)	1148 (62)	1252 (166)	1340 (254)	1414 (328)	1480 (32)	1538 (90)	1590 (142)	1638 (190)

Subsets and supersets

Since 362 factors into 2 × 181, 372edo has 2edo and 181edo as its subsets. 1448edo, which quadruples it, is a strong full 13-limit system.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5	393216/390625, [25 -48 22⟩	[⟨362 574 841]]	-0.3896	0.2822	8.51

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	117\362	387.85	5/4	Würschmidt

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct