364edo

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364edo

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Prime factorization	22 × 7 × 13
Step size	3.2967 ¢
Fifth	213\364 (702.198 ¢)
Semitones (A1:m2)	35:27 (115.4 ¢ : 89.01 ¢)
Consistency limit	21
Distinct consistency limit	21

Theory

364edo is consistent through the 21-odd-limit, tempering out 1600000/1594323 (amity comma) and [-65 0 28⟩; (28-5-comma) in the 5-limit; 65625/65536 (horwell), 390625/388962 (dimcomp), and 420175/419904 (wizma) in the 7-limit (supporting fifthplus and oquatonic); 1375/1372, 6250/6237, 19712/19683, and 41503/41472 in the 11-limit (as well as 9801/9800); 625/624, 1716/1715, 2080/2079, 2200/2197, and 14641/14625 in the 13-limit (as well as 4096/4095, 4225/4224, and 10985/10976); 715/714, 1089/1088, 1225/1224, 1275/1274, 2025/2023, and 8624/8619 in the 17-limit (as well as 2431/2430, 4914/4913, and 5832/5831); 1216/1215, 1331/1330, 1540/1539, and 1729/1728 in the 19-limit.

364 is divisible by, and thus contains sub-edos 1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182.

Prime harmonics

Approximation of prime harmonics in 364edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.24	-0.60	+0.40	-0.77	+0.13	+0.54	-0.81	+1.40	-1.01	-1.08
	Relative (%)	+0.0	+7.4	-18.2	+12.3	-23.3	+4.0	+16.4	-24.6	+42.3	-30.5	-32.7
Steps (reduced)		364 (0)	577 (213)	845 (117)	1022 (294)	1259 (167)	1347 (255)	1488 (32)	1546 (90)	1647 (191)	1768 (312)	1803 (347)

Miscellaneous properties

364edo can act as "pseudo-24024edo" in a sense that it can replicate being a multiple of 11edo, 12edo, 13edo and 14edo. It has 13 and 14 as its divisors, while at the same time supporting the Supermajor[11] scale from 91edo, which is a very precise temperament, and WorldCalendar[12] scale, which mimics 12edo. While it does not exactly replicate 11edo and 12edo, it comes close enough in harmonic parameters these EDos are sought after.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[577 -364⟩	[⟨364 577]]	-0.0766	0.0766	2.32
2.3.5	1600000/1594323, [-65 0 28⟩	[⟨364 577 845]]	+0.0350	0.1698	5.15
2.3.5.7	65625/65536, 390625/388962, 420125/419904	[⟨364 577 845 1022]]	-0.0098	0.1662	5.04
2.3.5.7.11	1375/1372, 6250/6237, 19712/19683, 41503/41472	[⟨364 577 845 1022 1259]]	+0.0366	0.1753	5.32
2.3.5.7.11.13	625/624, 1375/1372, 2080/2079, 2200/2197, 14641/14625	[⟨364 577 845 1022 1259 1347]]	+0.0245	0.1622	4.92
2.3.5.7.11.13.17	625/624, 715/714, 1089/1088, 1225/1224, 2025/2023, 2200/2197	[⟨364 577 845 1022 1259 1347 1488]]	+0.0022	0.1599	4.85
2.3.5.7.11.13.17.19	625/624, 715/714, 1089/1088, 1216/1215, 1225/1224, 1331/1330, 1729/1728	[⟨364 577 845 1022 1259 1347 1488 1546]]	+0.0257	0.1620	4.91

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	103\364	339.56	243/200	Amity / paramity
1	125\364	412.09	80/63	Witch
1	149\364	491.21	3645/2744	Fifthplus
1	151\364	497.80	4/3	Gary
2	57\364	187.91	49/44	Semiwitch
4	30\364	98.90	18/17	World calendar
13	151\364 (11\364)	497.80 (36.26)	4/3 (?)	Aluminium
26	151\364 (11\364)	497.80 (36.26)	4/3 (?)	Iron
28	151\364 (5\364)	497.80 (16.48)	4/3 (105/104)	Oquatonic
91	151\364 (3\364)	497.80 (3.30)	4/3 (176/175)	Protactinium

Scales

• WorldCalendar[12]: 31 30 30 31 30 30 31 30 30 31 30 30