320edo

← 319edo

320edo

321edo →

Prime factorization	26 × 5
Step size	3.75 ¢
Fifth	187\320 (701.25 ¢)
Semitones (A1:m2)	29:25 (108.8 ¢ : 93.75 ¢)
Consistency limit	19
Distinct consistency limit	19

Theory

320et tempers out 65625/65536 (horwell) and 420175/419904 (wizma) in the 7-limit and 441/440, 8019/8000 and 9801/9800 in the 11-limit, and so supports the varuna temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the optimal patent val. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out 729/728, 1001/1000, 1575/1573, 4225/4224 and 6656/6655 in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to a rank-3 temperament.

Prime harmonics

Approximation of prime harmonics in 320edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.71	-0.06	-1.33	-0.07	-0.53	+0.04	-1.26	+1.73	+1.67	-1.29
	Relative (%)	+0.0	-18.8	-1.7	-35.4	-1.8	-14.1	+1.2	-33.7	+46.0	+44.6	-34.3
Steps (reduced)		320 (0)	507 (187)	743 (103)	898 (258)	1107 (147)	1184 (224)	1308 (28)	1359 (79)	1448 (168)	1555 (275)	1585 (305)

Divisors

Since 320 factors into 2⁶ × 5, 320edo has subset edos 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-507 320⟩	[⟨320 507]]	+0.2224	0.2224	5.93
2.3.5	[23 6 -14⟩, [-28 25 -5⟩	[⟨320 507 743]]	+0.1574	0.2036	5.43
2.3.5.7	65625/65536, 235298/234375, 321489/320000	[⟨320 507 743 898]]	+0.2361	0.2229	5.94
2.3.5.7.11	441/440, 8019/8000, 41503/41472, 65625/65536	[⟨320 507 743 898 1107]]	+0.1928	0.2173	5.80
2.3.5.7.11.13	441/440, 729/728, 1001/1000, 4225/4224, 6656/6655	[⟨320 507 743 898 1107 1184]]	+0.1845	0.1993	5.31
2.3.5.7.11.13.17	441/440, 729/728, 833/832, 1001/1000, 1089/1088, 4225/4224	[⟨320 507 743 898 1107 1184 1308]]	+0.1565	0.1968	5.25
2.3.5.7.11.13.17.19	441/440, 513/512, 729/728, 833/832, 969/968, 1001/1000, 1521/1520	[⟨320 507 743 898 1107 1184 1308 1359]]	+0.1741	0.1899	5.06

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (Reduced)	Cents (Reduced)	Associated Ratio	Temperaments
1	7\320	26.25	[-2 13 -8⟩	Sfourth (5-limit)
1	131\320	491.25	3645/2744	Fifthplus
1	157\320	588.75	45/32	Untriton (5-limit)
1	93\320	348.75	6144/3757	Hectosaros leap week
2	19\320	71.25	25/24	Narayana
5	133\320 (5\320)	498.75 (18.75)	4/3 (81/80)	Pental
8	133\320 (9\320)	566.25 (33.75)	104/75 (55/54)	Octowerck
10	19\320 (13\320)	71.25 (48.75)	25/24 (36/35)	Decavish
10	133\320 (5\320)	498.75 (18.75)	4/3 (81/80)	Decal
32	133\320 (3\320)	498.75 (11.25)	4/3 (?)	Bezique
80	99\320 (3\320)	371.25 (11.25)	2275/1836 (?)	Mercury
80	133\320 (1\320)	498.75 (3.75)	4/3 (245/243)	Octogintic