320edo

The 320 equal division divides the octave into 320 equal parts of precisely 3.75 cents each.

It 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.

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