328edo

← 327edo

328edo

329edo →

Prime factorization	23 × 41
Step size	3.65854 ¢
Fifth	192\328 (702.439 ¢) (→ 24\41)
Semitones (A1:m2)	32:24 (117.1 ¢ : 87.8 ¢)
Consistency limit	13
Distinct consistency limit	13

The 328 equal divisions of the octave (328edo), or the 328(-tone) equal temperament (328tet, 328et) when viewed from a regular temperament perspective, divides the octave into 328 equal parts of about 3.66 cents each.

Theory

328edo is enfactored in the 5-limit, with the same tuning as 164edo. It tempers out 2401/2400, 3136/3125, and 6144/6125 in the 7-limit, 9801/9800, 16384/16335 and 19712/19683 in the 11-limit, 676/675, 1001/1000, 1716/1715 and 2080/2079 in the 13-limit, 936/935, 1156/1155 and 2601/2600 in the 17-limit, so that it supports würschmidt and hemiwürschmidt, and provides the optimal patent val for 7-limit hemiwürschmidt, 11- and 13-limit semihemiwür, and 13-limit semiporwell.

328 factors into 2³ × 41, with subset edos 2, 4, 8, 41, 82, and 164.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5.7	2401/2400, 3136/3125, 589824/588245	[⟨328 520 762 921]]	-0.298	0.229	6.27
2.3.5.7.11	2401/2400, 3136/3125, 9801/9800, 19712/19683	[⟨328 520 762 921 1135]]	-0.303	0.205	5.61
2.3.5.7.11.13	676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647	[⟨328 520 762 921 1135 1214]]	-0.295	0.188	5.15
2.3.5.7.11.13.17	676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125	[⟨328 520 762 921 1135 1214 1341]]	-0.293	0.174	4.77

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	53\328	193.90	28/25	Hemiwürschmidt
1	117\328	428.05	2800/2187	Osiris
2	17\328	62.20	28/27	Eagle
2	111\328 (53\328)	406.10 (193.90)	495/392 (28/25)	Semihemiwürschmidt
8	136\328 (13\328)	497.56 (47.56)	4/3 (36/35)	Twilight
41	49\328 (1\328)	179.27 (3.66)	567/512 (352/351)	Hemicounterpyth