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

Theory

328edo is enfactored in the 5-limit, with the same tuning as 164edo, but the approximation of higher harmonics are much improved. It has a sharp tendency, with harmonics 3 through 17 all tuned sharp. The equal temperament 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.

Prime harmonics

Approximation of prime harmonics in 328edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.48	+1.49	+0.69	+1.12	+0.94	+1.14	-1.17	+0.99	-1.53	+0.09
	Relative (%)	+0.0	+13.2	+40.8	+18.8	+30.6	+25.6	+31.2	-32.0	+27.2	-41.8	+2.4
Steps (reduced)		328 (0)	520 (192)	762 (106)	921 (265)	1135 (151)	1214 (230)	1341 (29)	1393 (81)	1484 (172)	1593 (281)	1625 (313)

Subsets and supersets

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

Regular temperament properties

Template:Comma basis begin |- | 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 Template:Comma basis end

Rank-2 temperaments

Note: 5-limit temperaments supported by 164et are not listed.

Template:Rank-2 begin |- | 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) | Hemicountercomp Template:Rank-2 end Template:Orf