375edo

← 374edo

375edo

376edo →

Prime factorization	3 × 53
Step size	3.2 ¢
Fifth	219\375 (700.8 ¢) (→ 73\125)
Semitones (A1:m2)	33:30 (105.6 ¢ : 96 ¢)
Dual sharp fifth	220\375 (704 ¢) (→ 44\75)
Dual flat fifth	219\375 (700.8 ¢) (→ 73\125)
Dual major 2nd	64\375 (204.8 ¢)
Consistency limit	3
Distinct consistency limit	3

Theory

375et is only consistent to the 3-odd-limit and the harmonic 3 is about halfway between its steps. It can be used in the 2.9.5.7.13.17.19 subgroup. Using the patent val, it tempers out 40500000/40353607, 52734375/52706752 and 6144/6125 in the 7-limit; 100663296/100656875, 10333575/10307264, 166698/166375, 759375/758912, 151263/151250, 540/539, 4302592/4296875, 825000/823543, 5632/5625, 16808715/16777216, 1362944/1361367, 4108797/4096000, 67110351/67108864, 805255/802816 and 1771561/1769472 in the 11-limit. It supports aufic and persephone.

Odd harmonics

Approximation of odd harmonics in 375edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-1.16	+0.89	+0.77	+0.89	-0.92	+1.07	-0.27	+0.64	+0.09	-0.38	-1.07
	Relative (%)	-36.1	+27.7	+24.2	+27.8	-28.7	+33.5	-8.4	+20.1	+2.7	-11.9	-33.6
Steps (reduced)		594 (219)	871 (121)	1053 (303)	1189 (64)	1297 (172)	1388 (263)	1465 (340)	1533 (33)	1593 (93)	1647 (147)	1696 (196)

Subsets and supersets

375 factors into 3 × 5³ with subset edos 3, 5, 15, 25, 75, and 125. 1175edo, which triples it, gives a good correction to the harmonic 3 and is consistent to the 15-odd-limit.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[1189 -375⟩	[⟨375 1189]]	-0.1404	0.1404	4.39
2.9.5	[8 7 -13⟩, [97 -24 -9⟩	[⟨375 1189 871]]	-0.2208	0.1615	5.05
2.9.5.7	250047/250000, 26873856/26796875, 26985857024/26904200625	[⟨375 1189 871 1053]]	-0.2345	0.1418	4.43