348edo

← 347edo

348edo

349edo →

Prime factorization	22 × 3 × 29
Step size	3.44828 ¢
Fifth	204\348 (703.448 ¢) (→ 17\29)
Semitones (A1:m2)	36:24 (124.1 ¢ : 82.76 ¢)
Dual sharp fifth	204\348 (703.448 ¢) (→ 17\29)
Dual flat fifth	203\348 (700 ¢) (→ 7\12)
Dual major 2nd	59\348 (203.448 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

348et is consistent to the 7-odd-limit, but the error of the harmonic 3 is quite large, commending itself as a 2.9.5.7.11.13 subgroup temperament.

Using the patent val, it tempers out 2401/2400, 15625/15552, 390625/388962 and 156250000/155649627 and in the 7-limit. It supports quadritikleismic and subneutral.

Odd harmonics

Approximation of odd harmonics in 348edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+1.49	-0.11	+0.14	-0.46	+0.41	+0.85	+1.39	-1.51	-0.96	+1.63	-0.69
	Relative (%)	+43.3	-3.1	+4.0	-13.4	+11.8	+24.7	+40.2	-43.7	-27.9	+47.4	-20.0
Steps (reduced)		552 (204)	808 (112)	977 (281)	1103 (59)	1204 (160)	1288 (244)	1360 (316)	1422 (30)	1478 (86)	1529 (137)	1574 (182)

Subsets and supersets

Since 348 factors into 2² × 3 × 29, 348edo has subset edos 2, 3, 4, 6, 12, 29, 58, 87, 116, and 174. 696edo, which doubles it, gives a good correction to the harmonic 3.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-1103 348⟩	[⟨348 1103]]	+0.0728	0.0728	2.11
2.9.5	32805/32768, [7 52 -74⟩	[⟨348 1103 808]]	+0.0639	0.0608	1.76
2.9.5.7	32805/32768, 250047/250000, [7 9 -2 -11⟩	[⟨348 1103 808 977]]	+0.0355	0.0721	2.09
2.9.5.7.11	9801/9800, 32805/32768, 46656/46585, 151263/151250	[⟨348 1103 808 977 1204]]	+0.0049	0.0889	2.58
2.9.5.7.11.13	729/728, 1575/1573, 2200/2197, 32805/32768, 31250/31213	[⟨348 1103 808 977 1204 1288]]	-0.0343	0.1194	3.46