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-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 156250000/155649627 and 2401/2400 in the 7-limit. It provides the optimal patent val for 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

348 factors into 2² × 3 × 29, with 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, [52 40 -77⟩	[⟨348 1103 808]]	+0.0639	0.0608	1.76
2.9.5.7	32805/32768, 250047/250000, 247669456896/247165842875	[⟨348 1103 808 977]]	+0.0355	0.0721	2.09
2.9.5.7.11	9801/9800, 32805/32768, 46656/46585, 250047/250000	[⟨348 1103 808 977 1204]]	+0.0049	0.0889	2.58
2.9.5.7.11.13	729/728, 1575/1573, 4096/4095, 67392/67375, 250047/250000	[⟨348 1103 808 977 1204 1288]]	-0.0343	0.1194	3.46