148edo

← 147edo

148edo

149edo →

Prime factorization	22 × 37
Step size	8.10811 ¢
Fifth	87\148 (705.405 ¢)
Semitones (A1:m2)	17:9 (137.8 ¢ : 72.97 ¢)
Dual sharp fifth	87\148 (705.405 ¢)
Dual flat fifth	86\148 (697.297 ¢) (→ 43\74)
Dual major 2nd	25\148 (202.703 ¢)
Consistency limit	5
Distinct consistency limit	5

148edo is the equal division of the octave into 148 equal parts of 8.108 cents each, near a kleisma. It provides the optimal patent val for 11-limit echidnic temperament, the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the patent val tempers out 686/675 and 1029/1024, but an alternative mapping <148 235 344 416| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of 80edo for 7- and 13- limit bidia temperament, the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.

148 = 4 * 37, with divisors 2, 4, 37, 74.

Prime harmonics

Approximation of odd harmonics in 148edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+3.45	+2.88	-3.96	-1.21	+0.03	+2.72	-1.78	+0.45	+2.49	-0.51	-3.95
	Relative (%)	+42.6	+35.5	-48.9	-14.9	+0.4	+33.5	-22.0	+5.5	+30.7	-6.3	-48.7
Steps (reduced)		235 (87)	344 (48)	415 (119)	469 (25)	512 (68)	548 (104)	578 (134)	605 (13)	629 (37)	650 (58)	669 (77)