148edo
| ← 147edo | 148edo | 149edo → |
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
| 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 (%) | +43 | +35 | -49 | -15 | +0 | +33 | -22 | +6 | +31 | -6 | -49 | |
| Steps (reduced) |
235 (87) |
344 (48) |
415 (119) |
469 (25) |
512 (68) |
548 (104) |
578 (134) |
605 (13) |
629 (37) |
650 (58) |
669 (77) | |