148edo

The 148 equal division divides 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.