267edo
267edo is the equal division of the octave into 267 parts of 4.494382 cents each. In the 5-limit, it tempers out both 129140163/128000000 and 274877906944/274658203125, enabling it to support both gravity and luna temperaments. In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support gamelismic, hemimean and trimyna temperaments among others. In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and 117440512/117406179. In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, 4096/4095, 4225/4224 and 59535/59488.