168edo

168edo is the equal division of the octave into 168 parts of 7.1429 cents each. It is closely related to 84edo, but the patent vals differ on the mapping for 11 and 17. It is contorted (or enfactored) in the 7-limit, tempering out 225/224, 1728/1715, and 78732/78125. Using the patent val, it tempers out 243/242, 2420/2401, 3025/3024, and 43923/43750 in the 11-limit; 351/350, 625/624, 640/637, 847/845, and 1573/1568 in the 13-limit; 375/374, 561/560, 715/714, 891/884, 936/935, and 1331/1326 in the 17-limit. Using the 168d val, it tempers out 3136/3125, 19683/19600, and 33075/32768 in the 7-limit; 243/242, 385/384, 3773/3750, and 9801/9800 in the 11-limit. Stacking alternating steps of 43 and 53 produces an optimal Whitewood [14] scale of 19 5 19 5 19 5 19 5 19 5 19 5 19 5 that spreads the overall flatness evenly between the major and minor thirds.