76edo

The 76 equal division 5-limit patent val is contorted (or enfactored) in the 5-limit, reflecting the fact that 76 = 4 * 19. In the 7-limit it tempers out 2401/2400 as well as 81/80, and so supports squares temperament. In the 11-limit, it tempers out 245/242 and 385/384, and supports the 24&26 temperament. In the 13-limit, it tempers out 105/104, 144/143, 351/350 and 364/363. While the 44\76 = 11\19 fifth is already flat, the 43\76 fifth, even flatter, is an almost perfect approximation to the hornbostel temperament POTE fifth, whereas its sharp fifth, 45\76, makes for an excellent superpyth fifth. Hence you can do hornbostel/mavila, squares/meantone, and superpyth all with the same equal division.

Using non-patent vals, 76edo provides an excellent tuning for teff temperament, a low complexity, medium accuracy, and high limit (17 or 19) temperament.