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313EDO is the equal division of the octave into 313 parts of 3.83387 cents each. It provides the optimal patent val for 11- and 13-limit hemischis temperament and the rank three madagascar temperament. It tempers out the schisma, 32805/32768, in the 5-limit; 6144/6125 and 19683/19600 in the 7-limit; 540/539, 5632/5625 and 8019/8000 in the 11-limit; 351/350 and 676/675 in the 13-limit.

313EDO is the 65th prime EDO.