313edo

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.

Scales

• Madagascar19

Madagascar[9] (or Barbados[9]) scale

Step	cents	distance to the nearest JI interval (selected ratios)
53	203.195	9/8 (-0.715 ¢)
12	249.201	15/13 (+1.46 ¢)
53	452.396	13/10 (-1,818 ¢)
12	498.403	4/3 (+0.358 ¢)
53	701.597	3/2 (-0.358 ¢)
12	747.604	20/13 (+1.818 ¢)
53	950.799	26/15 (-1.46 ¢)
12	996.805	16/9 (+0.715 ¢)
53	1200.000	Octave (2/1, ±0 ¢)

Music

• "Desert Island Rain" by Sevish (uses a 53 12 53 12 53 12 53 12 53 scale, from his 2015 album "Rhythm and Xen")