313edo
The 313 equal divisions of the octave (313edo) is the equal division of the octave into 313 parts of 3.83387 cents each.
Theory
313edo provides the optimal patent val for 11- and 13-limit hemischis temperament and the 13-limit rank-3 temperaments madagascar and hera. It tempers out the schisma, 32805/32768, in the 5-limit; 6144/6125 and 19683/19600 in the 7-limit; 540/539, 5632/5625, 8019/8000 and 16384/16335 in the 11-limit; 351/350, 676/675, 729/728, 1001/1000, 2080/2079 and 4096/4095 in the 13-limit.
313edo is the 65th prime EDO.
Prime harmonics
Script error: No such module "primes_in_edo".
Scales
- Madagascar19
- Madagascar[9] (or Barbados[9]):
| Step | Cents | JI Interpretation |
|---|---|---|
| 53 (53\313) | 203.195 | 9/8 (-0.715 ¢) |
| 12 (65\313) | 249.201 | 15/13 (+1.46 ¢) |
| 53 (118\313) | 452.396 | 13/10 (-1,818 ¢) |
| 12 (130\313) | 498.403 | 4/3 (+0.358 ¢) |
| 53 (183\313) | 701.597 | 3/2 (-0.358 ¢) |
| 12 (195\313) | 747.604 | 20/13 (+1.818 ¢) |
| 53 (248\313) | 950.799 | 26/15 (-1.46 ¢) |
| 12 (260\313) | 996.805 | 16/9 (+0.715 ¢) |
| 53 (313\313) | 1200.000 | 2/1 (±0 ¢) |