313edo: Difference between revisions
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{| class="wikitable" | {| class="wikitable" | ||
|+Madagascar[9] (or Barbados[9]) scale | |+Madagascar[9] (or Barbados[9]) scale | ||
! | !step | ||
!cents | !cents | ||
!distance to the nearest JI interval | !distance to the nearest JI interval | ||
Revision as of 15:32, 20 June 2021
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
| step | cents | distance to the nearest JI interval
(selected ratios) |
|---|---|---|
| 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 | 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")