313edo: Difference between revisions
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Added: table for the Madagascar[9] (or Barbados[9]) scale and its intervals/ratios/steps in 313-EDO. |
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| Line 12: | Line 12: | ||
(selected ratios) | (selected ratios) | ||
|- | |- | ||
|53 | |53 (53/313) | ||
|203.195 | |203.195 | ||
|[[9/8]] (-0.715 ¢) | |[[9/8]] (-0.715 ¢) | ||
|- | |- | ||
|12 | |12 (65/313) | ||
|249.201 | |249.201 | ||
|[[15/13]] (+1.46 ¢) | |[[15/13]] (+1.46 ¢) | ||
|- | |- | ||
|53 | |53 (118/313) | ||
|452.396 | |452.396 | ||
|[[13/10]] (-1,818 ¢) | |[[13/10]] (-1,818 ¢) | ||
|- | |- | ||
|12 | |12 (130/313) | ||
|498.403 | |498.403 | ||
|[[4/3]] (+0.358 ¢) | |[[4/3]] (+0.358 ¢) | ||
|- | |- | ||
|53 | |53 (183/313) | ||
|701.597 | |701.597 | ||
|[[3/2]] (-0.358 ¢) | |[[3/2]] (-0.358 ¢) | ||
|- | |- | ||
|12 | |12 (195/313) | ||
|747.604 | |747.604 | ||
|[[20/13]] (+1.818 ¢) | |[[20/13]] (+1.818 ¢) | ||
|- | |- | ||
|53 | |53 (248/313) | ||
|950.799 | |950.799 | ||
|[[26/15]] (-1.46 ¢) | |[[26/15]] (-1.46 ¢) | ||
|- | |- | ||
|12 | |12 (260/313) | ||
|996.805 | |996.805 | ||
|[[16/9]] (+0.715 ¢) | |[[16/9]] (+0.715 ¢) | ||
|- | |- | ||
|53 | |53 (313/313) | ||
|1200.000 | |1200.000 | ||
|[[Octave]] (2/1, ±0 ¢) | |[[Octave]] (2/1, ±0 ¢) | ||
Revision as of 15:31, 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")