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

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