313edo: Difference between revisions

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-'''313EDO''' is the [[EDO|equal division of the octave]] into 313 parts of 3.83387 [[cent]]s each. It provides the [[Optimal_patent_val|optimal patent val]] for 11- and 13-limit [[Porwell_temperaments#Hemischis|hemischis temperament]] and the rank three [[Cataharry_family|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.
+The '''313 equal divisions of the octave''' ('''313edo''') is the [[EDO|equal division of the octave]] into 313 parts of 3.83387 [[cent]]s each.
-EDO is the 65th [[prime EDO]].
+== Theory ==
+edo 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.
-==Scales==
+edo is the 65th [[prime EDO]].
-*[[Madagascar19]]
-*Madagascar[9] (or Barbados[9]):
+=== Prime harmonics ===
-{| class="wikitable"
+{{Primes in edo|313}}
+== Scales ==
+* [[Madagascar19]]
+* Madagascar[9] (or Barbados[9]):
+{| class="wikitable right-2"
 |+Madagascar[9] (or Barbados[9]) scale
-!step
+! Step
-!cents
+! Cents
-!distance to the nearest JI interval
+! JI Interpretation
-(selected ratios)
 |-
-|53  (53/313)
+| 53 (53\313)
-|203.195
+| 203.195
-|[[9/8]] (-0.715 ¢)
+| [[9/8]] (-0.715 ¢)
 |-
-|12  (65/313)
+| 12  (65\313)
-|249.201
+| 249.201
-|[[15/13]] (+1.46 ¢)
+| [[15/13]] (+1.46 ¢)
 |-
-|53  (118/313)
+| 53 (118\313)
-|452.396
+| 452.396
-|[[13/10]] (-1,818 ¢)
+| [[13/10]] (-1,818 ¢)
 |-
-|12  (130/313)
+| 12  (130\313)
-|498.403
+| 498.403
-|[[4/3]] (+0.358 ¢)
+| [[4/3]] (+0.358 ¢)
 |-
-|53  (183/313)
+| 53  (183\313)
-|701.597
+| 701.597
-|[[3/2]] (-0.358 ¢)
+| [[3/2]] (-0.358 ¢)
 |-
-|12  (195/313)
+| 12  (195\313)
-|747.604
+| 747.604
-|[[20/13]] (+1.818 ¢)
+| [[20/13]] (+1.818 ¢)
 |-
-|53  (248/313)
+| 53  (248\313)
-|950.799
+| 950.799
-|[[26/15]] (-1.46 ¢)
+| [[26/15]] (-1.46 ¢)
 |-
-|12  (260/313)
+| 12  (260\313)
-|996.805
+| 996.805
-|[[16/9]] (+0.715 ¢)
+| [[16/9]] (+0.715 ¢)
 |-
-|53  (313/313)
+| 53  (313\313)
-|1200.000
+| 1200.000
-|[[Octave]] (2/1, ±0 ¢)
+| [[2/1]] (±0 ¢)
 |}
 == Music ==
-*[https://youtu.be/Gcgawrr2xao "Desert Island Rain"] by Sevish (uses a 53 12 53 12 53 12 53 12 53 scale, from his 2015 album "Rhythm and Xen")
+* [https://youtu.be/Gcgawrr2xao "Desert Island Rain"] by Sevish (uses a 53 12 53 12 53 12 53 12 53 scale, from his 2015 album "Rhythm and Xen")
 [[Category:Equal divisions of the octave]]
 [[Category:Prime EDO]]