217edo: Difference between revisions

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-'''217edo''' is the [[EDO|equal division of the octave]] into 217 parts of 5.529954 [[cent]]s each. It is a strong 19-limit system, the smallest uniquely [[consistent]] in the 19-limit and consistent to the 21-limit. It tempers out the parakleisma, |8 14 -13&gt;, and the escapade comma, |32 -7 -9&gt; in the 5-limit; 3136/3125, 4375/4374, 10976/10935 and 823543/819200 in the 7-limit; 441/440, 4000/3993 and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079 in the 13-limit; 595/594, 833/832, 936/935, 1156/1155, 1225/1224, 1701/1700 in the 17-limit; 343/342, 476/475, 969/968, 1216/1215, 1445/1444, 1521/1520 and 1540/1539 in the 19-limit. It provides the [[optimal patent val]] for the [[Hemimean clan|arch temperament]] in the 11 and 13 limits.
+'''217EDO''' is the [[EDO|equal division of the octave]] into 217 parts of 5.529954 [[cent]]s each. It is a strong 19-limit system, the smallest uniquely [[consistent]] in the 19-limit and consistent to the 21-limit. It tempers out the parakleisma, |8 14 -13&gt;, and the escapade comma, |32 -7 -9&gt; in the 5-limit; 3136/3125, 4375/4374, 10976/10935 and 823543/819200 in the 7-limit; 441/440, 4000/3993 and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079 in the 13-limit; 595/594, 833/832, 936/935, 1156/1155, 1225/1224, 1701/1700 in the 17-limit; 343/342, 476/475, 969/968, 1216/1215, 1445/1444, 1521/1520 and 1540/1539 in the 19-limit. It provides the [[optimal patent val]] for the [[Hemimean clan|arch temperament]] in the 11 and 13 limits.
+{| class="wikitable"
+|+Approximation of primary intervals in 217 EDO
+! colspan="2" |Prime number
+!2
+!3
+!5
+!7
+!11
+!13
+!17
+!19
+!23
+!29
+!31
+|-
+! rowspan="2" |Error
+!absolute ([[Cent|¢]])
+| 0.0
+| +0.349
+| +0.783
+| -1.084
+| +1.677
+| +0.025
+| +0.114
+| +1.104
+| +2.140
+| -1.006
+| -0.335
+|-
+![[Relative error|relative]] (%)
+| 0.0
+| +6.31
+| +14.16
+| -19.60
+| +30.33
+| +0.46
+| +2.06
+| +19.97
+| +38.71
+| -18.19
+| -6.06
+|-
+! colspan="2" |Degree ([[Octave reduction|reduced]])
+|217 (0)
+|344 (127)
+|504 (70)
+|609 (175)
+|751 (100)
+|803 (152)
+|887 (19)
+|922 (54)
+|982 (114)
+|1054 (186)
+|1075 (207)
+|}
 [[Category:Equal divisions of the octave]]
 [[Category:Arch]]
 [[Category:Birds]]