71edo: Difference between revisions

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-The <b>71 equal temperament</b> or <b>71-EDO</b> divides the octave into 71 equal parts of 16.901 cents each. It tempers out 20480/19683 and 393216/390625 in the 5-limit, 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242 and 100/99 in the 11-limit, and 91/90 in the 13-limit. In the 13-limit it supplies the optimal patent val for the 29&amp;71 and 34&amp;37 temperaments.
+The '''71 equal temperament''' or '''71-EDO''' divides the octave into 71 equal parts of 16.901 cents each. It tempers out 20480/19683 and [[393216/390625]] in the [[5-limit]], 875/864, 4000/3969 and 1029/1024 in the [[7-limit]], 245/242 and [[100/99]] in the [[11-limit]], and 91/90 in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29&amp;71 and 34&amp;37 temperaments.
 edo is the 20th [[prime EDO]].
+{| class="wikitable center-all"
+|-
+|+ Approximation of primary intervals in 71 EDO
+|-
+! colspan="2" | Prime number
+! 3
+! 5
+! 7
+! 11
+! 13
+! 17
+! 19
+! 23
+|-
+! rowspan="2" | Error
+! absolute ([[cent|¢]])
+| +7.90
+| +2.42
+| -5.45
+| +6.43
+| +4.54
+| -3.55
+| +6.71
+| -2.92
+|-
+! [[Relative error|relative]] (%)
+| +46.8
+| +14.3
+| -32.2
+| +38.0
+| +26.9
+| -21.0
+| +39.7
+| -17.3
+|-
+! colspan="2" | Degree ([[octave reduction|reduced]])
+| 113 (42)
+| 165 (23)
+| 199 (57)
+| 246 (33)
+| 263 (50)
+| 290 (6)
+| 302 (18)
+| 321 (37)
+|}
 [[Category:Edo]]
 [[Category:Prime EDO]]