71edo: Difference between revisions

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-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.
+The '''71 equal temperament''' or '''71-EDO''' divides the octave into 71 equal parts of 16.901 cents each.
 edo is the 20th [[prime EDO]].
-{| class="wikitable center-all"
+== Theory ==
-|-
+{{Harmonics in equal|71}}
-|+ Approximation of [[prime interval]]s in 71 EDO
+[[Category:Equal divisions of the octave|##]]
-|-
+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.<!-- 2-digit number -->
-! 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:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Prime EDO]]