73edo: Difference between revisions

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-'''73-EDO''' divides the octave into 73 equal parts of 16.438 [[cent]]s each. It tempers out 78732/78125 and 262144/253125 in the [[5-limit]], [[126/125]] and [[245/243]] in the [[7-limit]], 176/175, 441/440 and 4000/3993 in the [[11-limit]], and 91/90, 169/168, 196/195, [[325/324]], [[351/350]] and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[Starling temperaments#Casablanca temperament-Marrakesh|marrakesh temperament]]. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp:
+'''73-EDO''' divides the octave into 73 equal parts of 16.438 [[cent]]s each. It tempers out 78732/78125 and 262144/253125 in the [[5-limit]], [[126/125]] and [[245/243]] in the [[7-limit]], 176/175, 441/440 and 4000/3993 in the [[11-limit]], and 91/90, 169/168, 196/195, [[325/324]], [[351/350]] and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[Starling temperaments#Casablanca temperament-Marrakesh|marrakesh temperament]]. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see approximation table.
 {| class="wikitable center-all"
-! prime !! steps !! delta [[cents|(¢)]]
 |-
-|   3  ||  116  || +0.298
+|+ 73-EDO approximation of primary intervals
 |-
-|   5  ||  170  || +0.499
+! colspan="2" | Prime number
+! 3
+! 5
+! 7
+! 11
+! 13
+! 17
+! 19
+! 23
 |-
-|   7  ||  205  || +0.063
+! rowspan="2" | Error
+! absolute ([[cent|¢]])
+| +4.89
+| +8.21
+| +1.04
+| +7.59
+| -2.17
+| -6.33
+| -1.62
+| -3.62
 |-
-|  11  ||  253  || +0.461
+! [[Relative error|relative]] (%)
+| +29.8
+| +49.9
+| +6.3
+| +46.1
+| -13.2
+| -38.5
+| -9.9
+| -22.0
+|-
+! colspan="2" | Degree ([[octave reduction|reduced]])
+| 116 (43)
+| 170 (24)
+| 205 (59)
+| 253 (34)
+| 270 (51)
+| 298 (6)
+| 310 (18)
+| 330 (38)
 |}