Meantone family: Difference between revisions

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 [[Comma|Comma]]s: 36/35, 64/63
-The wedgie for dominant is &lt;&lt;1 4 -2 4 -6 -16||. Now the interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo|12edo]], but it also works well with the Pythagorean tuning of pure [[3/2|3/2]] fifths, and with [[29edo|29edo]], [[41edo|41edo]], or [[53edo|53edo]].
+The wedgie for dominant is &lt;&lt;1 4 -2 4 -6 -16||. Now the interval class for 7 is obtained from two fourths in succession, so that 7/4 is a minor seventh. The 7/6 interval is, like 6/5, now a minor third, and 7/5 is a diminished fifth. An excellent tuning for dominant is [[12edo]], but it also works well with the Pythagorean tuning of pure [[3/2]] fifths, and with [[29edo]], [[41edo]], or [[53edo]].
 valid range: [700.000, 720.000] (12 to 5)
@@ Line 423: / Line 423: @@
 Map: [&lt;1 0 -4 6|, &lt;0 1 4 -2|]
-[[wedgie|Wedgie]]: &lt;&lt;1 4 -2 4 -6 -16||
+[[Wedgie]]: &lt;&lt;1 4 -2 4 -6 -16||
-EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[53edo|53]], [[65edo|65]]
+EDOs: [[5edo|5]], [[7edo|7]], [[12edo|12]], [[17edo|17c]], [[29edo|29cd]]
-[[Badness|Badness]]: 0.0207
+[[Badness]]: 0.0207
 ==11-limit==
@@ Line 485: / Line 485: @@
 Map: [&lt;1 0 -4 6 -6|, &lt;0 1 4 -2 6|]
-EDOs: 7, 12, 43de
+EDOs: 5e, 7, 12, 19d, 43de
 Badness: 0.0220
+===13-limit===
+Commas: 36/35, 45/44, 52/49, 64/63
+POTE generator: ~3/2 = 695.762
+Mapping generator: ~3
+Map: [&lt;1 0 -4 6 -6 10|, &lt;0 1 4 -2 6 -4|]
+EDOs: 5ef, 7, 12, 19d, 31def
+Badness: 0.0270
+===17-limit===
+Commas: 36/35, 45/44, 51/49, 52/49, 64/63
+POTE generator: ~3/2 = 696.115
+Mapping generator: ~3
+Map: [&lt;1 0 -4 6 -6 10 12|, &lt;0 1 4 -2 6 -4 -5|]
+EDOs: 5ef, 7, 12, 19d, 31def
+Badness: 0.0245
+===19-limit===
+Commas: 36/35, 39/38, 45/44, 51/49, 52/49, 57/56
+POTE generator: ~3/2 = 696.217
+Mapping generator: ~3
+Map: [&lt;1 0 -4 6 -6 10 12 9|, &lt;0 1 4 -2 6 -4 -5 -3|]
+EDOs: 5ef, 7, 12, 19d, 31def
+Badness: 0.0204
+===Dominatrix===
+Commas: 27/26, 36/35, 45/44, 64/63
+POTE generator: ~3/2 = 698.544
+Mapping generator: ~3
+Map: [&lt;1 0 -4 6 -6 -1|, &lt;0 1 4 -2 6 3|]
+EDOs: 5e, 7, 12f, 19df
 ==Domination==
@@ Line 514: / Line 564: @@
 Badness: 0.0274
-==Twelve==
-Commas: 81/80 64/63 45/44 65/64 256/255 153/152
-POTE generator: ~3/2 = 696.217
-Mapping generator: ~3
-Map: [&lt;1 0 -4 6 -6 10 12 9|, &lt;0 1 4 -2 6 -4 -5 -3|]
-EDOs: 7, 12, 19d, 31def
-Badness: 0.0204
 ==Arnold==
@@ Line 553: / Line 590: @@
 Badness: 0.0233
-==Dominatrix==
-Commas: 27/26 36/35 45/44 64/63
-POTE generator: ~3/2 = 698.544
-Mapping generator: ~3
-Map: [&lt;1 0 -4 6 -6 -1|, &lt;0 1 4 -2 6 3|]
-EDOs: 7, 12f
-Badness: 0.0183
 =Sharptone=