Wesley family: Difference between revisions

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-This tempers out the wesley comma, 78125/73728. The wesley comma is unchanged in Wesley Woolhouse's 7/26-comma meantone - it is an eigenmonzo, or unchanged-interval, in other words. Here is [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12793.html a talk by Gene Ward Smith].
+The '''wesley family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the [[wesley comma]], 78125/73728. The wesley comma is unchanged in [[Wesley Woolhouse]]'s 7/26-comma meantone – it is an [[Eigenmonzo|eigenmonzo (i.e. unchanged-interval)]]. Here is [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12793.html a talk by Gene Ward Smith].
 == Wesley ==
-Subgroup: 2.3.5
+[[Subgroup]]: 2.3.5
-[[Comma]]: 78125/73728
+[[Comma list]]: 78125/73728
-[[Mapping]]: [{{val| 1 4 3 }}, {{val| 0 -7 -2 }}]
+{{Mapping|legend=1| 1 4 3 | 0 -7 -2 }}
-[[POTE generator]]: ~125/96 = 414.509
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 414.509
 {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
@@ Line 15: / Line 15: @@
 == Septimal wesley ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 405/392, 875/864
-[[Mapping]]: [{{val| 1 4 3 8 }}, {{val| 0 -7 -2 -15 }}]
+{{Mapping|legend=1| 1 4 3 8 | 0 -7 -2 -15 }}
-{{Multival|legend=1|7 2 15 -13 4 29}}
+{{Multival|legend=1| 7 2 15 -13 4 29 }}
-[[POTE generator]]: ~9/7 = 415.519
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 415.519
 {{Optimal ET sequence|legend=1| 3d, 23d, 26 }}
@@ Line 34: / Line 34: @@
 Comma list: 45/44, 99/98, 875/864
-Mapping: [{{val| 1 4 3 8 9 }}, {{val| 0 -7 -2 -15 -16 }}]
+Mapping: {{mapping| 1 4 3 8 9 | 0 -7 -2 -15 -16 }}
-POTE generator: ~9/7 = 415.769
+Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769
 {{Optimal ET sequence|legend=1| 3de, 23de, 26, 75bcd }}
@@ Line 47: / Line 47: @@
 Comma list: 45/44, 78/77, 99/98, 325/324
-Mapping: [{{val| 1 4 3 8 9 12 }}, {{val| 0 -7 -2 -15 -16 -24 }}]
+Mapping: {{mapping| 1 4 3 8 9 12 | 0 -7 -2 -15 -16 -24 }}
-POTE generator: ~9/7 = 415.645
+Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645
 {{Optimal ET sequence|legend=1| 3def, 26 }}
@@ Line 56: / Line 56: @@
 == Snipes ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 225/224, 6125/5832
-[[Mapping]]: [{{val| 1 4 3 9 }}, {{val| 0 -7 -2 -18 }}]
+{{Mapping|legend=1| 1 4 3 9 | 0 -7 -2 -18 }}
 {{Multival|legend=1| 7 2 18 -13 9 36 }}
-[[POTE generator]]: ~35/27 = 413.513
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/27 = 413.513
 {{Optimal ET sequence|legend=1| 29, 90cd, 119ccdd }}
@@ Line 75: / Line 75: @@
 Comma list: 55/54, 225/224, 245/242
-Mapping: [{{val| 1 4 3 9 10 }}, {{val| 0 -7 -2 -18 -19 }}]
+Mapping: {{mapping| 1 4 3 9 10 | 0 -7 -2 -18 -19 }}
-POTE generator: ~14/11 = 413.490
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490
 {{Optimal ET sequence|legend=1| 29, 90cd, 119ccdde }}
@@ Line 84: / Line 84: @@
 == Roman ==
-{{see also|Avicennmic temperaments #Roman}}
+{{See also| Avicennmic temperaments #Roman }}
-=== 7-limit (Crusher) ===
+=== 7-limit a.k.a. crusher ===
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 525/512, 3125/3024
-[[Mapping]]: [{{val| 1 4 3 -1 }}, {{val| 0 -7 -2 11 }}]
+{{Mapping|legend=1| 1 4 3 -1 | 0 -7 -2 11 }}
-{{Multival|legend=1|7 2 -11 -13 -37 -31}}
+{{Multival|legend=1| 7 2 -11 -13 -37 -31 }}
-[[POTE generator]]: ~63/50 = 414.552
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~63/50 = 414.552
 {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
@@ Line 106: / Line 106: @@
 Comma list: 100/99, 245/242, 525/512
-Mapping: [{{val| 1 4 3 -1 0 }}, {{val| 0 -7 -2 11 10 }}]
+Mapping: {{mapping| 1 4 3 -1 0 | 0 -7 -2 11 10 }}
-POTE generator: ~14/11 = 414.471
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.471
 {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
@@ Line 119: / Line 119: @@
 Comma list: 65/64, 100/99, 105/104, 245/242
-Mapping: [{{val| 1 4 3 -1 0 3 }}, {{val| 0 -7 -2 11 10 2 }}]
+Mapping: {{mapping| 1 4 3 -1 0 3 | 0 -7 -2 11 10 2 }}
-POTE generator: ~14/11 = 414.472
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.472
 {{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }}
@@ Line 128: / Line 128: @@
 == Dubbla ==
-Subgroup: 2.3.5.7
+[[Subgroup]]: 2.3.5.7
 [[Comma list]]: 50/49, 78125/73728
-[[Mapping]]: [{{val| 2 1 4 5 }}, {{val| 0 7 2 2 }}]
+{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}
-{{Multival|legend=1|14 4 4 -26 -33 -2}}
+{{Multival|legend=1| 14 4 4 -26 -33 -2 }}
-[[POTE generator]]: ~192/175 = 185.738
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 185.738
 {{Optimal ET sequence|legend=1| 6, 26, 58c, 84c }}
@@ Line 147: / Line 147: @@
 Comma list: 50/49, 125/121, 1344/1331
-Mapping: [{{val| 2 1 4 5 6 }}, {{val| 0 7 2 2 3 }}]
+Mapping: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}
-POTE generator: ~11/10 = 185.879
+Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879
 {{Optimal ET sequence|legend=1| 6, 26, 58c, 84c }}
@@ Line 160: / Line 160: @@
 Comma list: 50/49, 105/104, 125/121, 144/143
-Mapping: [{{val| 2 1 4 5 6 4 }}, {{val| 0 7 2 2 3 11 }}]
+Mapping: {{mapping| 2 1 4 5 6 4 | 0 7 2 2 3 11 }}
-POTE generator: ~11/10 = 185.702
+Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.702
 {{Optimal ET sequence|legend=1| 26, 58c, 84c }}
@@ Line 170: / Line 170: @@
 [[Category:Temperament families]]
 [[Category:Wesley family| ]] <!-- main article -->
+[[Category:Wesley| ]] <!-- key article -->
 [[Category:Rank 2]]