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, in other words. More information on that can be found [http://tech.groups.yahoo.com/group/tuning-math/message/12793 here].
+{{Technical data page}}
+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=
+== Wesley ==
-Comma: 78125/73728
+[[Subgroup]]: 2.3.5
-POTE generator: ~125/96 = 414.509
+[[Comma list]]: 78125/73728
-Map: [&lt;1 4 3|, &lt;0 -7 -2|]
+{{Mapping|legend=1| 1 4 3 | 0 -7 -2 }}
-EDOs: 23, 26, 29, 55c
+: mapping generators: ~2, ~125/96
-Badness: 0.2477
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 414.509
-==7-limit==
+{{Optimal ET sequence|legend=1| 3, …, 23, 26, 29, 55c }}
-Commas: 405/392, 875/864
-POTE generator: ~9/7 = 415.519
+[[Badness]]: 0.247718
-Map: [&lt;1 4 3 8|, &lt;0 -7 -2 -15|]
+== Septimal wesley ==
+[[Subgroup]]: 2.3.5.7
-Wedgie: &lt;&lt;7 2 15 -13 4 29||
+[[Comma list]]: 405/392, 875/864
-EDOs: 26
+{{Mapping|legend=1| 1 4 3 8 | 0 -7 -2 -15 }}
-Badness: 0.0953
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 415.519
-==11-limit==
+{{Optimal ET sequence|legend=1| 3d, …, 23d, 26 }}
-Commas: 45/44, 99/98, 875/864
-POTE generator: ~9/7 = 415.769
+[[Badness]]: 0.095344
-Map: [&lt;1 4 3 8 9|, &lt;0 -7 -2 -15 -16|]
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-EDOs: 23de, 26, 75bcd
+Comma list: 45/44, 99/98, 875/864
-Badness: 0.0491
+Mapping: {{mapping| 1 4 3 8 9 | 0 -7 -2 -15 -16 }}
-==13-limit==
+Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769
-Commas: 45/44, 78/77, 99/98, 325/324
-POTE generator: ~9/7 = 415.645
+{{Optimal ET sequence|legend=1| 3de, …, 23de, 26 }}
-Map: [&lt;1 4 3 8 9 12|, &lt;0 -7 -2 -15 -16 -24|]
+Badness: 0.049066
-EDOs: 26
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
-Badness: 0.0384
+Comma list: 45/44, 78/77, 99/98, 325/324
-==Snipes==
+Mapping: {{mapping| 1 4 3 8 9 12 | 0 -7 -2 -15 -16 -24 }}
-Commas: 225/224, 6125/5832
-POTE generator: ~35/27 = 413.513
+Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645
-Map: [&lt;1 4 3 9|, &lt;0 -7 -2 -18|]
+{{Optimal ET sequence|legend=1| 3def, 23deff, 26 }}
-Wedgie: &lt;&lt;7 2 18 -13 9 36||
+Badness: 0.038402
-EDOs: 29, 90cd, 119cd
+== Snipes ==
+[[Subgroup]]: 2.3.5.7
-Badness: 0.1179
+[[Comma list]]: 225/224, 6125/5832
-==Crusher==
+{{Mapping|legend=1| 1 4 3 9 | 0 -7 -2 -18 }}
-Commas: 525/512, 3125/3024
-POTE generator: ~63/50 = 414.552
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/27 = 413.513
-Map: [&lt;1 4 3 -1|, &lt;0 -7 -2 11|]
+{{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }}
-Wedgie: &lt;&lt;7 2 -11 -13 -37 -31||
+[[Badness]]: 0.117943
-EDOs: 23, 26, 29, 55c
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Badness: 0.1134
+Comma list: 55/54, 225/224, 245/242
-=Dubbla=
+Mapping: {{mapping| 1 4 3 9 10 | 0 -7 -2 -18 -19 }}
-Commas: 50/49, 78125/73728
-POTE generator: ~192/175 = 185.738
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490
-Map: [&lt;2 1 4 5|, &lt;0 7 2 2|]
+{{Optimal ET sequence|legend=1| 3de, …, 26de, 29 }}
-Wedgie: &lt;&lt;14 4 4 -26 -33 -2||
+Badness: 0.054296
-EDOs: 6, 26, 58c, 84c
+== Roman ==
+{{See also| Avicennmic temperaments }}
-Badness: 0.1817
+=== 7-limit a.k.a. crusher ===
+[[Subgroup]]: 2.3.5.7
-==11-limit==
+[[Comma list]]: 525/512, 3125/3024
-Commas: 50/49, 125/121, 1344/1331
-POTE generator: ~11/10 = 185.879
+{{Mapping|legend=1| 1 4 3 -1 | 0 -7 -2 11 }}
-Map: [&lt;2 1 4 5 6|, &lt;0 7 2 2 3|]
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~63/50 = 414.552
-EDOs: 6, 26, 58c, 84c
+{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
-Badness: 0.0758
+[[Badness]]: 0.113386
-==13-limit==
+=== 11-limit ===
-Commas: 50/49, 105/104, 125/121, 144/143
+Subgroup: 2.3.5.7.11
-POTE generator: ~11/10 = 185.702
+Comma list: 100/99, 245/242, 525/512
-Map: [&lt;2 1 4 5 6 4|, &lt;0 7 2 2 3 11|]
+Mapping: {{mapping| 1 4 3 -1 0 | 0 -7 -2 11 10 }}
-EDOs: 26, 58c, 84c
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.471
-Badness: 0.0496
+{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
+Badness: 0.052841
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 65/64, 100/99, 105/104, 245/242
+Mapping: {{mapping| 1 4 3 -1 0 3 | 0 -7 -2 11 10 2 }}
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.472
+{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }}
+Badness: 0.030043
+== Dubbla ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 50/49, 78125/73728
+{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 185.738
+{{Optimal ET sequence|legend=1| 6, 20b, 26, 58c }}
+[[Badness]]: 0.181726
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 50/49, 125/121, 1344/1331
+Mapping: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}
+Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879
+{{Optimal ET sequence|legend=1| 6, 20b, 26 }}
+Badness: 0.075842
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 50/49, 105/104, 125/121, 144/143
+Mapping: {{mapping| 2 1 4 5 6 4 | 0 7 2 2 3 11 }}
+Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.702
+{{Optimal ET sequence|legend=1| 6f, 20bff, 26 }}
+Badness: 0.049603
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Wesley family| ]] <!-- main article -->
+[[Category:Wesley| ]] <!-- key article -->
+[[Category:Rank 2]]