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Wesley family: Difference between revisions

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{{Technical data page}}
{{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].  
The '''wesley family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] 78125/73728, the [[wesley comma]]. The wesley comma is unchanged in [[Wesley Woolhouse]]'s 7/26-comma meantone – it is an [[eigenmonzo|eigenmonzo (i.e. unchanged-interval)]], which [[Gene Ward Smith]] has talked about<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12793.html Yahoo! Tuning Group | ''26et and meantone projections'']</ref>.  


== Wesley ==
== Wesley ==
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{{Mapping|legend=1| 1 4 3 | 0 -7 -2 }}
{{Mapping|legend=1| 1 4 3 | 0 -7 -2 }}
: mapping generators: ~2, ~125/96
: mapping generators: ~2, ~125/96


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 414.509
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~125/96 = 414.509{{c}}


{{Optimal ET sequence|legend=1| 3, …, 23, 26, 29, 55c }}
{{Optimal ET sequence|legend=1| 3, …, 23, 26, 29, 55c }}


[[Badness]]: 0.247718
[[Badness]] (Smith): 0.247718


== Septimal wesley ==
== Septimal wesley ==
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{{Mapping|legend=1| 1 4 3 8 | 0 -7 -2 -15 }}
{{Mapping|legend=1| 1 4 3 8 | 0 -7 -2 -15 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 415.519
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~9/7 = 415.519{{c}}


{{Optimal ET sequence|legend=1| 3d, …, 23d, 26 }}
{{Optimal ET sequence|legend=1| 3d, …, 23d, 26 }}


[[Badness]]: 0.095344
[[Badness]] (Smith): 0.095344


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 4 3 8 9 | 0 -7 -2 -15 -16 }}
Mapping: {{mapping| 1 4 3 8 9 | 0 -7 -2 -15 -16 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 415.769{{c}}


{{Optimal ET sequence|legend=1| 3de, …, 23de, 26 }}
{{Optimal ET sequence|legend=0| 3de, …, 23de, 26 }}


Badness: 0.049066
Badness (Smith): 0.049066


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 4 3 8 9 12 | 0 -7 -2 -15 -16 -24 }}
Mapping: {{mapping| 1 4 3 8 9 12 | 0 -7 -2 -15 -16 -24 }}


Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~9/7 = 415.645{{c}}


{{Optimal ET sequence|legend=1| 3def, 23deff, 26 }}
{{Optimal ET sequence|legend=0| 3def, 23deff, 26 }}


Badness: 0.038402
Badness (Smith): 0.038402


== Snipes ==
== Snipes ==
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{{Mapping|legend=1| 1 4 3 9 | 0 -7 -2 -18 }}
{{Mapping|legend=1| 1 4 3 9 | 0 -7 -2 -18 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/27 = 413.513
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~35/27 = 413.513{{c}}


{{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }}
{{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }}


[[Badness]]: 0.117943
[[Badness]] (Smith): 0.117943


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 4 3 9 10 | 0 -7 -2 -18 -19 }}
Mapping: {{mapping| 1 4 3 9 10 | 0 -7 -2 -18 -19 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 413.490{{c}}


{{Optimal ET sequence|legend=1| 3de, …, 26de, 29 }}
{{Optimal ET sequence|legend=0| 3de, …, 26de, 29 }}


Badness: 0.054296
Badness (Smith): 0.054296


== Roman ==
== Roman ==
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{{Mapping|legend=1| 1 4 3 -1 | 0 -7 -2 11 }}
{{Mapping|legend=1| 1 4 3 -1 | 0 -7 -2 11 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~63/50 = 414.552
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~63/50 = 414.552{{c}}


{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}


[[Badness]]: 0.113386
[[Badness]] (Smith): 0.113386


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 1 4 3 -1 0 | 0 -7 -2 11 10 }}
Mapping: {{mapping| 1 4 3 -1 0 | 0 -7 -2 11 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.471
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 414.471{{c}}


{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
{{Optimal ET sequence|legend=0| 3, 23, 26, 29, 55c }}


Badness: 0.052841
Badness (Smith): 0.052841


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 1 4 3 -1 0 3 | 0 -7 -2 11 10 2 }}
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 tuning (POTE): ~2 = 1200.000{{c}}, ~14/11 = 414.472{{c}}


{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }}
{{Optimal ET sequence|legend=0| 3, 23, 26, 29, 55cf }}


Badness: 0.030043
Badness (Smith): 0.030043


== Dubbla ==
== Dubbla ==
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{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}
{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 185.738
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~192/175 = 185.738{{c}}


{{Optimal ET sequence|legend=1| 6, 20b, 26, 58c }}
{{Optimal ET sequence|legend=1| 6, 20b, 26, 58c }}


[[Badness]]: 0.181726
[[Badness]] (Smith): 0.181726


=== 11-limit ===
=== 11-limit ===
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Mapping: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}
Mapping: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}


Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 185.879{{c}}


{{Optimal ET sequence|legend=1| 6, 20b, 26 }}
{{Optimal ET sequence|legend=0| 6, 20b, 26 }}


Badness: 0.075842
Badness (Smith): 0.075842


=== 13-limit ===
=== 13-limit ===
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Mapping: {{mapping| 2 1 4 5 6 4 | 0 7 2 2 3 11 }}
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 tuning (POTE): ~2 = 1200.000{{c}}, ~11/10 = 185.702{{c}}
 
{{Optimal ET sequence|legend=0| 6f, 20bff, 26 }}


{{Optimal ET sequence|legend=1| 6f, 20bff, 26 }}
Badness (Smith): 0.049603


Badness: 0.049603
== References ==


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Wesley family| ]] <!-- main article -->
[[Category:Wesley family| ]] <!-- main article -->
[[Category:Wesley| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Wesley_family"