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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 [[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 ==
[[Comma]]: 78125/73728
The generator of wesley is one half of a [[~]][[5/2]], around 786 [[cent]]s, seven of which after [[octave reduction]] reach the [[3/2|perfect fifth]]. The [[ploidacot]] signature of this temperament is delta-heptacot. A good tuning for the generator may be found between [[26edo|17\26]] and [[29edo|19\29]].


[[Mapping]]: [&lt;1 4 3|, &lt;0 -7 -2|]
[[Subgroup]]: 2.3.5


[[POTE tuning|POTE generator]]: ~125/96 = 414.509
[[Comma list]]: 78125/73728


[[EDO|Vals]]: {{Val list| 3, 23, 26, 29, 55c }}
{{Mapping|legend=1| 1 -3 1 | 0 7 2 }}
: mapping generators: ~2, ~192/125


[[Badness]]: 0.247718
[[Optimal tuning]]s:
* [[WE]] ~2 = 1202.9225{{c}}, ~192/125 = 787.4042{{c}}
: [[error map]]: {{val| +2.922 +1.107 -8.583 }}
* [[CWE]] ~2 = 1200.0000{{c}}, ~192/125 = 785.7808{{c}}
: error map: {{val| 0.000 -1.490 -14.752 }}
 
{{Optimal ET sequence|legend=1| 3, …, 23, 26, 29, 55c }}
 
[[Badness]] (Sintel): 5.81
 
== Septimal wesley ==
[[Subgroup]]: 2.3.5.7


== 7-limit ==
[[Comma list]]: 405/392, 875/864
[[Comma list]]: 405/392, 875/864


[[Mapping]]: [&lt;1 4 3 8|, &lt;0 -7 -2 -15|]
{{Mapping|legend=1| 1 -3 1 -7 | 0 7 2 15 }}


[[Wedgie]]: &lt;&lt;7 2 15 -13 4 29||
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1203.6434{{c}}, ~14/9 = 786.8631{{c}}
: [[error map]]: {{val| +3.634 -4.844 -8.944 +8.617 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~14/9 = 784.7754{{c}}
: error map: {{val| 0.000 -8.527 -16.763 +2.805 }}


[[POTE tuning|POTE generator]]: ~9/7 = 415.519
{{Optimal ET sequence|legend=1| 3d, …, 23d, 26 }}


[[EDO|Vals]]: {{Val list| 3d, 23d, 26 }}
[[Badness]] (Sintel): 2.41


[[Badness]]: 0.095344
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 45/44, 99/98, 875/864
Comma list: 45/44, 99/98, 875/864


Mapping: [&lt;1 4 3 8 9|, &lt;0 -7 -2 -15 -16|]
Mapping: {{mapping| 1 -3 1 -7 -7 | 0 7 2 15 16 }}
 
Optimal tunings:
* WE: ~2 = 1203.6405{{c}}, ~11/7 = 786.6101{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 784.5242{{c}}


POTE generator: ~9/7 = 415.769
{{Optimal ET sequence|legend=0| 3de, …, 23de, 26 }}


Vals: {{Val list| 3de, 23de, 26, 75bcd }}
Badness (Sintel): 1.62


Badness: 0.049066
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 13-limit ==
Comma list: 45/44, 78/77, 99/98, 325/324
Comma list: 45/44, 78/77, 99/98, 325/324


Mapping: [&lt;1 4 3 8 9 12|, &lt;0 -7 -2 -15 -16 -24|]
Mapping: {{mapping| 1 -3 1 -7 -7 -12 | 0 7 2 15 16 24 }}
 
Optimal tunings:
* WE: ~2 = 1200.0000{{c}}, ~11/7 = 786.5973{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 784.5923{{c}}


POTE generator: ~9/7 = 415.645
{{Optimal ET sequence|legend=0| 3def, 23deff, 26 }}


Vals: {{Val list| 3def, 26 }}
Badness (Sintel): 1.59


Badness: 0.038402
== Snipes ==
[[Subgroup]]: 2.3.5.7


= Snipes =
[[Comma list]]: 225/224, 6125/5832
[[Comma list]]: 225/224, 6125/5832


[[Mapping]]: [&lt;1 4 3 9|, &lt;0 -7 -2 -18|]
{{Mapping|legend=1| 1 -3 1 -9 | 0 7 2 18 }}
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.9268{{c}}, ~54/35 = 787.7496{{c}}
: [[error map]]: {{val| +1.927 +6.511 -8.888 -6.675 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/35 = 786.6189{{c}}
: error map: {{val| 0.000 +4.377 -13.076 -9.686 }}
 
{{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }}


[[Wedgie]]: &lt;&lt;7 2 18 -13 9 36||
[[Badness]] (Sintel): 2.98


[[POTE tuning|POTE generator]]: ~35/27 = 413.513
=== 11-limit ===
Subgroup: 2.3.5.7.11


[[EDO|Vals]]: {{Val list| 29, 90cd, 119cd }}
Comma list: 55/54, 225/224, 245/242


[[Badness]]: 0.117943
Mapping: {{mapping| 1 -3 1 -9 -9 | 0 7 2 18 19 }}


= Crusher =
Optimal tunings:
This temperament is also known as ''roman temperament''.
* WE: ~2 = 1201.9201{{c}}, ~11/7 = 787.7690{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 786.6402{{c}}
 
{{Optimal ET sequence|legend=0| 3de, …, 26de, 29 }}
 
Badness (Sintel): 1.79
 
== Roman ==
Roman tempers out 525/512, the [[avicennma]]. The 7-limit version has also been proposed as ''crusher''.
 
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 525/512, 3125/3024
[[Comma list]]: 525/512, 3125/3024


[[Mapping]]: [&lt;1 4 3 -1|, &lt;0 -7 -2 11|]
{{Mapping|legend=1| 1 -3 1 10 | 0 7 2 -11 }}


[[Wedgie]]: &lt;&lt;7 2 -11 -13 -37 -31||
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1203.0258{{c}}, ~63/40 = 787.4289{{c}}
: [[error map]]: {{val| +3.026 +0.970 -8.430 -0.286 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~63/40 = 785.4717{{c}}
: error map: {{val| 0.000 -3.653 -15.370 -9.0145 }}


[[POTE tuning|POTE generator]]: ~63/50 = 414.552
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}


[[EDO|Vals]]: {{Val list| 3, 23, 26, 29, 55c }}
[[Badness]] (Sintel): 2.87


[[Badness]]: 0.113386
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 100/99, 245/242, 525/512
Comma list: 100/99, 245/242, 525/512


Mapping: [&lt;1 4 3 -1 0|, &lt;0 -7 -2 11 10|]
Mapping: {{mapping| 1 -3 1 10 10 | 0 7 2 -11 -10 }}


POTE generator: ~14/11 = 414.471
Optimal tunings:  
* WE: ~2 = 1202.7762{{c}}, ~11/7 = 787.3465{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 785.5130{{c}}


Vals: {{Val list| 3, 23, 26, 29, 55c }}
{{Optimal ET sequence|legend=0| 3, 23, 26, 29, 55c }}


Badness: 0.052841
Badness (Sintel): 1.75
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 13-limit ==
Comma list: 65/64, 100/99, 105/104, 245/242
Comma list: 65/64, 100/99, 105/104, 245/242


Mapping: [&lt;1 4 3 -1 0 3|, &lt;0 -7 -2 11 10 2|]
Mapping: {{mapping| 1 -3 1 10 10 5 | 0 7 2 -11 -10 -2 }}


POTE generator: ~14/11 = 414.472
Optimal tunings:  
* WE: ~2 = 1202.8327{{c}}, ~11/7 = 787.3820{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 785.5085{{c}}


Vals: {{Val list| 3, 23, 26, 29, 55cf }}
{{Optimal ET sequence|legend=0| 3, 23, 26, 29, 55cf }}


Badness: 0.030043
Badness (Sintel): 1.24
 
== Dubbla ==
[[Subgroup]]: 2.3.5.7


= Dubbla =
[[Comma list]]: 50/49, 78125/73728
[[Comma list]]: 50/49, 78125/73728


[[Mapping]]: [&lt;2 1 4 5|, &lt;0 7 2 2|]
{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}
: mapping generators: ~7/5, ~192/175


[[Wedgie]]: &lt;&lt;14 4 4 -26 -33 -2||
[[Optimal tuning]]s:  
* [[WE]]: ~7/5 = 600.8055{{c}}, ~192/175 = 185.9882{{c}}
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~192/175 = 185.8808{{c}}


[[POTE tuning|POTE generator]]: ~192/175 = 185.738
{{Optimal ET sequence|legend=1| 6, 20b, 26, 58c }}


[[EDO|Vals]]: {{Val list| 6, 26, 58c, 84c }}
[[Badness]] (Sintel): 4.60


[[Badness]]: 0.181726
=== 11-limit ===
Subgroup: 2.3.5.7.11


== 11-limit ==
Comma list: 50/49, 125/121, 1344/1331
Comma list: 50/49, 125/121, 1344/1331


Mapping: [&lt;2 1 4 5 6|, &lt;0 7 2 2 3|]
Mapping: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}


POTE generator: ~11/10 = 185.879
Optimal tunings:  
* WE: ~7/5 = 600.3702{{c}}, ~11/10 = 185.9936{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~11/10 = 185.9408{{c}}


Vals: {{Val list| 6, 26, 58c, 84c }}
{{Optimal ET sequence|legend=0| 6, 20b, 26 }}


Badness: 0.075842
Badness (Sintel): 2.51
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


== 13-limit ==
Comma list: 50/49, 105/104, 125/121, 144/143
Comma list: 50/49, 105/104, 125/121, 144/143


Mapping: [&lt;2 1 4 5 6 4|, &lt;0 7 2 2 3 11|]
Mapping: {{mapping| 2 1 4 5 6 4 | 0 7 2 2 3 11 }}
 
Optimal tunings:
* WE: ~7/5 = 600.3563{{c}}, ~11/10 = 185.8121{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~11/10 = 185.7623{{c}}


POTE generator: ~11/10 = 185.702
{{Optimal ET sequence|legend=0| 6f, 20bff, 26 }}


Vals: {{Val list| 26, 58c, 84c }}
Badness (Sintel): 2.05


Badness: 0.049603
== References ==


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