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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>.  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-30 14:50:03 UTC</tt>.<br>
: The original revision id was <tt>327549118</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">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]].


=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]].


POTE generator: ~125/96 = 414.509
[[Subgroup]]: 2.3.5


Map: [&lt;1 4 3|, &lt;0 -7 -2|]
[[Comma list]]: 78125/73728
EDOs: 23, 26, 29, 55c
Badness: 0.2477


==7-limit==
{{Mapping|legend=1| 1 -3 1 | 0 7 2 }}
Commas: 405/392, 875/864
: mapping generators: ~2, ~192/125


POTE generator: ~9/7 = 415.519
[[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 }}


Map: [&lt;1 4 3 8|, &lt;0 -7 -2 -15|]
{{Optimal ET sequence|legend=1| 3, …, 23, 26, 29, 55c }}
Wedgie: &lt;&lt;7 2 15 -13 4 29||
EDOs: 26
Badness: 0.0953


==11-limit==
[[Badness]] (Sintel): 5.81
Commas: 45/44, 99/98, 875/864


POTE generator: ~9/7 = 415.769
== Septimal wesley ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 4 3 8 9|, &lt;0 -7 -2 -15 -16|]
[[Comma list]]: 405/392, 875/864
EDOs: 23de, 26, 75bcd
Badness: 0.0491


==13-limit==
{{Mapping|legend=1| 1 -3 1 -7 | 0 7 2 15 }}
Commas: 45/44, 78/77, 99/98, 325/324


POTE generator: ~9/7 = 415.645
[[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 }}


Map: [&lt;1 4 3 8 9 12|, &lt;0 -7 -2 -15 -16 -24|]
{{Optimal ET sequence|legend=1| 3d, …, 23d, 26 }}
EDOs: 26
Badness: 0.0384


==Snipes==
[[Badness]] (Sintel): 2.41
Commas: 225/224, 6125/5832


POTE generator: ~35/27 = 413.513
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 4 3 9|, &lt;0 -7 -2 -18|]
Comma list: 45/44, 99/98, 875/864
Wedgie: &lt;&lt;7 2 18 -13 9 36||
EDOs: 29, 90cd, 119cd
Badness: 0.1179


==Crusher==
Mapping: {{mapping| 1 -3 1 -7 -7 | 0 7 2 15 16 }}
Commas: 525/512, 3125/3024


POTE generator: ~63/50 = 414.552
Optimal tunings:  
* WE: ~2 = 1203.6405{{c}}, ~11/7 = 786.6101{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 784.5242{{c}}


Map: [&lt;1 4 3 -1|, &lt;0 -7 -2 11|]
{{Optimal ET sequence|legend=0| 3de, …, 23de, 26 }}
Wedgie: &lt;&lt;7 2 -11 -13 -37 -31||
EDOs: 23, 26, 29, 55c
Badness: 0.1134


=Dubbla=
Badness (Sintel): 1.62
Commas: 50/49, 78125/73728


POTE generator: ~192/175 = 185.738
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;2 1 4 5|, &lt;0 7 2 2|]
Comma list: 45/44, 78/77, 99/98, 325/324
Wedgie: &lt;&lt;14 4 4 -26 -33 -2||
EDOs: 6, 26, 58c, 84c
Badness: 0.1817


==11-limit==
Mapping: {{mapping| 1 -3 1 -7 -7 -12 | 0 7 2 15 16 24 }}
Commas: 50/49, 125/121, 1344/1331


POTE generator: ~11/10 = 185.879
Optimal tunings:  
* WE: ~2 = 1200.0000{{c}}, ~11/7 = 786.5973{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 784.5923{{c}}


Map: [&lt;2 1 4 5 6|, &lt;0 7 2 2 3|]
{{Optimal ET sequence|legend=0| 3def, 23deff, 26 }}
EDOs: 6, 26, 58c, 84c
Badness: 0.0758


==13-limit==
Badness (Sintel): 1.59
Commas: 50/49, 105/104, 125/121, 144/143


POTE generator: ~11/10 = 185.702
== Snipes ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;2 1 4 5 6 4|, &lt;0 7 2 2 3 11|]
[[Comma list]]: 225/224, 6125/5832
EDOs: 26, 58c, 84c
 
Badness: 0.0496
{{Mapping|legend=1| 1 -3 1 -9 | 0 7 2 18 }}
</pre></div>
 
<h4>Original HTML content:</h4>
[[Optimal tuning]]s:  
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Wesley family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;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 &lt;a class="wiki_link_ext" href="http://tech.groups.yahoo.com/group/tuning-math/message/12793" rel="nofollow"&gt;here&lt;/a&gt;.&lt;br /&gt;
* [[WE]]: ~2 = 1201.9268{{c}}, ~54/35 = 787.7496{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +1.927 +6.511 -8.888 -6.675 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Wesley"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Wesley&lt;/h1&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~54/35 = 786.6189{{c}}
Comma: 78125/73728&lt;br /&gt;
: error map: {{val| 0.000 +4.377 -13.076 -9.686 }}
&lt;br /&gt;
 
POTE generator: ~125/96 = 414.509&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3|, &amp;lt;0 -7 -2|]&lt;br /&gt;
[[Badness]] (Sintel): 2.98
EDOs: 23, 26, 29, 55c&lt;br /&gt;
 
Badness: 0.2477&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Wesley-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
 
Commas: 405/392, 875/864&lt;br /&gt;
Comma list: 55/54, 225/224, 245/242
&lt;br /&gt;
 
POTE generator: ~9/7 = 415.519&lt;br /&gt;
Mapping: {{mapping| 1 -3 1 -9 -9 | 0 7 2 18 19 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3 8|, &amp;lt;0 -7 -2 -15|]&lt;br /&gt;
Optimal tunings:  
Wedgie: &amp;lt;&amp;lt;7 2 15 -13 4 29||&lt;br /&gt;
* WE: ~2 = 1201.9201{{c}}, ~11/7 = 787.7690{{c}}
EDOs: 26&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 786.6402{{c}}
Badness: 0.0953&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 3de, …, 26de, 29 }}
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Wesley-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 
Commas: 45/44, 99/98, 875/864&lt;br /&gt;
Badness (Sintel): 1.79
&lt;br /&gt;
 
POTE generator: ~9/7 = 415.769&lt;br /&gt;
== Roman ==
&lt;br /&gt;
Roman tempers out 525/512, the [[avicennma]]. The 7-limit version has also been proposed as ''crusher''.
Map: [&amp;lt;1 4 3 8 9|, &amp;lt;0 -7 -2 -15 -16|]&lt;br /&gt;
 
EDOs: 23de, 26, 75bcd&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
Badness: 0.0491&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 525/512, 3125/3024
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Wesley-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
 
Commas: 45/44, 78/77, 99/98, 325/324&lt;br /&gt;
{{Mapping|legend=1| 1 -3 1 10 | 0 7 2 -11 }}
&lt;br /&gt;
 
POTE generator: ~9/7 = 415.645&lt;br /&gt;
[[Optimal tuning]]s:
&lt;br /&gt;
* [[WE]]: ~2 = 1203.0258{{c}}, ~63/40 = 787.4289{{c}}
Map: [&amp;lt;1 4 3 8 9 12|, &amp;lt;0 -7 -2 -15 -16 -24|]&lt;br /&gt;
: [[error map]]: {{val| +3.026 +0.970 -8.430 -0.286 }}
EDOs: 26&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~63/40 = 785.4717{{c}}
Badness: 0.0384&lt;br /&gt;
: error map: {{val| 0.000 -3.653 -15.370 -9.0145 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Wesley-Snipes"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Snipes&lt;/h2&gt;
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
Commas: 225/224, 6125/5832&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 2.87
POTE generator: ~35/27 = 413.513&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
Map: [&amp;lt;1 4 3 9|, &amp;lt;0 -7 -2 -18|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
Wedgie: &amp;lt;&amp;lt;7 2 18 -13 9 36||&lt;br /&gt;
 
EDOs: 29, 90cd, 119cd&lt;br /&gt;
Comma list: 100/99, 245/242, 525/512
Badness: 0.1179&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 -3 1 10 10 | 0 7 2 -11 -10 }}
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Wesley-Crusher"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Crusher&lt;/h2&gt;
 
Commas: 525/512, 3125/3024&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1202.7762{{c}}, ~11/7 = 787.3465{{c}}
POTE generator: ~63/50 = 414.552&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 785.5130{{c}}
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3 -1|, &amp;lt;0 -7 -2 11|]&lt;br /&gt;
{{Optimal ET sequence|legend=0| 3, 23, 26, 29, 55c }}
Wedgie: &amp;lt;&amp;lt;7 2 -11 -13 -37 -31||&lt;br /&gt;
 
EDOs: 23, 26, 29, 55c&lt;br /&gt;
Badness (Sintel): 1.75
Badness: 0.1134&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Dubbla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Dubbla&lt;/h1&gt;
Subgroup: 2.3.5.7.11.13
Commas: 50/49, 78125/73728&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 65/64, 100/99, 105/104, 245/242
POTE generator: ~192/175 = 185.738&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 -3 1 10 10 5 | 0 7 2 -11 -10 -2 }}
Map: [&amp;lt;2 1 4 5|, &amp;lt;0 7 2 2|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;14 4 4 -26 -33 -2||&lt;br /&gt;
Optimal tunings:
EDOs: 6, 26, 58c, 84c&lt;br /&gt;
* WE: ~2 = 1202.8327{{c}}, ~11/7 = 787.3820{{c}}
Badness: 0.1817&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~11/7 = 785.5085{{c}}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Dubbla-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
{{Optimal ET sequence|legend=0| 3, 23, 26, 29, 55cf }}
Commas: 50/49, 125/121, 1344/1331&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.24
POTE generator: ~11/10 = 185.879&lt;br /&gt;
 
&lt;br /&gt;
== Dubbla ==
Map: [&amp;lt;2 1 4 5 6|, &amp;lt;0 7 2 2 3|]&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
EDOs: 6, 26, 58c, 84c&lt;br /&gt;
 
Badness: 0.0758&lt;br /&gt;
[[Comma list]]: 50/49, 78125/73728
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Dubbla-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}
Commas: 50/49, 105/104, 125/121, 144/143&lt;br /&gt;
: mapping generators: ~7/5, ~192/175
&lt;br /&gt;
 
POTE generator: ~11/10 = 185.702&lt;br /&gt;
[[Optimal tuning]]s:  
&lt;br /&gt;
* [[WE]]: ~7/5 = 600.8055{{c}}, ~192/175 = 185.9882{{c}}
Map: [&amp;lt;2 1 4 5 6 4|, &amp;lt;0 7 2 2 3 11|]&lt;br /&gt;
* [[CWE]]: ~7/5 = 600.0000{{c}}, ~192/175 = 185.8808{{c}}
EDOs: 26, 58c, 84c&lt;br /&gt;
 
Badness: 0.0496&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Optimal ET sequence|legend=1| 6, 20b, 26, 58c }}
 
[[Badness]] (Sintel): 4.60
 
=== 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 tunings:
* WE: ~7/5 = 600.3702{{c}}, ~11/10 = 185.9936{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~11/10 = 185.9408{{c}}
 
{{Optimal ET sequence|legend=0| 6, 20b, 26 }}
 
Badness (Sintel): 2.51
 
=== 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 tunings:
* WE: ~7/5 = 600.3563{{c}}, ~11/10 = 185.8121{{c}}
* CWE: ~7/5 = 600.0000{{c}}, ~11/10 = 185.7623{{c}}
 
{{Optimal ET sequence|legend=0| 6f, 20bff, 26 }}
 
Badness (Sintel): 2.05
 
== References ==
 
[[Category:Wesley family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Wesley_family"