Wesley family: Difference between revisions

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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 [[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].  
: 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
[[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
Badness: 0.2477


==7-limit==
: mapping generators: ~2, ~125/96
Commas: 405/392, 875/864


POTE generator: ~9/7 = 415.519
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 414.509


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]]: 0.247718
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 4 3 8 | 0 -7 -2 -15 }}
Commas: 45/44, 78/77, 99/98, 325/324


POTE generator: ~9/7 = 415.645
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 415.519


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]]: 0.095344
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 4 3 8 9 | 0 -7 -2 -15 -16 }}
Commas: 525/512, 3125/3024


POTE generator: ~63/50 = 414.552
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.769


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


=Dubbla=
Badness: 0.049066
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 4 3 8 9 12 | 0 -7 -2 -15 -16 -24 }}
Commas: 50/49, 125/121, 1344/1331


POTE generator: ~11/10 = 185.879
Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.645


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


==13-limit==
Badness: 0.038402
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 4 3 9 | 0 -7 -2 -18 }}
</pre></div>
 
<h4>Original HTML content:</h4>
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~35/27 = 413.513
<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;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3d, …, 26d, 29 }}
&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;
 
Comma: 78125/73728&lt;br /&gt;
[[Badness]]: 0.117943
&lt;br /&gt;
 
POTE generator: ~125/96 = 414.509&lt;br /&gt;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
Map: [&amp;lt;1 4 3|, &amp;lt;0 -7 -2|]&lt;br /&gt;
 
EDOs: 23, 26, 29, 55c&lt;br /&gt;
Comma list: 55/54, 225/224, 245/242
Badness: 0.2477&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 4 3 9 10 | 0 -7 -2 -18 -19 }}
&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;
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 413.490
&lt;br /&gt;
 
POTE generator: ~9/7 = 415.519&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3de, …, 26de, 29 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3 8|, &amp;lt;0 -7 -2 -15|]&lt;br /&gt;
Badness: 0.054296
Wedgie: &amp;lt;&amp;lt;7 2 15 -13 4 29||&lt;br /&gt;
 
EDOs: 26&lt;br /&gt;
== Roman ==
Badness: 0.0953&lt;br /&gt;
{{See also| Avicennmic temperaments }}
&lt;br /&gt;
 
&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;
=== 7-limit a.k.a. crusher ===
Commas: 45/44, 99/98, 875/864&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
POTE generator: ~9/7 = 415.769&lt;br /&gt;
[[Comma list]]: 525/512, 3125/3024
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3 8 9|, &amp;lt;0 -7 -2 -15 -16|]&lt;br /&gt;
{{Mapping|legend=1| 1 4 3 -1 | 0 -7 -2 11 }}
EDOs: 23de, 26, 75bcd&lt;br /&gt;
 
Badness: 0.0491&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~63/50 = 414.552
&lt;br /&gt;
 
&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;
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
Commas: 45/44, 78/77, 99/98, 325/324&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.113386
POTE generator: ~9/7 = 415.645&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
Map: [&amp;lt;1 4 3 8 9 12|, &amp;lt;0 -7 -2 -15 -16 -24|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 26&lt;br /&gt;
 
Badness: 0.0384&lt;br /&gt;
Comma list: 100/99, 245/242, 525/512
&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;
Mapping: {{mapping| 1 4 3 -1 0 | 0 -7 -2 11 10 }}
Commas: 225/224, 6125/5832&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.471
POTE generator: ~35/27 = 413.513&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55c }}
Map: [&amp;lt;1 4 3 9|, &amp;lt;0 -7 -2 -18|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;7 2 18 -13 9 36||&lt;br /&gt;
Badness: 0.052841
EDOs: 29, 90cd, 119cd&lt;br /&gt;
 
Badness: 0.1179&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&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;
Comma list: 65/64, 100/99, 105/104, 245/242
&lt;br /&gt;
 
POTE generator: ~63/50 = 414.552&lt;br /&gt;
Mapping: {{mapping| 1 4 3 -1 0 3 | 0 -7 -2 11 10 2 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 4 3 -1|, &amp;lt;0 -7 -2 11|]&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 414.472
Wedgie: &amp;lt;&amp;lt;7 2 -11 -13 -37 -31||&lt;br /&gt;
 
EDOs: 23, 26, 29, 55c&lt;br /&gt;
{{Optimal ET sequence|legend=1| 3, 23, 26, 29, 55cf }}
Badness: 0.1134&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.030043
&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;
 
Commas: 50/49, 78125/73728&lt;br /&gt;
== Dubbla ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
POTE generator: ~192/175 = 185.738&lt;br /&gt;
 
&lt;br /&gt;
[[Comma list]]: 50/49, 78125/73728
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;
{{Mapping|legend=1| 2 1 4 5 | 0 7 2 2 }}
EDOs: 6, 26, 58c, 84c&lt;br /&gt;
 
Badness: 0.1817&lt;br /&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~192/175 = 185.738
&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=1| 6, 20b, 26, 58c }}
Commas: 50/49, 125/121, 1344/1331&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.181726
POTE generator: ~11/10 = 185.879&lt;br /&gt;
 
&lt;br /&gt;
=== 11-limit ===
Map: [&amp;lt;2 1 4 5 6|, &amp;lt;0 7 2 2 3|]&lt;br /&gt;
Subgroup: 2.3.5.7.11
EDOs: 6, 26, 58c, 84c&lt;br /&gt;
 
Badness: 0.0758&lt;br /&gt;
Comma list: 50/49, 125/121, 1344/1331
&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: {{mapping| 2 1 4 5 6 | 0 7 2 2 3 }}
Commas: 50/49, 105/104, 125/121, 144/143&lt;br /&gt;
 
&lt;br /&gt;
Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 185.879
POTE generator: ~11/10 = 185.702&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 6, 20b, 26 }}
Map: [&amp;lt;2 1 4 5 6 4|, &amp;lt;0 7 2 2 3 11|]&lt;br /&gt;
 
EDOs: 26, 58c, 84c&lt;br /&gt;
Badness: 0.075842
Badness: 0.0496&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== 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]]

Latest revision as of 00:36, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The wesley family of rank-2 temperaments tempers out the wesley comma, 78125/73728. The wesley comma is unchanged in Wesley Woolhouse's 7/26-comma meantone – it is an eigenmonzo (i.e. unchanged-interval). Here is a talk by Gene Ward Smith.

Wesley

Subgroup: 2.3.5

Comma list: 78125/73728

Mapping: [⟨1 4 3], ⟨0 -7 -2]]

mapping generators: ~2, ~125/96

Optimal tuning (POTE): ~2 = 1\1, ~125/96 = 414.509

Optimal ET sequence: 3, …, 23, 26, 29, 55c

Badness: 0.247718

Septimal wesley

Subgroup: 2.3.5.7

Comma list: 405/392, 875/864

Mapping: [⟨1 4 3 8], ⟨0 -7 -2 -15]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 415.519

Optimal ET sequence: 3d, …, 23d, 26

Badness: 0.095344

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 99/98, 875/864

Mapping: [⟨1 4 3 8 9], ⟨0 -7 -2 -15 -16]]

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

Optimal ET sequence: 3de, …, 23de, 26

Badness: 0.049066

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 78/77, 99/98, 325/324

Mapping: [⟨1 4 3 8 9 12], ⟨0 -7 -2 -15 -16 -24]]

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

Optimal ET sequence: 3def, 23deff, 26

Badness: 0.038402

Snipes

Subgroup: 2.3.5.7

Comma list: 225/224, 6125/5832

Mapping: [⟨1 4 3 9], ⟨0 -7 -2 -18]]

Optimal tuning (POTE): ~2 = 1\1, ~35/27 = 413.513

Optimal ET sequence: 3d, …, 26d, 29

Badness: 0.117943

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 225/224, 245/242

Mapping: [⟨1 4 3 9 10], ⟨0 -7 -2 -18 -19]]

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

Optimal ET sequence: 3de, …, 26de, 29

Badness: 0.054296

Roman

See also: Avicennmic temperaments

7-limit a.k.a. crusher

Subgroup: 2.3.5.7

Comma list: 525/512, 3125/3024

Mapping: [⟨1 4 3 -1], ⟨0 -7 -2 11]]

Optimal tuning (POTE): ~2 = 1\1, ~63/50 = 414.552

Optimal ET sequence: 3, 23, 26, 29, 55c

Badness: 0.113386

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 525/512

Mapping: [⟨1 4 3 -1 0], ⟨0 -7 -2 11 10]]

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

Optimal ET sequence: 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: [⟨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: 3, 23, 26, 29, 55cf

Badness: 0.030043

Dubbla

Subgroup: 2.3.5.7

Comma list: 50/49, 78125/73728

Mapping: [⟨2 1 4 5], ⟨0 7 2 2]]

Optimal tuning (POTE): ~2 = 1\1, ~192/175 = 185.738

Optimal ET sequence: 6, 20b, 26, 58c

Badness: 0.181726

11-limit

Subgroup: 2.3.5.7.11

Comma list: 50/49, 125/121, 1344/1331

Mapping: [⟨2 1 4 5 6], ⟨0 7 2 2 3]]

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

Optimal ET sequence: 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: [⟨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: 6f, 20bff, 26

Badness: 0.049603

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