Marvel family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 274512084 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 277079326 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-11 17:37:21 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-18 16:14:52 UTC</tt>.<br>
: The original revision id was <tt>274512084</tt>.<br>
: The original revision id was <tt>277079326</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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Map: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
Map: [&lt;1 0 0 -5|, &lt;0 1 0 2|, &lt;0 0 1 2|]
Generators: 2, 3, 5
Generators: 2, 3, 5
[[edo|EDOs]]: [[9edo|9]], [[10edo|10]], [[11edo|11]], [[12edo|12]], [[19edo|19]], [[22edo|22]], [[29edo|29]], [[31edo|31]], [[41edo|41]], [[50edo|50]], [[53edo|53]], [[72edo|72]], [[84edo|84]], [[94edo|94]], [[125edo|125]], [[197edo|197]], [[228edo|228]], [[269edo|269c]]
[[edo|EDOs]]: [[10edo|10]], [[12edo|12]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]],[[72edo|72]], [[197edo|197]], [[269edo|269c]]
Badness: 0.0000365
Badness: 0.0000365


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Map: [&lt;1 0 0 -5 12|, &lt;0 1 0 2 -1|, &lt;0 0 1 2 -3|]
Map: [&lt;1 0 0 -5 12|, &lt;0 1 0 2 -1|, &lt;0 0 1 2 -3|]
[[Generator|Generators]]: 2, 3, 5
[[Generator|Generators]]: 2, 3, 5
[[edo|Edos]]: [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[50edo|50]], [[53edo|53]], [[72edo|72]], [[166edo|166]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]]
[[edo|Edos]]: [[10edo|10]], [[12edo|12e]], [[19edo|19]], [[22edo|22]], [[31edo|31]], [[41edo|41]], [[53edo|53]], [[72edo|72]], [[166edo|166]], [[197edo|197e]], [[269edo|269ce]], [[341edo|341ce]]
Badness: 0.000255
Badness: 0.000255


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Map: [&lt;1 0 0 -5 12 -4|, &lt;0 1 0 2 -1 -1|, &lt;0 0 1 2 -3 4|]
Map: [&lt;1 0 0 -5 12 -4|, &lt;0 1 0 2 -1 -1|, &lt;0 0 1 2 -3 4|]
EDOs: 19, 22, 31, 50, 53, 72, 103, [[175edo|175f]]
EDOs: 19, 22, 31, 50, 53, 72, 103, [[175edo|175f]], [[300edo|300cef]], [[403bcef]]
Badness: 0.000690
Badness: 0.000690


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Map: [&lt;1 0 0 -5 12 2|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -2|]
Map: [&lt;1 0 0 -5 12 2|, &lt;0 1 0 2 -1 4|, &lt;0 0 1 2 -3 -2|]
EDOs: 19, 41, 53, 72, 166, 238cf, 404cef
EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef
Badness: 0.000721
Badness: 0.000721


Projection pairs: 7 225/32 11 4096/375 13 324/25
Projection pairs: 7 225/32 11 4096/375 13 324/25
[[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11
[[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11
==17-limit==
Commas: 225/224, 385/384, 325/324, 595/594
Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 -6|]
EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg
Badness: 0.000869
==Enodia==
Commas: 225/224, 385/384, 325/324, 375/374
Map: [&lt;1 0 0 -5 12 2 18|, &lt;0 1 0 2 -1 4 0|, &lt;0 0 1 2 -3 -2 6|]
EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg
Badness: .000917


=Marvell=
=Marvell=
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Projection pairs: 7 225/32 11 45/4 13 3375/256</pre></div>
Projection pairs: 7 225/32 11 45/4 13 3375/256</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Marvel family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:42:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;a href="#Marvel"&gt;Marvel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt; | &lt;a href="#Hecate"&gt;Hecate&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Marvell"&gt;Marvell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Isis"&gt;Isis&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Deecee"&gt;Deecee&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt; | &lt;a href="#Tripod"&gt;Tripod&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Prodigy"&gt;Prodigy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Minerva"&gt;Minerva&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Spectacle"&gt;Spectacle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Apollo"&gt;Apollo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Potassium"&gt;Potassium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;
<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;Marvel family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:46:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;a href="#Marvel"&gt;Marvel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt; | &lt;a href="#Hecate"&gt;Hecate&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Marvell"&gt;Marvell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Isis"&gt;Isis&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Deecee"&gt;Deecee&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Tripod"&gt;Tripod&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Prodigy"&gt;Prodigy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Minerva"&gt;Minerva&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Spectacle"&gt;Spectacle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Apollo"&gt;Apollo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Potassium"&gt;Potassium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;
&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Marvel&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Marvel"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Marvel&lt;/h1&gt;
The head of the marvel family is marvel, which tempers out &lt;a class="wiki_link" href="/225_224"&gt;225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt; or &lt;a class="wiki_link" href="/marvel%20comma"&gt;marvel comma&lt;/a&gt;. Marvel has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal list basis&lt;/a&gt; of [2, 3, 5]; hence a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by &lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;. &lt;br /&gt;
The head of the marvel family is marvel, which tempers out &lt;a class="wiki_link" href="/225_224"&gt;225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt; or &lt;a class="wiki_link" href="/marvel%20comma"&gt;marvel comma&lt;/a&gt;. Marvel has a &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal list basis&lt;/a&gt; of [2, 3, 5]; hence a &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; scale can be converted to marvel simply by tempering it. One way to do that, and an excellent marvel tuning, is given by &lt;a class="wiki_link" href="/197edo"&gt;197edo&lt;/a&gt;. &lt;br /&gt;
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Map: [&amp;lt;1 0 0 -5|, &amp;lt;0 1 0 2|, &amp;lt;0 0 1 2|]&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5|, &amp;lt;0 1 0 2|, &amp;lt;0 0 1 2|]&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
Generators: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/11edo"&gt;11&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/84edo"&gt;84&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/125edo"&gt;125&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197&lt;/a&gt;, &lt;a class="wiki_link" href="/228edo"&gt;228&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269c&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;EDOs&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;,&lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269c&lt;/a&gt;&lt;br /&gt;
Badness: 0.0000365&lt;br /&gt;
Badness: 0.0000365&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Map: [&amp;lt;1 0 0 -5 12|, &amp;lt;0 1 0 2 -1|, &amp;lt;0 0 1 2 -3|]&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12|, &amp;lt;0 1 0 2 -1|, &amp;lt;0 0 1 2 -3|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generators&lt;/a&gt;: 2, 3, 5&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197e&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269ce&lt;/a&gt;, &lt;a class="wiki_link" href="/341edo"&gt;341ce&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/edo"&gt;Edos&lt;/a&gt;: &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12e&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/197edo"&gt;197e&lt;/a&gt;, &lt;a class="wiki_link" href="/269edo"&gt;269ce&lt;/a&gt;, &lt;a class="wiki_link" href="/341edo"&gt;341ce&lt;/a&gt;&lt;br /&gt;
Badness: 0.000255&lt;br /&gt;
Badness: 0.000255&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 -4|, &amp;lt;0 1 0 2 -1 -1|, &amp;lt;0 0 1 2 -3 4|]&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 -4|, &amp;lt;0 1 0 2 -1 -1|, &amp;lt;0 0 1 2 -3 4|]&lt;br /&gt;
EDOs: 19, 22, 31, 50, 53, 72, 103, &lt;a class="wiki_link" href="/175edo"&gt;175f&lt;/a&gt;&lt;br /&gt;
EDOs: 19, 22, 31, 50, 53, 72, 103, &lt;a class="wiki_link" href="/175edo"&gt;175f&lt;/a&gt;, &lt;a class="wiki_link" href="/300edo"&gt;300cef&lt;/a&gt;, &lt;a class="wiki_link" href="/403bcef"&gt;403bcef&lt;/a&gt;&lt;br /&gt;
Badness: 0.000690&lt;br /&gt;
Badness: 0.000690&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2|, &amp;lt;0 1 0 2 -1 4|, &amp;lt;0 0 1 2 -3 -2|]&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2|, &amp;lt;0 1 0 2 -1 4|, &amp;lt;0 0 1 2 -3 -2|]&lt;br /&gt;
EDOs: 19, 41, 53, 72, 166, 238cf, 404cef&lt;br /&gt;
EDOs: 19, 41, 53, 72, 113, 125f, 166, 238cf, 404cef&lt;br /&gt;
Badness: 0.000721&lt;br /&gt;
Badness: 0.000721&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 4/3, 5/4, 16/15, 15/14, 6/5, 9/8, 7/5, 9/7, 7/6, 10/9, 8/7, 18/13, 11/8, 12/11, 13/12, 11/9, 11/10, 15/13, 15/11, 16/13, 13/11, 14/13, 13/10, 14/11&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Marvell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Marvell&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Hecate-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;17-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 325/324, 595/594&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2 18|, &amp;lt;0 1 0 2 -1 4 0|, &amp;lt;0 0 1 2 -3 -2 -6|]&lt;br /&gt;
EDOs: 19, 41, 53g, 72, 113, 166g, 238cfg, 351cfg, 404cefg&lt;br /&gt;
Badness: 0.000869&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Hecate-Enodia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Enodia&lt;/h2&gt;
Commas: 225/224, 385/384, 325/324, 375/374&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 -5 12 2 18|, &amp;lt;0 1 0 2 -1 4 0|, &amp;lt;0 0 1 2 -3 -2 6|]&lt;br /&gt;
EDOs: 41g, 53, 72, 125f, 166g, 238cfg, 363cefg, 404cefg&lt;br /&gt;
Badness: .000917&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Marvell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Marvell&lt;/h1&gt;
Commas: 225/224, 385/384, 1573/1568&lt;br /&gt;
Commas: 225/224, 385/384, 1573/1568&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 400: Line 428:
Badness: 0.000862&lt;br /&gt;
Badness: 0.000862&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Isis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Isis&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Isis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Isis&lt;/h1&gt;
Commas: 225/224, 385/384, 275/273&lt;br /&gt;
Commas: 225/224, 385/384, 275/273&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Projection pairs: 7 225/32 11 4096/375 13 131072/10125&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 131072/10125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Deecee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Deecee&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Deecee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Deecee&lt;/h1&gt;
Commas: 225/224, 385/384, 364/363&lt;br /&gt;
Commas: 225/224, 385/384, 364/363&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Tripod"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Tripod&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Tripod"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Tripod&lt;/h1&gt;
Commas: 105/104, 144/143, 196/195&lt;br /&gt;
Commas: 105/104, 144/143, 196/195&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Projection pairs: 7 225/32 11 4096/375 13 3375/256&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 3375/256&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Prodigy&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Prodigy&lt;/h1&gt;
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;miracle temperament&lt;/a&gt;. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.&lt;br /&gt;
Prodigy shrinks 1024/1029, 243/242, 384/385 and 2400/2401 down to the same tiny interval. Hence in practice it probably makes the most sense to temper this out as well, leading to &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;miracle temperament&lt;/a&gt;. This, however, does not render it pointless to consider prodigy; for one thing, scales in prodigy such as hobbit scales translate into interesting scales for miracle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Scales: &lt;a class="wiki_link" href="/prodigy11"&gt;prodigy11&lt;/a&gt;, &lt;a class="wiki_link" href="/prodigy12"&gt;prodigy12&lt;/a&gt;, &lt;a class="wiki_link" href="/prodigy29"&gt;prodigy29&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/prodigy11"&gt;prodigy11&lt;/a&gt;, &lt;a class="wiki_link" href="/prodigy12"&gt;prodigy12&lt;/a&gt;, &lt;a class="wiki_link" href="/prodigy29"&gt;prodigy29&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Prodigy-Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Hobbit bases&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Prodigy-Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Hobbit bases&lt;/h2&gt;
{2, 3, 5} subgroup&lt;br /&gt;
{2, 3, 5} subgroup&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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41: 34171875/33554432, 32805/32768&lt;br /&gt;
41: 34171875/33554432, 32805/32768&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Minerva"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Minerva&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Minerva"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Minerva&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 99/98, 176/175&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 99/98, 176/175&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Semicomma%20family"&gt;orwell&lt;/a&gt;&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Semicomma%20family"&gt;orwell&lt;/a&gt;&lt;br /&gt;
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Scales: &lt;a class="wiki_link" href="/minerva12"&gt;minerva12&lt;/a&gt;, &lt;a class="wiki_link" href="/minerva22x"&gt;minerva22x&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/minerva12"&gt;minerva12&lt;/a&gt;, &lt;a class="wiki_link" href="/minerva22x"&gt;minerva22x&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Minerva-Athene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Athene&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Minerva-Athene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Athene&lt;/h2&gt;
Commas: 99/98, 176/175, 275/273&lt;br /&gt;
Commas: 99/98, 176/175, 275/273&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 5625/512 13 625/48&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 5625/512 13 625/48&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Spectacle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Spectacle&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Spectacle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Spectacle&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 243/242&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 243/242&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;marvo&lt;/a&gt;&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;marvo&lt;/a&gt;&lt;br /&gt;
Line 512: Line 540:
Scales: &lt;a class="wiki_link" href="/spectacle31"&gt;spectacle31&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/spectacle31"&gt;spectacle31&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Apollo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Apollo&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Apollo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Apollo&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 100/99, 225/224&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 100/99, 225/224&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic&lt;/a&gt;&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Magic%20family"&gt;Magic&lt;/a&gt;&lt;br /&gt;
Line 523: Line 551:
Projection pairs: 7 225/32 11 100/9&lt;br /&gt;
Projection pairs: 7 225/32 11 100/9&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Potassium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Potassium&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Potassium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Potassium&lt;/h1&gt;
Commas: 45/44, 56/55&lt;br /&gt;
Commas: 45/44, 56/55&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 534: Line 562:
Projection pairs: 7 225/32 11 45/4&lt;br /&gt;
Projection pairs: 7 225/32 11 45/4&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Potassium-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Potassium-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
Commas: 45/44, 56/55, 78/77&lt;br /&gt;
Commas: 45/44, 56/55, 78/77&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;