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Marvel family: Difference between revisions

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**Imported revision 257521798 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 258350896 - 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>2011-09-23 12:18:14 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-26 14:34:40 UTC</tt>.<br>
: The original revision id was <tt>257521798</tt>.<br>
: The original revision id was <tt>258350896</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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[[Projection pair]]s: 7 225/32
[[Projection pair]]s: 7 225/32
[[Spectrum of a temperament|Spectrum]]: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9


Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]]
Scales: [[marvel9]], [[marvel10]], [[marvel11]], [[marvel12]], [[marvel19]], [[marvel22]], [[pump12_1]], [[pump12_2]], [[pump13]], [[pump14]], [[pump15]], [[pump16]], [[pump17]], [[pump18]]
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[[http://chrisvaisvil.com/?p=314|Semimarvelous Blue Drawf]] by [[Chris Vaisvil]]
[[http://chrisvaisvil.com/?p=314|Semimarvelous Blue Drawf]] by [[Chris Vaisvil]]


==Eleven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.


=Unidecimal marvel (Unimarv)=
==11-limit (Unimarv)==
[[Comma|Commas]]: 225/224, 385/384
[[Comma|Commas]]: 225/224, 385/384
Related linear temperament: [[Kleismic family|catakleismic temperament]]
Related linear temperament: [[Kleismic family|catakleismic temperament]]
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[[Projection pair]]s: 7 225/32 11 4096/375
[[Projection pair]]s: 7 225/32 11 4096/375
 
[[Spectrum of a temperament|Spectrum]]: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]
Scales: [[marvel22_11]], [[unimarv19]], [[unimarv22]]


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41: 3125/3072, 34171875/33554432
41: 3125/3072, 34171875/33554432


==Hecate==
==13-limit==
Commas: 225/224, 385/384, 351/350
 
13-limit eigenmonzo subgroup: 2.11/9.13/9
15-limit eigenmonzo subgroup: 2.15/11.15/13
 
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
Badness: 0.000690
 
[[Spectrum of a temperament|Spectrum]]: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11
 
==Other eleven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.
 
=Hecate=
Commas: 225/224, 385/384, 325/324
Commas: 225/224, 385/384, 325/324


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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


==Marvell==
=Marvell=
Commas: 225/224, 385/384, 1573/1568
Commas: 225/224, 385/384, 1573/1568


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Badness: 0.000862
Badness: 0.000862


==Isis==
=Isis=
Commas: 225/224, 385/384, 275/273
Commas: 225/224, 385/384, 275/273


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Projection pairs: 7 225/32 11 4096/375 13 131072/10125
Projection pairs: 7 225/32 11 4096/375 13 131072/10125


==Deecee==
=Deecee=
Commas: 225/224, 385/384, 364/363
Commas: 225/224, 385/384, 364/363


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Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875
Projection pairs: 7 225/32 11 4096/375 13 134217728/10546875


==Tripod==
=Tripod=
Commas: 105/104, 144/143, 196/195
Commas: 105/104, 144/143, 196/195


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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:40:&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:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;a href="#Marvel"&gt;Marvel&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&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;a href="#Unidecimal marvel (Unimarv)"&gt;Unidecimal marvel (Unimarv)&lt;/a&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;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Prodigy"&gt;Prodigy&lt;/a&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="#Minerva"&gt;Minerva&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;a href="#Spectacle"&gt;Spectacle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Apollo"&gt;Apollo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Potassium"&gt;Potassium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&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: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;
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:64 --&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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&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 4/3, 5/4, 7/5, 7/6, 8/7, 6/5, 9/8, 9/7, 10/9&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/marvel9"&gt;marvel9&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel10"&gt;marvel10&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel11"&gt;marvel11&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel12"&gt;marvel12&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel19"&gt;marvel19&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel22"&gt;marvel22&lt;/a&gt;, &lt;a class="wiki_link" href="/pump12_1"&gt;pump12_1&lt;/a&gt;, &lt;a class="wiki_link" href="/pump12_2"&gt;pump12_2&lt;/a&gt;, &lt;a class="wiki_link" href="/pump13"&gt;pump13&lt;/a&gt;, &lt;a class="wiki_link" href="/pump14"&gt;pump14&lt;/a&gt;, &lt;a class="wiki_link" href="/pump15"&gt;pump15&lt;/a&gt;, &lt;a class="wiki_link" href="/pump16"&gt;pump16&lt;/a&gt;, &lt;a class="wiki_link" href="/pump17"&gt;pump17&lt;/a&gt;, &lt;a class="wiki_link" href="/pump18"&gt;pump18&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/marvel9"&gt;marvel9&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel10"&gt;marvel10&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel11"&gt;marvel11&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel12"&gt;marvel12&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel19"&gt;marvel19&lt;/a&gt;, &lt;a class="wiki_link" href="/marvel22"&gt;marvel22&lt;/a&gt;, &lt;a class="wiki_link" href="/pump12_1"&gt;pump12_1&lt;/a&gt;, &lt;a class="wiki_link" href="/pump12_2"&gt;pump12_2&lt;/a&gt;, &lt;a class="wiki_link" href="/pump13"&gt;pump13&lt;/a&gt;, &lt;a class="wiki_link" href="/pump14"&gt;pump14&lt;/a&gt;, &lt;a class="wiki_link" href="/pump15"&gt;pump15&lt;/a&gt;, &lt;a class="wiki_link" href="/pump16"&gt;pump16&lt;/a&gt;, &lt;a class="wiki_link" href="/pump17"&gt;pump17&lt;/a&gt;, &lt;a class="wiki_link" href="/pump18"&gt;pump18&lt;/a&gt;&lt;br /&gt;
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&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=314" rel="nofollow"&gt;Semimarvelous Blue Drawf&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=314" rel="nofollow"&gt;Semimarvelous Blue Drawf&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Marvel-Eleven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Eleven limit children&lt;/h2&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Unidecimal marvel (Unimarv)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Unidecimal marvel (Unimarv)&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Marvel-11-limit (Unimarv)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit (Unimarv)&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 385/384&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Commas&lt;/a&gt;: 225/224, 385/384&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt;&lt;br /&gt;
Related linear temperament: &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 4096/375&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 7 225/32 11 4096/375&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 5/4, 4/3, 7/6, 8/7, 7/5, 6/5, 9/7, 12/11, 9/8, 11/8, 11/9, 10/9, 11/10, 14/11&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/marvel22_11"&gt;marvel22_11&lt;/a&gt;, &lt;a class="wiki_link" href="/unimarv19"&gt;unimarv19&lt;/a&gt;, &lt;a class="wiki_link" href="/unimarv22"&gt;unimarv22&lt;/a&gt;&lt;br /&gt;
Scales: &lt;a class="wiki_link" href="/marvel22_11"&gt;marvel22_11&lt;/a&gt;, &lt;a class="wiki_link" href="/unimarv19"&gt;unimarv19&lt;/a&gt;, &lt;a class="wiki_link" href="/unimarv22"&gt;unimarv22&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Unidecimal marvel (Unimarv)--Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Hobbit bases&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Marvel-11-limit (Unimarv)-Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Hobbit bases&lt;/h3&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: 3125/3072, 34171875/33554432&lt;br /&gt;
41: 3125/3072, 34171875/33554432&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Unidecimal marvel (Unimarv)-Hecate"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Hecate&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Marvel-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 351/350&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.11/9.13/9&lt;br /&gt;
15-limit eigenmonzo subgroup: 2.15/11.15/13&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;
EDOs: 19, 22, 31, 50, 53, 72, 103&lt;br /&gt;
Badness: 0.000690&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 5/4, 4/3, 16/15, 15/14, 9/7, 6/5, 7/6, 11/8, 7/5, 9/8, 8/7, 10/9, 12/11, 13/10, 11/10, 15/11, 16/13, 11/9, 15/13, 14/13, 13/12, 14/11, 18/13, 13/11&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Marvel-Other eleven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Other eleven limit children&lt;/h2&gt;
The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 11-limit family member we are looking at. Adding 4125/4096 gives unidecimal marvel, 91125/90112 gives prodigy, 5632/5625 minerva and 243/242 spectacle.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Hecate"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Hecate&lt;/h1&gt;
Commas: 225/224, 385/384, 325/324&lt;br /&gt;
Commas: 225/224, 385/384, 325/324&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 359: Line 388:
&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 324/25&lt;br /&gt;
Projection pairs: 7 225/32 11 4096/375 13 324/25&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:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Unidecimal marvel (Unimarv)-Marvell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Marvell&lt;/h2&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;
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 370: Line 400:
Badness: 0.000862&lt;br /&gt;
Badness: 0.000862&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Unidecimal marvel (Unimarv)-Isis"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Isis&lt;/h2&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;
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;
Line 379: Line 409:
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:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Unidecimal marvel (Unimarv)-Deecee"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Deecee&lt;/h2&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;
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;
Line 391: Line 421:
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:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Unidecimal marvel (Unimarv)-Tripod"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Tripod&lt;/h2&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;
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;
Line 403: Line 433:
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:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Prodigy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Prodigy&lt;/h1&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;
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;
Line 428: Line 458:
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:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Prodigy-Hobbit bases"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Hobbit bases&lt;/h2&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;
{2, 3, 5} subgroup&lt;br /&gt;
{2, 3, 5} subgroup&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 434: Line 464:
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:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Minerva"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Minerva&lt;/h1&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;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;
Line 453: Line 483:
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:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Minerva-Athene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Athene&lt;/h2&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;
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;
Line 465: Line 495:
&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:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Spectacle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Spectacle&lt;/h1&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;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 482: Line 512:
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:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Apollo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Apollo&lt;/h1&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;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 493: Line 523:
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:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Potassium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Potassium&lt;/h1&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;
Commas: 45/44, 56/55&lt;br /&gt;
Commas: 45/44, 56/55&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 504: Line 534:
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:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Potassium-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&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;
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;
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