Marvel temperaments: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 337659208 - Original comment: **
Wikispaces>phylingual
**Imported revision 353613468 - 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>2012-05-20 19:21:43 UTC</tt>.<br>
: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-07-17 21:38:37 UTC</tt>.<br>
: The original revision id was <tt>337659208</tt>.<br>
: The original revision id was <tt>353613468</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>
<h4>Original Wikitext content:</h4>
<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">[[toc]]
<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">[[toc]]
This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =[[225_224| 225/224]], the [[marvel comma]] or [[septimal kleisma]]. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.
This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =[[225_224| 225/224]], the [[marvel comma]] or [[septimal kleisma]]. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.


Line 15: Line 14:
[[Comma]]s: 49/48, 225/224
[[Comma]]s: 49/48, 225/224


[[POTE tuning|POTE temperament]]: 125.608
[[POTE tuning|POTE temperament]]: ~15/14 = 125.608


[[Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
[[Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
Line 24: Line 23:
Commas: 45/44, 49/48, 56/55
Commas: 45/44, 49/48, 56/55


[[POTE tuning|POTE generator]]: 126.474
[[POTE tuning|POTE generator]]: ~15/14 = 126.474


Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
Line 33: Line 32:
Commas: 45/44, 49/48, 56/55, 78/77
Commas: 45/44, 49/48, 56/55, 78/77


[[POTE tuning|POTE generator]]: 126.431
[[POTE tuning|POTE generator]]: ~14/13 = 126.431


Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
Line 74: Line 73:
Badness: 0.0202
Badness: 0.0202


=Negroni=
=Negroni=  
Commas: 49/48, 55/54, 225/224
Commas: 49/48, 55/54, 225/224


Line 92: Line 91:
Badness: 0.3864
Badness: 0.3864


==7-limit==
==7-limit==  
Commas: 225/224, 118098/117649
Commas: 225/224, 118098/117649


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Badness: 0.0592
Badness: 0.0592


==11-limit==
==11-limit==  
Commas: 45/44, 56/55, 1029/1000
Commas: 45/44, 56/55, 1029/1000


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Badness: 0.3785
Badness: 0.3785


==7-limit==
==7-limit==  
Commas: 225/224, 50421/50000
Commas: 225/224, 50421/50000


Line 247: Line 246:
Badness: 0.4538
Badness: 0.4538


==7-limit==
==7-limit==  
Commas: 225/224, 2500000/2470629
Commas: 225/224, 2500000/2470629


Line 257: Line 256:
Badness: 0.0551
Badness: 0.0551


==11-limit==
==11-limit==  
Commas: 225/224, 441/440, 1344/1331
Commas: 225/224, 441/440, 1344/1331


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Badness: 0.0364
Badness: 0.0364


==13-limit==
==13-limit==  
Commas: 144/143, 225/224, 364/363, 441/440
Commas: 144/143, 225/224, 364/363, 441/440


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Badness: 0.6709
Badness: 0.6709


==7-limit==
==7-limit==  
Commas: 225/224, 84035/82944
Commas: 225/224, 84035/82944


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Badness: 0.0304
Badness: 0.0304


==13-limit==
==13-limit==  
Commas: 169/168 225/224 364/363 1716/1715
Commas: 169/168 225/224 364/363 1716/1715


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Badness: 0.0223
Badness: 0.0223


=Submajor=
=Submajor=  
Comma: 69198046875/68719476736
Comma: 69198046875/68719476736


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Badness: 0.1302
Badness: 0.1302


==7-limit==
==7-limit==  
Commas: 225/224, 51200/50421  
Commas: 225/224, 51200/50421


POTE generator: ~49/40 = 362.255
POTE generator: ~49/40 = 362.255
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Badness: 0.0605
Badness: 0.0605


==11-limit==
==11-limit==  
Commas: 225/224, 385/384, 6655/6561
Commas: 225/224, 385/384, 6655/6561


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Badness: 0.0506
Badness: 0.0506


==13-limit==
==13-limit==  
Commas: 169/168, 225/224, 275/273, 385/384
Commas: 169/168, 225/224, 275/273, 385/384


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Badness: 0.0277
Badness: 0.0277


==Interpental==
==Interpental==  
Commas: 99/98, 176/175, 51200/50421
Commas: 99/98, 176/175, 51200/50421


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Badness: 0.0518
Badness: 0.0518


===13-limit===
===13-limit===  
Commas: 99/98, 169/168, 176/175, 640/637
Commas: 99/98, 169/168, 176/175, 640/637


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Badness: 0.0297
Badness: 0.0297


=Alphorn=
=Alphorn=  
Commas: 225/224, 5764801/5668704
Commas: 225/224, 5764801/5668704


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Badness: 0.1293
Badness: 0.1293


==11-limit==
==11-limit==  
Commas: 225/224, 385/384, 12250/11979
Commas: 225/224, 385/384, 12250/11979


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Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
EDOs: 41, 315cde
EDOs: 41, 315cde
Badness: 0.0735
Badness: 0.0735</pre></div>
</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 temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:112:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;/div&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 temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:112:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:112 --&gt;&lt;!-- ws:start:WikiTextTocRule:113: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;/div&gt;
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&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alphorn-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alphorn-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;This page discusses some of the temperaments tempering out |-5 2 2 -1&amp;gt; =&lt;a class="wiki_link" href="/225_224"&gt; 225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/marvel%20comma"&gt;marvel comma&lt;/a&gt; or &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.&lt;br /&gt;
This page discusses some of the temperaments tempering out |-5 2 2 -1&amp;gt; =&lt;a class="wiki_link" href="/225_224"&gt; 225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/marvel%20comma"&gt;marvel comma&lt;/a&gt; or &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.&lt;br /&gt;
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-9/7 versions of the augmented triad. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.&lt;br /&gt;
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  &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 225/224&lt;br /&gt;
  &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 125.608&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~15/14 = 125.608&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
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  Commas: 45/44, 49/48, 56/55&lt;br /&gt;
  Commas: 45/44, 49/48, 56/55&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 126.474&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~15/14 = 126.474&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -4 3 -2 -5|]&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -4 3 -2 -5|]&lt;br /&gt;
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  Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
  Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 126.431&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/13 = 126.431&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 4|, &amp;lt;0 -4 3 -2 -5 -3|]&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 4|, &amp;lt;0 -4 3 -2 -5 -3|]&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Negroni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Negroni&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Negroni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Negroni&lt;/h1&gt;
Commas: 49/48, 55/54, 225/224&lt;br /&gt;
Commas: 49/48, 55/54, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.539&lt;br /&gt;
POTE generator: ~15/14 = 124.539&lt;br /&gt;
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&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="Wizard-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Wizard-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 118098/117649&lt;br /&gt;
Commas: 225/224, 118098/117649&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.256&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.256&lt;br /&gt;
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&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="Triton-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Triton-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 56/55, 1029/1000&lt;br /&gt;
Commas: 45/44, 56/55, 1029/1000&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 569.144&lt;br /&gt;
POTE generator: ~7/5 = 569.144&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Tritonic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Tritonic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 580.286&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 580.286&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Merman-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Merman-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 2500000/2470629&lt;br /&gt;
Commas: 225/224, 2500000/2470629&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.585&lt;br /&gt;
POTE generator: ~7/5 = 585.585&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Merman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Merman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 441/440, 1344/1331&lt;br /&gt;
Commas: 225/224, 441/440, 1344/1331&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.606&lt;br /&gt;
POTE generator: ~7/5 = 585.606&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Merman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Merman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;13-limit&lt;/h2&gt;
Commas: 144/143, 225/224, 364/363, 441/440&lt;br /&gt;
Commas: 144/143, 225/224, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.657&lt;br /&gt;
POTE generator: ~7/5 = 585.657&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Septimin-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc30"&gt;&lt;a name="Septimin-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 84035/82944&lt;br /&gt;
Commas: 225/224, 84035/82944&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.632&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.632&lt;br /&gt;
Line 1,009: Line 1,006:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Enneaportent-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Enneaportent-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168 225/224 364/363 1716/1715&lt;br /&gt;
Commas: 169/168 225/224 364/363 1716/1715&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.047&lt;br /&gt;
POTE generator: ~5/4 = 383.047&lt;br /&gt;
Line 1,018: Line 1,015:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc48"&gt;&lt;a name="Submajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Submajor&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc48"&gt;&lt;a name="Submajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;Submajor&lt;/h1&gt;
Comma: 69198046875/68719476736&lt;br /&gt;
Comma: 69198046875/68719476736&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10125/8192 = 362.321&lt;br /&gt;
POTE generator: ~10125/8192 = 362.321&lt;br /&gt;
Line 1,027: Line 1,024:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Submajor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;7-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc49"&gt;&lt;a name="Submajor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 51200/50421 &lt;br /&gt;
Commas: 225/224, 51200/50421&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 362.255&lt;br /&gt;
POTE generator: ~49/40 = 362.255&lt;br /&gt;
Line 1,037: Line 1,034:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Submajor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Submajor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 6655/6561&lt;br /&gt;
Commas: 225/224, 385/384, 6655/6561&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/22 = 362.101&lt;br /&gt;
POTE generator: ~27/22 = 362.101&lt;br /&gt;
Line 1,046: Line 1,043:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Submajor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;13-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Submajor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 275/273, 385/384&lt;br /&gt;
Commas: 169/168, 225/224, 275/273, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 362.105&lt;br /&gt;
POTE generator: ~16/13 = 362.105&lt;br /&gt;
Line 1,055: Line 1,052:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Submajor-Interpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;Interpental&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Submajor-Interpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;Interpental&lt;/h2&gt;
Commas: 99/98, 176/175, 51200/50421&lt;br /&gt;
Commas: 99/98, 176/175, 51200/50421&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 362.418&lt;br /&gt;
POTE generator: ~49/40 = 362.418&lt;br /&gt;
Line 1,064: Line 1,061:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc53"&gt;&lt;a name="Submajor-Interpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc53"&gt;&lt;a name="Submajor-Interpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;13-limit&lt;/h3&gt;
Commas: 99/98, 169/168, 176/175, 640/637&lt;br /&gt;
Commas: 99/98, 169/168, 176/175, 640/637&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 362.402&lt;br /&gt;
POTE generator: ~16/13 = 362.402&lt;br /&gt;
Line 1,073: Line 1,070:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc54"&gt;&lt;a name="Alphorn"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;Alphorn&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc54"&gt;&lt;a name="Alphorn"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;Alphorn&lt;/h1&gt;
Commas: 225/224, 5764801/5668704&lt;br /&gt;
Commas: 225/224, 5764801/5668704&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 556.221&lt;br /&gt;
POTE generator: ~48/35 = 556.221&lt;br /&gt;
Line 1,083: Line 1,080:
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Alphorn-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;11-limit&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc55"&gt;&lt;a name="Alphorn-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 12250/11979&lt;br /&gt;
Commas: 225/224, 385/384, 12250/11979&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 556.144&lt;br /&gt;
POTE generator: ~11/8 = 556.144&lt;br /&gt;