Marvel temperaments: Difference between revisions

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**Imported revision 203968408 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 213446802 - 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>2011-02-22 09:49:34 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-23 22:40:03 UTC</tt>.<br>
: The original revision id was <tt>203968408</tt>.<br>
: The original revision id was <tt>213446802</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">This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.
<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|flat]]
 
This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.


Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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.
Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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.


==Negri==
=Negri=
Commas: 49/48, 225/224
Commas: 49/48, 225/224


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EDOs: 9, 10, 19, 86
EDOs: 9, 10, 19, 86


===11-limit===
==11-limit==
Commas: 45/44, 49/48, 56/55
Commas: 45/44, 49/48, 56/55


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EDOs: 9, 10, 19
EDOs: 9, 10, 19


===13-limit===
==13-limit==
Commas: 45/44, 49/48, 56/55, 78/77
Commas: 45/44, 49/48, 56/55, 78/77


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EDOs: 9, 10, 19
EDOs: 9, 10, 19


===Negric===
=Negric=
====11-limit====
Commas: 33/32, 49/48, 77/75
Commas: 33/32, 49/48, 77/75


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Badness: 0.0306
Badness: 0.0306


====13-limit====
==13-limit==
Commas: 33/32, 49/48, 65/64, 91/90
Commas: 33/32, 49/48, 65/64, 91/90


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Badness: 0.0202
Badness: 0.0202


==Wizard==
=Wizard=
Commas: 225/224, 118098/117649
Commas: 225/224, 118098/117649


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EDOs: 22, 50, 72, 382, 454
EDOs: 22, 50, 72, 382, 454


===11-limit===
==11-limit==
Commas: 225/224, 385/384, 4000/3993
Commas: 225/224, 385/384, 4000/3993


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EDOs: 22, 50, 72, 166, 310
EDOs: 22, 50, 72, 166, 310


===13-limit===
==13-limit==
Commas: 225/224, 351/350, 364/363, 385/384
Commas: 225/224, 351/350, 364/363, 385/384


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EDOs: 22, 50, 72
EDOs: 22, 50, 72


===17-limit===
==17-limit==
Commas: 221/220, 273/272, 289/288, 351/350, 375/374
Commas: 221/220, 273/272, 289/288, 351/350, 375/374


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EDOs: 22, 50, 72
EDOs: 22, 50, 72


===19-limit===
==19-limit==
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


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EDOs: 22, 50, 72, 194, 460
EDOs: 22, 50, 72, 194, 460


==Tritonic==
=Tritonic=
Commas: 225/224, 50421/50000
Commas: 225/224, 50421/50000


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EDOs: 29, 31, 60, 91, 122, 213
EDOs: 29, 31, 60, 91, 122, 213


===11-limit===
==11-limit==
Commas: 225/224, 385/384, 27783/27500
Commas: 225/224, 385/384, 27783/27500


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EDOs: 29, 31, 60, 91, 122, 153
EDOs: 29, 31, 60, 91, 122, 153


==Septimin==
=Septimin=
Commas: 225/224, 84035/82944
Commas: 225/224, 84035/82944


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EDOs: 9, 32, 41, 91, 132
EDOs: 9, 32, 41, 91, 132


===11-limit===
==11-limit==
Commas: 225/224, 385/384, 2401/2376
Commas: 225/224, 385/384, 2401/2376


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EDOs: 9, 32, 41, 91
EDOs: 9, 32, 41, 91


===13-limit===
==13-limit==
Commas: 105/104, 144/143, 196/195, 245/242
Commas: 105/104, 144/143, 196/195, 245/242


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EDOs: 9, 41, 91
EDOs: 9, 41, 91


==Slender==
=Slender=
Commas: 225/225, 589824/588245
Commas: 225/225, 589824/588245


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EDOs: 31, 94, 125
EDOs: 31, 94, 125


===11-limit===
==11-limit==
Commas: 225/224, 385/384, 1331/1323
Commas: 225/224, 385/384, 1331/1323


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EDOs: 31, 63, 94, 125
EDOs: 31, 63, 94, 125


==Triton==
=Triton=
Commas: 225/224, 1029/1000
Commas: 225/224, 1029/1000


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EDOs: 19, 135, 289
EDOs: 19, 135, 289


==Marvo==
=Marvo=
Commas: 225/224, 78125000/78121827
Commas: 225/224, 78125000/78121827


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EDOs: 65, 72
EDOs: 65, 72


===11-limit===
==11-limit==
Commas: 225/224, 243/242, 4000/3993
Commas: 225/224, 243/242, 4000/3993


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EDOs: 65, 72, 281, 497</pre></div>
EDOs: 65, 72, 281, 497</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;This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.&lt;br /&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: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="#Negri"&gt;Negri&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;a href="#Negric"&gt;Negric&lt;/a&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="#Wizard"&gt;Wizard&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;a href="#Tritonic"&gt;Tritonic&lt;/a&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="#Septimin"&gt;Septimin&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;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Slender"&gt;Slender&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="#Triton"&gt;Triton&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Marvo"&gt;Marvo&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;
&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;br /&gt;
This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton 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)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Negri&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Negri&lt;/h1&gt;
Commas: 49/48, 225/224&lt;br /&gt;
Commas: 49/48, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 9, 10, 19, 86&lt;br /&gt;
EDOs: 9, 10, 19, 86&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Negri-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Negri-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
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;
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EDOs: 9, 10, 19&lt;br /&gt;
EDOs: 9, 10, 19&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Negri-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Negri-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
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;
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EDOs: 9, 10, 19&lt;br /&gt;
EDOs: 9, 10, 19&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Negri-Negric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Negric&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Negric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Negric&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc4"&gt;&lt;a name="x-Negri-Negric-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h4&gt;
Commas: 33/32, 49/48, 77/75&lt;br /&gt;
Commas: 33/32, 49/48, 77/75&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0306&lt;br /&gt;
Badness: 0.0306&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h4&amp;gt; --&gt;&lt;h4 id="toc5"&gt;&lt;a name="x-Negri-Negric-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h4&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Negric-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Badness: 0.0202&lt;br /&gt;
Badness: 0.0202&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Wizard&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Wizard&lt;/h1&gt;
Commas: 225/224, 118098/117649&lt;br /&gt;
Commas: 225/224, 118098/117649&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 22, 50, 72, 382, 454&lt;br /&gt;
EDOs: 22, 50, 72, 382, 454&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Wizard-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Wizard-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 4000/3993&lt;br /&gt;
Commas: 225/224, 385/384, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 22, 50, 72, 166, 310&lt;br /&gt;
EDOs: 22, 50, 72, 166, 310&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x-Wizard-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Wizard-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h2&gt;
Commas: 225/224, 351/350, 364/363, 385/384&lt;br /&gt;
Commas: 225/224, 351/350, 364/363, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 22, 50, 72&lt;br /&gt;
EDOs: 22, 50, 72&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Wizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;17-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Wizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;17-limit&lt;/h2&gt;
Commas: 221/220, 273/272, 289/288, 351/350, 375/374&lt;br /&gt;
Commas: 221/220, 273/272, 289/288, 351/350, 375/374&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 22, 50, 72&lt;br /&gt;
EDOs: 22, 50, 72&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="x-Wizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;19-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Wizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;19-limit&lt;/h2&gt;
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342&lt;br /&gt;
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 22, 50, 72, 194, 460&lt;br /&gt;
EDOs: 22, 50, 72, 194, 460&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="x-Tritonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Tritonic&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Tritonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Tritonic&lt;/h1&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 278: Line 280:
EDOs: 29, 31, 60, 91, 122, 213&lt;br /&gt;
EDOs: 29, 31, 60, 91, 122, 213&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x-Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 27783/27500&lt;br /&gt;
Commas: 225/224, 385/384, 27783/27500&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 29, 31, 60, 91, 122, 153&lt;br /&gt;
EDOs: 29, 31, 60, 91, 122, 153&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="x-Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Septimin&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Septimin&lt;/h1&gt;
Commas: 225/224, 84035/82944&lt;br /&gt;
Commas: 225/224, 84035/82944&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 9, 32, 41, 91, 132&lt;br /&gt;
EDOs: 9, 32, 41, 91, 132&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="x-Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 2401/2376&lt;br /&gt;
Commas: 225/224, 385/384, 2401/2376&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 303: Line 305:
EDOs: 9, 32, 41, 91&lt;br /&gt;
EDOs: 9, 32, 41, 91&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="x-Septimin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Septimin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 144/143, 196/195, 245/242&lt;br /&gt;
Commas: 105/104, 144/143, 196/195, 245/242&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 311: Line 313:
EDOs: 9, 41, 91&lt;br /&gt;
EDOs: 9, 41, 91&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="x-Slender"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Slender&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Slender"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Slender&lt;/h1&gt;
Commas: 225/225, 589824/588245&lt;br /&gt;
Commas: 225/225, 589824/588245&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 31, 94, 125&lt;br /&gt;
EDOs: 31, 94, 125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x-Slender-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Slender-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 1331/1323&lt;br /&gt;
Commas: 225/224, 385/384, 1331/1323&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 31, 63, 94, 125&lt;br /&gt;
EDOs: 31, 63, 94, 125&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x-Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Triton&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Triton&lt;/h1&gt;
Commas: 225/224, 1029/1000&lt;br /&gt;
Commas: 225/224, 1029/1000&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 19, 135, 289&lt;br /&gt;
EDOs: 19, 135, 289&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="x-Marvo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Marvo&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Marvo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Marvo&lt;/h1&gt;
Commas: 225/224, 78125000/78121827&lt;br /&gt;
Commas: 225/224, 78125000/78121827&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 346: Line 348:
EDOs: 65, 72&lt;br /&gt;
EDOs: 65, 72&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="x-Marvo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Marvo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 243/242, 4000/3993&lt;br /&gt;
Commas: 225/224, 243/242, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;

Revision as of 22:40, 23 March 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2011-03-23 22:40:03 UTC.
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Original Wikitext content:

[[toc|flat]]

This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.

Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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.

=Negri=
Commas: 49/48, 225/224

[[POTE tuning|POTE temperament]]: 125.608

Map: [<1 2 2 3|, <0 -4 3 -2|]
Wedgie: <<4 -3 2 -14 -8 13||
EDOs: 9, 10, 19, 86

==11-limit==
Commas: 45/44, 49/48, 56/55

[[POTE tuning|POTE temperament]]: 126.474

Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]
EDOs: 9, 10, 19

==13-limit==
Commas: 45/44, 49/48, 56/55, 78/77

[[POTE tuning|POTE generator]]: 126.431

Map: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]
EDOs: 9, 10, 19

=Negric=
Commas: 33/32, 49/48, 77/75

POTE generator: ~15/14 = 127.039

Map: [<1 2 2 3 3|, <0 -4 3 -2 4|]
EDOs: 9, 19, 85
Badness: 0.0306

==13-limit==
Commas: 33/32, 49/48, 65/64, 91/90

POTE generator: ~15/14 = 127.039

Map: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]
EDOs: 9, 19, 85
Badness: 0.0202

=Wizard=
Commas: 225/224, 118098/117649

[[POTE tuning|POTE temperament]]: 383.256

Map: [<2 1 5 2|, <0 6 -1 10|]
Wedgie: <<12 -2 20 -31 -2 52||
EDOs: 22, 50, 72, 382, 454

==11-limit==
Commas: 225/224, 385/384, 4000/3993

[[POTE tuning|POTE temperament]]: 383.232

Map: [<2 1 5 2 8|, <0 6 -1 10 -3|]
EDOs: 22, 50, 72, 166, 310

==13-limit==
Commas: 225/224, 351/350, 364/363, 385/384

[[POTE tuning|POTE temperament]]: 383.389

Map: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]
EDOs: 22, 50, 72

==17-limit==
Commas: 221/220, 273/272, 289/288, 351/350, 375/374

[[POTE tuning|POTE temperament]]: 383.381

Map: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]
EDOs: 22, 50, 72

==19-limit==
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342

[[POTE tuning|POTE temperament]]: 383.477

Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|]
EDOs: 22, 50, 72, 194, 460

=Tritonic=
Commas: 225/224, 50421/50000

[[POTE tuning|POTE temperament]]: 580.286

Map: [<1 4 -3 -3|, <0 -5 11 12|]
Wedgie: <<5 -11 -12 -29 -33 3||
EDOs: 29, 31, 60, 91, 122, 213

==11-limit==
Commas: 225/224, 385/384, 27783/27500

[[POTE tuning|POTE temperament]]: 580.389

Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]
EDOs: 29, 31, 60, 91, 122, 153

=Septimin=
Commas: 225/224, 84035/82944

[[POTE tuning|POTE temperament]]: 263.632

Map: [<1 4 1 5|, <0 -11 6 -10|]
Wedgie: <<11 -6 10 -35 -15 40||
EDOs: 9, 32, 41, 91, 132

==11-limit==
Commas: 225/224, 385/384, 2401/2376

[[POTE tuning|POTE temperament]]: 263.634

Map: [<1 4 1 5 5|, <0 -11 6 -10 -7|]
EDOs: 9, 32, 41, 91

==13-limit==
Commas: 105/104, 144/143, 196/195, 245/242

[[POTE tuning|POTE temperament]]: 263.700

Map: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|]
EDOs: 9, 41, 91

=Slender=
Commas: 225/225, 589824/588245

[[POTE tuning|POTE temperament]]: (~49/48) 38.413

Map: [<1 2 2 3|, <0 -13 10 -6|]
Wedgie: <<13 -10 6 -46 -27 42||
EDOs: 31, 94, 125

==11-limit==
Commas: 225/224, 385/384, 1331/1323

[[POTE tuning|POTE temperament]]: 38.387

Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|]
EDOs: 31, 63, 94, 125

=Triton=
Commas: 225/224, 1029/1000

[[POTE tuning|POTE temperament]]: 568.865

Map: [<1 0 6 7|, <0 3 -7 -8|]
Wedgie: <<3 -7 -8 -18 -21 1||
EDOs: 19, 135, 289

=Marvo=
Commas: 225/224, 78125000/78121827

[[POTE tuning|POTE temperament]]: (~27/20) 516.694

Map: [<1 5 12 29|, <0 -6 -17 -46|]
Wedgie: <<6, 17, 46, 13, 56 59||
EDOs: 65, 72

==11-limit==
Commas: 225/224, 243/242, 4000/3993

[[POTE tuning|POTE temperament]]: 516.699

Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|]
EDOs: 65, 72, 281, 497

Original HTML content:

<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:40:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: -->
<!-- ws:end:WikiTextTocRule:61 --><br />
This page discusses some of the temperaments tempering out 225/224, the marvel comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.<br />
<br />
Since (5/4)^3 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess 5/4-5/4-9/7 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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1>
Commas: 49/48, 225/224<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br />
<br />
Map: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br />
Wedgie: &lt;&lt;4 -3 2 -14 -8 13||<br />
EDOs: 9, 10, 19, 86<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2>
Commas: 45/44, 49/48, 56/55<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 126.474<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br />
EDOs: 9, 10, 19<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2>
Commas: 45/44, 49/48, 56/55, 78/77<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 126.431<br />
<br />
Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]<br />
EDOs: 9, 10, 19<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negric</h1>
Commas: 33/32, 49/48, 77/75<br />
<br />
POTE generator: ~15/14 = 127.039<br />
<br />
Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]<br />
EDOs: 9, 19, 85<br />
Badness: 0.0306<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2>
Commas: 33/32, 49/48, 65/64, 91/90<br />
<br />
POTE generator: ~15/14 = 127.039<br />
<br />
Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]<br />
EDOs: 9, 19, 85<br />
Badness: 0.0202<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:10 -->Wizard</h1>
Commas: 225/224, 118098/117649<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.256<br />
<br />
Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]<br />
Wedgie: &lt;&lt;12 -2 20 -31 -2 52||<br />
EDOs: 22, 50, 72, 382, 454<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2>
Commas: 225/224, 385/384, 4000/3993<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.232<br />
<br />
Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]<br />
EDOs: 22, 50, 72, 166, 310<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Wizard-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2>
Commas: 225/224, 351/350, 364/363, 385/384<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.389<br />
<br />
Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]<br />
EDOs: 22, 50, 72<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Wizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->17-limit</h2>
Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.381<br />
<br />
Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]<br />
EDOs: 22, 50, 72<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Wizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->19-limit</h2>
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 383.477<br />
<br />
Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]<br />
EDOs: 22, 50, 72, 194, 460<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:20 -->Tritonic</h1>
Commas: 225/224, 50421/50000<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.286<br />
<br />
Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]<br />
Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||<br />
EDOs: 29, 31, 60, 91, 122, 213<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2>
Commas: 225/224, 385/384, 27783/27500<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 580.389<br />
<br />
Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br />
EDOs: 29, 31, 60, 91, 122, 153<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:24 -->Septimin</h1>
Commas: 225/224, 84035/82944<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br />
<br />
Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]<br />
Wedgie: &lt;&lt;11 -6 10 -35 -15 40||<br />
EDOs: 9, 32, 41, 91, 132<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2>
Commas: 225/224, 385/384, 2401/2376<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.634<br />
<br />
Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]<br />
EDOs: 9, 32, 41, 91<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2>
Commas: 105/104, 144/143, 196/195, 245/242<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.700<br />
<br />
Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]<br />
EDOs: 9, 41, 91<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:30 -->Slender</h1>
Commas: 225/225, 589824/588245<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: (~49/48) 38.413<br />
<br />
Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]<br />
Wedgie: &lt;&lt;13 -10 6 -46 -27 42||<br />
EDOs: 31, 94, 125<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2>
Commas: 225/224, 385/384, 1331/1323<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 38.387<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]<br />
EDOs: 31, 63, 94, 125<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:34 -->Triton</h1>
Commas: 225/224, 1029/1000<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 568.865<br />
<br />
Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]<br />
Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||<br />
EDOs: 19, 135, 289<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:36 -->Marvo</h1>
Commas: 225/224, 78125000/78121827<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: (~27/20) 516.694<br />
<br />
Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]<br />
Wedgie: &lt;&lt;6, 17, 46, 13, 56 59||<br />
EDOs: 65, 72<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2>
Commas: 225/224, 243/242, 4000/3993<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 516.699<br />
<br />
Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]<br />
EDOs: 65, 72, 281, 497</body></html>