Marvel temperaments: Difference between revisions

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**Imported revision 190372592 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 203968408 - 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>2010-12-31 16:29:53 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-22 09:49:34 UTC</tt>.<br>
: The original revision id was <tt>190372592</tt>.<br>
: The original revision id was <tt>203968408</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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Commas: 45/44, 49/48, 56/55, 78/77
Commas: 45/44, 49/48, 56/55, 78/77


[[POTE tuning|POTE temperament]]: 126.431
[[POTE tuning|POTE generator]]: 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|]
EDOs: 9, 10, 19
EDOs: 9, 10, 19
===Negric===
====11-limit====
Commas: 33/32, 49/48, 77/75
POTE generator: ~15/14 = 127.039
Map: [&lt;1 2 2 3 3|, &lt;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: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]
EDOs: 9, 19, 85
Badness: 0.0202


==Wizard==
==Wizard==
Line 185: Line 204:
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 temperament&lt;/a&gt;: 126.431&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 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;
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;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Wizard&lt;/h2&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: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;
&lt;br /&gt;
POTE generator: ~15/14 = 127.039&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 3|, &amp;lt;0 -4 3 -2 4|]&lt;br /&gt;
EDOs: 9, 19, 85&lt;br /&gt;
Badness: 0.0306&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;
Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 127.039&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 3 4|, &amp;lt;0 -4 3 -2 4 -3|]&lt;br /&gt;
EDOs: 9, 19, 85&lt;br /&gt;
Badness: 0.0202&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;
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:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Wizard-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h3&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;
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:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Wizard-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h3&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;
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:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Wizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;17-limit&lt;/h3&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;
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:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Wizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;19-limit&lt;/h3&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;
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:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Tritonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Tritonic&lt;/h2&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;
Commas: 225/224, 50421/50000&lt;br /&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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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:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x-Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h3&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;
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:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Septimin&lt;/h2&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;
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:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="x-Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h3&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;
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;
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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:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="x-Septimin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h3&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;
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 273: Line 311:
EDOs: 9, 41, 91&lt;br /&gt;
EDOs: 9, 41, 91&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-Slender"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Slender&lt;/h2&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;
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:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="x-Slender-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h3&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;
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:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x-Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Triton&lt;/h2&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;
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:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="x-Marvo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Marvo&lt;/h2&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;
Commas: 225/224, 78125000/78121827&lt;br /&gt;
Commas: 225/224, 78125000/78121827&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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EDOs: 65, 72&lt;br /&gt;
EDOs: 65, 72&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-Marvo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h3&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;
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 09:49, 22 February 2011

IMPORTED REVISION FROM WIKISPACES

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

This revision was by author genewardsmith and made on 2011-02-22 09:49:34 UTC.
The original revision id was 203968408.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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===
====11-limit====
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>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;h2&gt; --><h2 id="toc0"><a name="x-Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h2>
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;h3&gt; --><h3 id="toc1"><a name="x-Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h3>
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;h3&gt; --><h3 id="toc2"><a name="x-Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h3>
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;h3&gt; --><h3 id="toc3"><a name="x-Negri-Negric"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negric</h3>
<!-- ws:start:WikiTextHeadingRule:8:&lt;h4&gt; --><h4 id="toc4"><a name="x-Negri-Negric-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h4>
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:10:&lt;h4&gt; --><h4 id="toc5"><a name="x-Negri-Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->13-limit</h4>
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:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Wizard"></a><!-- ws:end:WikiTextHeadingRule:12 -->Wizard</h2>
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:14:&lt;h3&gt; --><h3 id="toc7"><a name="x-Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->11-limit</h3>
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:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Wizard-13-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->13-limit</h3>
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:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Wizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->17-limit</h3>
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:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Wizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->19-limit</h3>
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:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-Tritonic"></a><!-- ws:end:WikiTextHeadingRule:22 -->Tritonic</h2>
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:24:&lt;h3&gt; --><h3 id="toc12"><a name="x-Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h3>
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:26:&lt;h2&gt; --><h2 id="toc13"><a name="x-Septimin"></a><!-- ws:end:WikiTextHeadingRule:26 -->Septimin</h2>
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:28:&lt;h3&gt; --><h3 id="toc14"><a name="x-Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h3>
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:30:&lt;h3&gt; --><h3 id="toc15"><a name="x-Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h3>
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:32:&lt;h2&gt; --><h2 id="toc16"><a name="x-Slender"></a><!-- ws:end:WikiTextHeadingRule:32 -->Slender</h2>
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:34:&lt;h3&gt; --><h3 id="toc17"><a name="x-Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h3>
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:36:&lt;h2&gt; --><h2 id="toc18"><a name="x-Triton"></a><!-- ws:end:WikiTextHeadingRule:36 -->Triton</h2>
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:38:&lt;h2&gt; --><h2 id="toc19"><a name="x-Marvo"></a><!-- ws:end:WikiTextHeadingRule:38 -->Marvo</h2>
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:40:&lt;h3&gt; --><h3 id="toc20"><a name="x-Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h3>
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>