Marvel temperaments: Difference between revisions

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**Imported revision 214248954 - Original comment: **
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**Imported revision 214249270 - 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>2011-03-26 17:20:07 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-26 17:22:44 UTC</tt>.<br>
: The original revision id was <tt>214248954</tt>.<br>
: The original revision id was <tt>214249270</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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Badness: 0.0185
Badness: 0.0185


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


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Badness: 0.0218
Badness: 0.0218


==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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Badness: 0.0145
Badness: 0.0145


==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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Badness: 0.0185&lt;br /&gt;
Badness: 0.0185&lt;br /&gt;
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&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;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Wizard-Lizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Lizard&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;
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Badness: 0.0218&lt;br /&gt;
Badness: 0.0218&lt;br /&gt;
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&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;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Wizard-Lizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&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;
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Badness: 0.0145&lt;br /&gt;
Badness: 0.0145&lt;br /&gt;
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&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;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="Wizard-Lizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&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;

Revision as of 17:22, 26 March 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 2011-03-26 17:22:44 UTC.
The original revision id was 214249270.
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:

[[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
Badness: 0.0408

==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
Badness: 0.0185

==Lizard==
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
Badness: 0.0218

===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
Badness: 0.0145

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

[[POTE tuning|POTE generator]]: ~5/4 = 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
Badness: 0.0157

==Gizzard==
Commas: 225/224, 385/384, 325/324, 1573/1568

POTE generator: ~5/4 = 383.170

Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|]
EDOs: 22, 28, 50, 72, 94, 166
Badness: 0.0203

===17-limit===
Commas: 225/224, 289/288, 325/324, 375/374, 385/384

POTE generator: ~5/4 = 383.175

Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|]
EDOs: 22, 72, 94, 166, 238
Badness: 0.0136

===19-limit=== 
Commas: 225/224, 289/28, 325/324, 385/384, 494/493, 969/968

POTE generator: ~5/4 = 383.138

Map: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|]
EDOs: 22, 72, 94, 166
Badness: 0.0148

=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
Badness: 0.0569

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

[[POTE tuning|POTE temperament]]: ~49/48 = 38.387

Map: [<1 2 2 3 4|, <0 -13 10 -6 -17|]
EDOs: 31, 63, 94, 125
Badness: 25.342

==13-limit==
Commas: 225/224, 275/273, 385/384, 1331/1323

POTE generator: ~49/48 = 38.314

Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|]
EDOs: 31, 63, 94
Badness: 25.913

=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:48:&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:48 --><!-- ws:start:WikiTextTocRule:49: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: -->
<!-- ws:end:WikiTextTocRule:73 --><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 />
Badness: 0.0408<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 />
Badness: 0.0185<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:14 -->Lizard</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 />
Badness: 0.0218<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Wizard-Lizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->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 />
Badness: 0.0145<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Wizard-Lizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->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 generator</a>: ~5/4 = 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 />
Badness: 0.0157<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:20 -->Gizzard</h2>
Commas: 225/224, 385/384, 325/324, 1573/1568<br />
<br />
POTE generator: ~5/4 = 383.170<br />
<br />
Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]<br />
EDOs: 22, 28, 50, 72, 94, 166<br />
Badness: 0.0203<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Wizard-Gizzard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->17-limit</h3>
Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br />
<br />
POTE generator: ~5/4 = 383.175<br />
<br />
Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]<br />
EDOs: 22, 72, 94, 166, 238<br />
Badness: 0.0136<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Wizard-Gizzard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->19-limit</h3>
 Commas: 225/224, 289/28, 325/324, 385/384, 494/493, 969/968<br />
<br />
POTE generator: ~5/4 = 383.138<br />
<br />
Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]<br />
EDOs: 22, 72, 94, 166<br />
Badness: 0.0148<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:26 -->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:28:&lt;h2&gt; --><h2 id="toc14"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->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:30:&lt;h1&gt; --><h1 id="toc15"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:30 -->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:32:&lt;h2&gt; --><h2 id="toc16"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->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:34:&lt;h2&gt; --><h2 id="toc17"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->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:36:&lt;h1&gt; --><h1 id="toc18"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:36 -->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 />
Badness: 0.0569<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2>
Commas: 225/224, 385/384, 1331/1323<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~49/48 = 38.387<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]<br />
EDOs: 31, 63, 94, 125<br />
Badness: 25.342<br />
<br />
<!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->13-limit</h2>
Commas: 225/224, 275/273, 385/384, 1331/1323<br />
<br />
POTE generator: ~49/48 = 38.314<br />
<br />
Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]<br />
EDOs: 31, 63, 94<br />
Badness: 25.913<br />
<br />
<!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:42 -->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:44:&lt;h1&gt; --><h1 id="toc22"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:44 -->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:46:&lt;h2&gt; --><h2 id="toc23"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->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>