Marvel temperaments: Difference between revisions

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[[toc|flat]]
This page discusses some of the temperaments tempering out |-5 2 2 -1> =[[225_224| 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)^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.

=Negri= 
[[Comma]]s: 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: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]

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

[[POTE tuning|POTE generator]]: 126.474

Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|]
EDOs: 9, 10, 19
[[Badness]]: 0.0262

==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

=Negril= 
Commas: 49/48, 100/99, 225/224

POTE generator: ~15/14 = 124.767

Map: [<1 2 2 3 2|, <0 -4 3 -2 14|]
EDOs: 9, 10, 19, [[29edo|29]], [[48edo|48]], [[77edo|77]]
Badness: 0.0387

==13-limit== 
Commas: 49/48, 65/64, 91/90, 875/858

POTE generator: ~15/14 = 124.716

Map: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|]
EDOs: 9, 10, 19, 29, 48, 77
Badness: 0.0244

=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, [[85edo|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: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[382edo|382]], [[454edo|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, [[166edo|166]], [[310edo|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, [[194edo|194]], [[460edo|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, [[28edo|28]], 50, 72, [[94edo|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, [[238edo|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: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], [[213edo|213]]

==11-limit== 
Commas: 121/120, 225/224, 441/440

[[POTE tuning|POTE generator]]: ~7/5 = 580.267

Map: [<1 4 -3 -3 2|, <0 -5 11 12 3|]
EDOs: 29, 31
Badness: 0.0237

==Tritoni== 
Commas: 225/224, 385/384, 27783/27500

POTE generator: ~7/5 = 580.389

Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]
EDOs: 31, 91, 122
Badness: 0.0455

=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, [[32edo|32]], 41, 91, [[132edo|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:54:&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:54 --><!-- ws:start:WikiTextTocRule:55: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Negril">Negril</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- 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="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: -->
<!-- ws:end:WikiTextTocRule:82 -->This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =<a class="wiki_link" href="/225_224"> 225/224</a>, the <a class="wiki_link" href="/marvel%20comma">marvel comma</a> or <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>. 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)^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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1>
 <a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 225/224<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br />
<br />
<a class="wiki_link" href="/Map">Map</a>: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;4 -3 2 -14 -8 13||<br />
EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/10edo">10</a>, <a class="wiki_link" href="/19edo">19</a>, <a class="wiki_link" href="/86edo">86</a><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 generator</a>: 126.474<br />
<br />
Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br />
EDOs: 9, 10, 19<br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.0262<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="Negril"></a><!-- ws:end:WikiTextHeadingRule:6 -->Negril</h1>
 Commas: 49/48, 100/99, 225/224<br />
<br />
POTE generator: ~15/14 = 124.767<br />
<br />
Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]<br />
EDOs: 9, 10, 19, <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/48edo">48</a>, <a class="wiki_link" href="/77edo">77</a><br />
Badness: 0.0387<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Negril-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2>
 Commas: 49/48, 65/64, 91/90, 875/858<br />
<br />
POTE generator: ~15/14 = 124.716<br />
<br />
Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]<br />
EDOs: 9, 10, 19, 29, 48, 77<br />
Badness: 0.0244<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Negric"></a><!-- ws:end:WikiTextHeadingRule:10 -->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, <a class="wiki_link" href="/85edo">85</a><br />
Badness: 0.0306<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Negric-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->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:14:&lt;h1&gt; --><h1 id="toc7"><a name="Wizard"></a><!-- ws:end:WikiTextHeadingRule:14 -->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: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/382edo">382</a>, <a class="wiki_link" href="/454edo">454</a><br />
Badness: 0.0408<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Wizard-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->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, <a class="wiki_link" href="/166edo">166</a>, <a class="wiki_link" href="/310edo">310</a><br />
Badness: 0.0185<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Wizard-Lizard"></a><!-- ws:end:WikiTextHeadingRule:18 -->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:20:&lt;h3&gt; --><h3 id="toc10"><a name="Wizard-Lizard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->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:22:&lt;h3&gt; --><h3 id="toc11"><a name="Wizard-Lizard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->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, <a class="wiki_link" href="/194edo">194</a>, <a class="wiki_link" href="/460edo">460</a><br />
Badness: 0.0157<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Wizard-Gizzard"></a><!-- ws:end:WikiTextHeadingRule:24 -->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, <a class="wiki_link" href="/28edo">28</a>, 50, 72, <a class="wiki_link" href="/94edo">94</a>, 166<br />
Badness: 0.0203<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Wizard-Gizzard-17-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->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, <a class="wiki_link" href="/238edo">238</a><br />
Badness: 0.0136<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Wizard-Gizzard-19-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->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:30:&lt;h1&gt; --><h1 id="toc15"><a name="Tritonic"></a><!-- ws:end:WikiTextHeadingRule:30 -->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: <a class="wiki_link" href="/29edo">29</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/60edo">60</a>, <a class="wiki_link" href="/91edo">91</a>, <a class="wiki_link" href="/122edo">122</a>, <a class="wiki_link" href="/213edo">213</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2>
 Commas: 121/120, 225/224, 441/440<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/5 = 580.267<br />
<br />
Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]<br />
EDOs: 29, 31<br />
Badness: 0.0237<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:34 -->Tritoni</h2>
 Commas: 225/224, 385/384, 27783/27500<br />
<br />
POTE generator: ~7/5 = 580.389<br />
<br />
Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br />
EDOs: 31, 91, 122<br />
Badness: 0.0455<br />
<br />
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:36 -->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, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->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:40:&lt;h2&gt; --><h2 id="toc20"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->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:42:&lt;h1&gt; --><h1 id="toc21"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:42 -->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:44:&lt;h2&gt; --><h2 id="toc22"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->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:46:&lt;h2&gt; --><h2 id="toc23"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->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:48:&lt;h1&gt; --><h1 id="toc24"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:48 -->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:50:&lt;h1&gt; --><h1 id="toc25"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:50 -->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:52:&lt;h2&gt; --><h2 id="toc26"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->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>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-07-10 09:58:22 UTC</tt>.<br>
+: This revision was by author [[User:Natebedell|Natebedell]] and made on <tt>2011-09-06 12:53:05 UTC</tt>.<br>
-: The original revision id was <tt>240696999</tt>.<br>
+: The original revision id was <tt>251226512</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>
 <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|flat]]
+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 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 [[225_224|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)^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.
@@ Line 38: / Line 37: @@
 EDOs: 9, 10, 19
 =Negril=
 Commas: 49/48, 100/99, 225/224
 POTE generator: ~15/14 = 124.767
 Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]
 EDOs: 9, 10, 19, [[29edo|29]], [[48edo|48]], [[77edo|77]]
 Badness: 0.0387
 ==13-limit==
 Commas: 49/48, 65/64, 91/90, 875/858
 POTE generator: ~15/14 = 124.716
 Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]
 EDOs: 9, 10, 19, 29, 48, 77
 Badness: 0.0244
@@ Line 165: / Line 164: @@
 Badness: 0.0237
 ==Tritoni==
 Commas: 225/224, 385/384, 27783/27500
@@ Line 254: / Line 253: @@
 <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:54:&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:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Negril"&gt;Negril&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Negric"&gt;Negric&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Wizard"&gt;Wizard&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Tritonic"&gt;Tritonic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Septimin"&gt;Septimin&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Slender"&gt;Slender&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#Triton"&gt;Triton&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt; | &lt;a href="#Marvo"&gt;Marvo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:82 --&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 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 &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 and marvo. Considered elsewhere are meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august, compton, sharp, escapade and mavila.&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;
@@ Line 286: / Line 284: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Negril"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Negril&lt;/h1&gt;
-Commas: 49/48, 100/99, 225/224&lt;br /&gt;
+ Commas: 49/48, 100/99, 225/224&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~15/14 = 124.767&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 2 2 3 2|, &amp;lt;0 -4 3 -2 14|] &lt;br /&gt;
+Map: [&amp;lt;1 2 2 3 2|, &amp;lt;0 -4 3 -2 14|]&lt;br /&gt;
 EDOs: 9, 10, 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77&lt;/a&gt;&lt;br /&gt;
 Badness: 0.0387&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Negril-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
-Commas: 49/48, 65/64, 91/90, 875/858&lt;br /&gt;
+ Commas: 49/48, 65/64, 91/90, 875/858&lt;br /&gt;
 &lt;br /&gt;
 POTE generator: ~15/14 = 124.716&lt;br /&gt;
 &lt;br /&gt;
-Map: [&amp;lt;1 2 2 3 2 4|, &amp;lt;0 -4 3 -2 14 -3|] &lt;br /&gt;
+Map: [&amp;lt;1 2 2 3 2 4|, &amp;lt;0 -4 3 -2 14 -3|]&lt;br /&gt;
 EDOs: 9, 10, 19, 29, 48, 77&lt;br /&gt;
 Badness: 0.0244&lt;br /&gt;
@@ Line 413: / Line 411: @@
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Tritonic-Tritoni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Tritoni&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;
 POTE generator: ~7/5 = 580.389&lt;br /&gt;

Marvel temperaments: Difference between revisions

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