Marvel temperaments: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 237843849 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 238258159 - Original comment: some edo links added** |
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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: | : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-06-22 17:25:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238258159</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>some edo links added</tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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. | 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. | 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= | =Negri= | ||
[[Comma]]s: 49/48, 225/224 | |||
[[POTE tuning|POTE temperament]]: 125.608 | [[POTE tuning|POTE temperament]]: 125.608 | ||
Map: [<1 2 2 3|, <0 -4 3 -2|] | [[Map]]: [<1 2 2 3|, <0 -4 3 -2|] | ||
Wedgie: <<4 -3 2 -14 -8 13|| | [[Wedgie]]: <<4 -3 2 -14 -8 13|| | ||
EDOs: 9, 10, 19, 86 | EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]] | ||
==11-limit== | ==11-limit== | ||
| Line 28: | Line 28: | ||
Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|] | Map: [<1 2 2 3 4|, <0 -4 3 -2 -5|] | ||
EDOs: 9, 10, 19 | EDOs: 9, 10, 19 | ||
Badness: 0.0262 | [[Badness]]: 0.0262 | ||
==13-limit== | ==13-limit== | ||
| Line 44: | Line 44: | ||
Map: [<1 2 2 3 2|, <0 -4 3 -2 14|] | Map: [<1 2 2 3 2|, <0 -4 3 -2 14|] | ||
EDOs: 9, 10, 19, 29, 48, 77 | EDOs: 9, 10, 19, [[29edo|29]], [[48edo|48]], [[77edo|77]] | ||
Badness: 0.0387 | Badness: 0.0387 | ||
| Line 62: | Line 62: | ||
Map: [<1 2 2 3 3|, <0 -4 3 -2 4|] | Map: [<1 2 2 3 3|, <0 -4 3 -2 4|] | ||
EDOs: 9, 19, 85 | EDOs: 9, 19, [[85edo|85]] | ||
Badness: 0.0306 | Badness: 0.0306 | ||
| Line 81: | Line 81: | ||
Map: [<2 1 5 2|, <0 6 -1 10|] | Map: [<2 1 5 2|, <0 6 -1 10|] | ||
Wedgie: <<12 -2 20 -31 -2 52|| | Wedgie: <<12 -2 20 -31 -2 52|| | ||
EDOs: 22, 50, 72, 382, 454 | EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[382edo|382]], [[454edo|454]] | ||
Badness: 0.0408 | Badness: 0.0408 | ||
| Line 90: | Line 90: | ||
Map: [<2 1 5 2 8|, <0 6 -1 10 -3|] | Map: [<2 1 5 2 8|, <0 6 -1 10 -3|] | ||
EDOs: 22, 50, 72, 166, 310 | EDOs: 22, 50, 72, [[166edo|166]], [[310edo|310]] | ||
Badness: 0.0185 | Badness: 0.0185 | ||
| Line 117: | Line 117: | ||
Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|] | Map: [<2 1 5 2 8 11 6 2|, <0 6 -1 10 -3 -10 6 18|] | ||
EDOs: 22, 50, 72, 194, 460 | EDOs: 22, 50, 72, [[194edo|194]], [[460edo|460]] | ||
Badness: 0.0157 | Badness: 0.0157 | ||
| Line 126: | Line 126: | ||
Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|] | Map: [<2 1 5 2 8 -2|, <0 6 -1 10 -3 26|] | ||
EDOs: 22, 28, 50, 72, 94, 166 | EDOs: 22, [[28edo|28]], 50, 72, [[94edo|94]], 166 | ||
Badness: 0.0203 | Badness: 0.0203 | ||
| Line 135: | Line 135: | ||
Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|] | Map: [<2 1 5 2 8 -2 6|, <0 6 -1 10 -3 26 6|] | ||
EDOs: 22, 72, 94, 166, 238 | EDOs: 22, 72, 94, 166, [[238edo|238]] | ||
Badness: 0.0136 | Badness: 0.0136 | ||
| Line 154: | Line 154: | ||
Map: [<1 4 -3 -3|, <0 -5 11 12|] | Map: [<1 4 -3 -3|, <0 -5 11 12|] | ||
Wedgie: <<5 -11 -12 -29 -33 3|| | Wedgie: <<5 -11 -12 -29 -33 3|| | ||
EDOs: 29, 31, 60, 91, 122, 213 | EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], [[213edo|213]] | ||
==11-limit== | ==11-limit== | ||
| Line 162: | Line 162: | ||
Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|] | Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|] | ||
EDOs: 29, 31, 60, 91, 122, 153 | EDOs: 29, 31, 60, 91, 122, [[153edo|153]] | ||
=Septimin= | =Septimin= | ||
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Map: [<1 4 1 5|, <0 -11 6 -10|] | Map: [<1 4 1 5|, <0 -11 6 -10|] | ||
Wedgie: <<11 -6 10 -35 -15 40|| | Wedgie: <<11 -6 10 -35 -15 40|| | ||
EDOs: 9, 32, 41, 91, 132 | EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]] | ||
==11-limit== | ==11-limit== | ||
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<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"><html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:52:&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:52 --><!-- ws:start:WikiTextTocRule:53: --><a href="#Negri">Negri</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="#Negril">Negril</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- 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: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Septimin">Septimin</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="#Slender">Slender</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="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <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"><html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:52:&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:52 --><!-- ws:start:WikiTextTocRule:53: --><a href="#Negri">Negri</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="#Negril">Negril</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- 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: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Septimin">Septimin</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="#Slender">Slender</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="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | ||
<!-- ws:end:WikiTextTocRule:79 --><br /> | <!-- ws:end:WikiTextTocRule:79 --><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 /> | This page discusses some of the temperaments tempering out <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 /> | <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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Negri"></a><!-- ws:end:WikiTextHeadingRule:0 -->Negri</h1> | <!-- 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 /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 125.608<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br /> | <a class="wiki_link" href="/Map">Map</a>: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]<br /> | ||
Wedgie: &lt;&lt;4 -3 2 -14 -8 13||<br /> | <a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;4 -3 2 -14 -8 13||<br /> | ||
EDOs: 9, 10, 19, 86<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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Negri-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> | ||
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Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br /> | Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]<br /> | ||
EDOs: 9, 10, 19<br /> | EDOs: 9, 10, 19<br /> | ||
Badness: 0.0262<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0262<br /> | ||
<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> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> | ||
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<br /> | <br /> | ||
Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|] <br /> | Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|] <br /> | ||
EDOs: 9, 10, 19, 29, 48, 77<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 /> | Badness: 0.0387<br /> | ||
<br /> | <br /> | ||
| Line 299: | Line 299: | ||
<br /> | <br /> | ||
Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]<br /> | Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]<br /> | ||
EDOs: 9, 19, 85<br /> | EDOs: 9, 19, <a class="wiki_link" href="/85edo">85</a><br /> | ||
Badness: 0.0306<br /> | Badness: 0.0306<br /> | ||
<br /> | <br /> | ||
| Line 318: | Line 318: | ||
Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]<br /> | Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]<br /> | ||
Wedgie: &lt;&lt;12 -2 20 -31 -2 52||<br /> | Wedgie: &lt;&lt;12 -2 20 -31 -2 52||<br /> | ||
EDOs: 22, 50, 72, 382, 454<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 /> | Badness: 0.0408<br /> | ||
<br /> | <br /> | ||
| Line 327: | Line 327: | ||
<br /> | <br /> | ||
Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]<br /> | Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]<br /> | ||
EDOs: 22, 50, 72, 166, 310<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 /> | Badness: 0.0185<br /> | ||
<br /> | <br /> | ||
| Line 354: | Line 354: | ||
<br /> | <br /> | ||
Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]<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 /> | 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 /> | Badness: 0.0157<br /> | ||
<br /> | <br /> | ||
| Line 363: | Line 363: | ||
<br /> | <br /> | ||
Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]<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 /> | 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 /> | Badness: 0.0203<br /> | ||
<br /> | <br /> | ||
| Line 372: | Line 372: | ||
<br /> | <br /> | ||
Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]<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 /> | EDOs: 22, 72, 94, 166, <a class="wiki_link" href="/238edo">238</a><br /> | ||
Badness: 0.0136<br /> | Badness: 0.0136<br /> | ||
<br /> | <br /> | ||
| Line 391: | Line 391: | ||
Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]<br /> | Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]<br /> | ||
Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||<br /> | Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||<br /> | ||
EDOs: 29, 31, 60, 91, 122, 213<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 /> | <br /> | ||
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<br /> | <br /> | ||
Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br /> | Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]<br /> | ||
EDOs: 29, 31, 60, 91, 122, 153<br /> | EDOs: 29, 31, 60, 91, 122, <a class="wiki_link" href="/153edo">153</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:34 -->Septimin</h1> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:34 -->Septimin</h1> | ||
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Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]<br /> | Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]<br /> | ||
Wedgie: &lt;&lt;11 -6 10 -35 -15 40||<br /> | Wedgie: &lt;&lt;11 -6 10 -35 -15 40||<br /> | ||
EDOs: 9, 32, 41, 91, 132<br /> | EDOs: 9, <a class="wiki_link" href="/32edo">32</a>, 41, 91, <a class="wiki_link" href="/132edo">132</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Revision as of 17:25, 22 June 2011
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author xenwolf and made on 2011-06-22 17:25:47 UTC.
- The original revision id was 238258159.
- The revision comment was: some edo links added
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[[toc|flat]] 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. =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: 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, [[153edo|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, [[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
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<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:52:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><a href="#Negri">Negri</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="#Negril">Negril</a><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --> | <a href="#Wizard">Wizard</a><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- 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: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Septimin">Septimin</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="#Slender">Slender</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="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> <!-- ws:end:WikiTextTocRule:79 --><br /> This page discusses some of the temperaments tempering out <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:<h1> --><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>: [<1 2 2 3|, <0 -4 3 -2|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<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:<h2> --><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: [<1 2 2 3 4|, <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:<h2> --><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: [<1 2 2 3 4 4|, <0 -4 3 -2 -5 -3|]<br /> EDOs: 9, 10, 19<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><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: [<1 2 2 3 2|, <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:<h2> --><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: [<1 2 2 3 2 4|, <0 -4 3 -2 14 -3|] <br /> EDOs: 9, 10, 19, 29, 48, 77<br /> Badness: 0.0244<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><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: [<1 2 2 3 3|, <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:<h2> --><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: [<1 2 2 3 3 4|, <0 -4 3 -2 4 -3|]<br /> EDOs: 9, 19, 85<br /> Badness: 0.0202<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><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: [<2 1 5 2|, <0 6 -1 10|]<br /> Wedgie: <<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:<h2> --><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: [<2 1 5 2 8|, <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:<h2> --><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: [<2 1 5 2 8 11|, <0 6 -1 10 -3 -10|]<br /> EDOs: 22, 50, 72<br /> Badness: 0.0218<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h3> --><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: [<2 1 5 2 8 11 6|, <0 6 -1 10 -3 -10 6|]<br /> EDOs: 22, 50, 72<br /> Badness: 0.0145<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h3> --><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: [<2 1 5 2 8 11 6 2|, <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:<h2> --><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: [<2 1 5 2 8 -2|, <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:<h3> --><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: [<2 1 5 2 8 -2 6|, <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:<h3> --><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: [<2 1 5 2 8 -2 6 15|, <0 6 -1 10 -3 26 6 -18|]<br /> EDOs: 22, 72, 94, 166<br /> Badness: 0.0148<br /> <br /> <!-- ws:start:WikiTextHeadingRule:30:<h1> --><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: [<1 4 -3 -3|, <0 -5 11 12|]<br /> Wedgie: <<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:<h2> --><h2 id="toc16"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->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: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]<br /> EDOs: 29, 31, 60, 91, 122, <a class="wiki_link" href="/153edo">153</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h1> --><h1 id="toc17"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:34 -->Septimin</h1> Commas: 225/224, 84035/82944<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 263.632<br /> <br /> Map: [<1 4 1 5|, <0 -11 6 -10|]<br /> Wedgie: <<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:36:<h2> --><h2 id="toc18"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->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: [<1 4 1 5 5|, <0 -11 6 -10 -7|]<br /> EDOs: 9, 32, 41, 91<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h2> --><h2 id="toc19"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->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: [<1 4 1 5 5 7|, <0 -11 6 -10 -7 -15|]<br /> EDOs: 9, 41, 91<br /> <br /> <!-- ws:start:WikiTextHeadingRule:40:<h1> --><h1 id="toc20"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:40 -->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: [<1 2 2 3|, <0 -13 10 -6|]<br /> Wedgie: <<13 -10 6 -46 -27 42||<br /> EDOs: 31, 94, 125<br /> Badness: 0.0569<br /> <br /> <!-- ws:start:WikiTextHeadingRule:42:<h2> --><h2 id="toc21"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->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: [<1 2 2 3 4|, <0 -13 10 -6 -17|]<br /> EDOs: 31, 63, 94, 125<br /> Badness: 25.342<br /> <br /> <!-- ws:start:WikiTextHeadingRule:44:<h2> --><h2 id="toc22"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> Commas: 225/224, 275/273, 385/384, 1331/1323<br /> <br /> POTE generator: ~49/48 = 38.314<br /> <br /> Map: [<1 2 2 3 4 3|, <0 -13 10 -6 -17 22|]<br /> EDOs: 31, 63, 94<br /> Badness: 25.913<br /> <br /> <!-- ws:start:WikiTextHeadingRule:46:<h1> --><h1 id="toc23"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:46 -->Triton</h1> Commas: 225/224, 1029/1000<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 568.865<br /> <br /> Map: [<1 0 6 7|, <0 3 -7 -8|]<br /> Wedgie: <<3 -7 -8 -18 -21 1||<br /> EDOs: 19, 135, 289<br /> <br /> <!-- ws:start:WikiTextHeadingRule:48:<h1> --><h1 id="toc24"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:48 -->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: [<1 5 12 29|, <0 -6 -17 -46|]<br /> Wedgie: <<6, 17, 46, 13, 56 59||<br /> EDOs: 65, 72<br /> <br /> <!-- ws:start:WikiTextHeadingRule:50:<h2> --><h2 id="toc25"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->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: [<1 5 12 29 12|, <0 -6 -17 -46 -15|]<br /> EDOs: 65, 72, 281, 497</body></html>