Marvel temperaments: Difference between revisions
Wikispaces>lobawad **Imported revision 219787948 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 224344794 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-30 17:11:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>224344794</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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Commas: 45/44, 49/48, 56/55 | Commas: 45/44, 49/48, 56/55 | ||
[[POTE tuning|POTE | [[POTE tuning|POTE generator]]: 126.474 | ||
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 | |||
==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, 29, 48, 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 | |||
==13-limit== | ==13-limit== | ||
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EDOs: 65, 72, 281, 497</pre></div> | EDOs: 65, 72, 281, 497</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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: --><!-- 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: | <!-- ws:end:WikiTextTocRule:79 -->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 /> | <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 /> | ||
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Commas: 45/44, 49/48, 56/55<br /> | Commas: 45/44, 49/48, 56/55<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 126.474<br /> | ||
<br /> | <br /> | ||
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 /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Negri-Negril"></a><!-- ws:end:WikiTextHeadingRule:4 -->Negril</h2> | |||
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, 29, 48, 77<br /> | |||
Badness: 0.0387<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Negri-Negril-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h3> | |||
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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Negri-13-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->13-limit</h2> | ||
Commas: 45/44, 49/48, 56/55, 78/77<br /> | Commas: 45/44, 49/48, 56/55, 78/77<br /> | ||
<br /> | <br /> | ||
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EDOs: 9, 10, 19<br /> | EDOs: 9, 10, 19<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 33/32, 49/48, 77/75<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0306<br /> | Badness: 0.0306<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 33/32, 49/48, 65/64, 91/90<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 118098/117649<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0408<br /> | Badness: 0.0408<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 385/384, 4000/3993<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0185<br /> | Badness: 0.0185<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 351/350, 364/363, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0218<br /> | Badness: 0.0218<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 221/220, 273/272, 289/288, 351/350, 375/374<br /> | ||
<br /> | <br /> | ||
| Line 308: | Line 346: | ||
Badness: 0.0145<br /> | Badness: 0.0145<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0157<br /> | Badness: 0.0157<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 385/384, 325/324, 1573/1568<br /> | ||
<br /> | <br /> | ||
| Line 326: | Line 364: | ||
Badness: 0.0203<br /> | Badness: 0.0203<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 289/288, 325/324, 375/374, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0136<br /> | Badness: 0.0136<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 289/28, 325/324, 385/384, 494/493, 969/968<br /> | ||
<br /> | <br /> | ||
| Line 344: | Line 382: | ||
Badness: 0.0148<br /> | Badness: 0.0148<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- 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 /> | Commas: 225/224, 50421/50000<br /> | ||
<br /> | <br /> | ||
| Line 353: | Line 391: | ||
EDOs: 29, 31, 60, 91, 122, 213<br /> | EDOs: 29, 31, 60, 91, 122, 213<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Tritonic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 27783/27500<br /> | Commas: 225/224, 385/384, 27783/27500<br /> | ||
<br /> | <br /> | ||
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EDOs: 29, 31, 60, 91, 122, 153<br /> | EDOs: 29, 31, 60, 91, 122, 153<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:34 -->Septimin</h1> | ||
Commas: 225/224, 84035/82944<br /> | Commas: 225/224, 84035/82944<br /> | ||
<br /> | <br /> | ||
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EDOs: 9, 32, 41, 91, 132<br /> | EDOs: 9, 32, 41, 91, 132<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 2401/2376<br /> | Commas: 225/224, 385/384, 2401/2376<br /> | ||
<br /> | <br /> | ||
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EDOs: 9, 32, 41, 91<br /> | EDOs: 9, 32, 41, 91<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><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 /> | Commas: 105/104, 144/143, 196/195, 245/242<br /> | ||
<br /> | <br /> | ||
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EDOs: 9, 41, 91<br /> | EDOs: 9, 41, 91<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:40 -->Slender</h1> | ||
Commas: 225/225, 589824/588245<br /> | Commas: 225/225, 589824/588245<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0569<br /> | Badness: 0.0569<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 225/224, 385/384, 1331/1323<br /> | Commas: 225/224, 385/384, 1331/1323<br /> | ||
<br /> | <br /> | ||
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Badness: 25.342<br /> | Badness: 25.342<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><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 /> | Commas: 225/224, 275/273, 385/384, 1331/1323<br /> | ||
<br /> | <br /> | ||
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Badness: 25.913<br /> | Badness: 25.913<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:46 -->Triton</h1> | ||
Commas: 225/224, 1029/1000<br /> | Commas: 225/224, 1029/1000<br /> | ||
<br /> | <br /> | ||
| Line 423: | Line 461: | ||
EDOs: 19, 135, 289<br /> | EDOs: 19, 135, 289<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h1&gt; --><h1 id="toc24"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:48 -->Marvo</h1> | ||
Commas: 225/224, 78125000/78121827<br /> | Commas: 225/224, 78125000/78121827<br /> | ||
<br /> | <br /> | ||
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EDOs: 65, 72<br /> | EDOs: 65, 72<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2> | ||
Commas: 225/224, 243/242, 4000/3993<br /> | Commas: 225/224, 243/242, 4000/3993<br /> | ||
<br /> | <br /> | ||