Marvel temperaments: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 267652626 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 268076700 - 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>2011-10- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-24 16:16:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>268076700</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> | ||
<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 |-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. | 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. | ||
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Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|] | Map: [<1 5 12 29 12|, <0 -6 -17 -46 -15|] | ||
EDOs: 65, 72, 281, 497</pre></div> | EDOs: 65, 72, 281, 497 | ||
=Amavil= | |||
Commas: 225/224, 17496/16807 | |||
POTE generator: ~48/35 = 529.979 | |||
Map: [<1 6 1 9|, <0 -10 3 -14|] | |||
Wedgie: <<10 -3 14 -28 -6 41|| | |||
EDOs: 9, 34d, 43, 77d | |||
Badness: 0.1096 | |||
==11-limit== | |||
Commas: 99/98, 176/175, 864/847 | |||
POTE generator: ~15/11 = 529.974 | |||
Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|] | |||
EDOs: 9, 34d, 43, 77de | |||
Badness: 0.0426 | |||
==13-limit== | |||
Commas: 78/77, 99/98, 144/143, 176/175 | |||
POTE generator: ~15/11 = 529.951 | |||
Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|] | |||
EDOs: 9, 34d, 43, 77de | |||
Badness: 0.0258</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:62:&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:62 --><!-- ws:start:WikiTextTocRule:63: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Negril">Negril</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Wizard">Wizard</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: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Amavil">Amavil</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --> | ||
< | <!-- ws:end:WikiTextTocRule:94 --><br /> | ||
<br /> | |||
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 /> | <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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<br /> | <br /> | ||
Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]<br /> | Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]<br /> | ||
EDOs: 65, 72, 281, 497</body></html></pre></div> | EDOs: 65, 72, 281, 497<br /> | ||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:56 -->Amavil</h1> | |||
Commas: 225/224, 17496/16807<br /> | |||
<br /> | |||
POTE generator: ~48/35 = 529.979<br /> | |||
<br /> | |||
Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]<br /> | |||
Wedgie: &lt;&lt;10 -3 14 -28 -6 41||<br /> | |||
EDOs: 9, 34d, 43, 77d<br /> | |||
Badness: 0.1096<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->11-limit</h2> | |||
Commas: 99/98, 176/175, 864/847<br /> | |||
<br /> | |||
POTE generator: ~15/11 = 529.974<br /> | |||
<br /> | |||
Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]<br /> | |||
EDOs: 9, 34d, 43, 77de<br /> | |||
Badness: 0.0426<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Amavil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> | |||
Commas: 78/77, 99/98, 144/143, 176/175<br /> | |||
<br /> | |||
POTE generator: ~15/11 = 529.951<br /> | |||
<br /> | |||
Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]<br /> | |||
EDOs: 9, 34d, 43, 77de<br /> | |||
Badness: 0.0258</body></html></pre></div> | |||
Revision as of 16:16, 24 October 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 2011-10-24 16:16:04 UTC.
- The original revision id was 268076700.
- 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 |-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: [[28edo|22]], [[28edo|28]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|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]], 213bcd ==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, 60e Badness: 0.0237 ==13-limit== Commas: 105/104, 121/120, 196/195, 275/273 POTE generator: ~7/5 = 580.108 Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|] EDOs: 29, 31, 60e, 151cde Badness: 0.0230 ==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 =Amavil= Commas: 225/224, 17496/16807 POTE generator: ~48/35 = 529.979 Map: [<1 6 1 9|, <0 -10 3 -14|] Wedgie: <<10 -3 14 -28 -6 41|| EDOs: 9, 34d, 43, 77d Badness: 0.1096 ==11-limit== Commas: 99/98, 176/175, 864/847 POTE generator: ~15/11 = 529.974 Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|] EDOs: 9, 34d, 43, 77de Badness: 0.0426 ==13-limit== Commas: 78/77, 99/98, 144/143, 176/175 POTE generator: ~15/11 = 529.951 Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|] EDOs: 9, 34d, 43, 77de Badness: 0.0258
Original HTML content:
<html><head><title>Marvel temperaments</title></head><body><!-- ws:start:WikiTextTocRule:62:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><a href="#Negri">Negri</a><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --> | <a href="#Negril">Negril</a><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Negric">Negric</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Wizard">Wizard</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: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --> | <a href="#Tritonic">Tritonic</a><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --> | <a href="#Septimin">Septimin</a><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --> | <a href="#Slender">Slender</a><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Triton">Triton</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#Marvo">Marvo</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Amavil">Amavil</a><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --> <!-- ws:end:WikiTextTocRule:94 --><br /> <br /> This page discusses some of the temperaments tempering out |-5 2 2 -1> =<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: <a class="wiki_link" href="/28edo">22</a>, <a class="wiki_link" href="/28edo">28</a>, <a class="wiki_link" href="/50edo">50</a>, <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/94edo">94</a>, <a class="wiki_link" href="/166edo">166</a><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>, 213bcd<br /> <br /> <!-- ws:start:WikiTextHeadingRule:32:<h2> --><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: [<1 4 -3 -3 2|, <0 -5 11 12 3|]<br /> EDOs: 29, 31, 60e<br /> Badness: 0.0237<br /> <br /> <!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Tritonic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> Commas: 105/104, 121/120, 196/195, 275/273<br /> <br /> POTE generator: ~7/5 = 580.108<br /> <br /> Map: [<1 4 -3 -3 2 -5|, <0 -5 11 12 3 18|]<br /> EDOs: 29, 31, 60e, 151cde<br /> Badness: 0.0230<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:36:<h2> --><h2 id="toc18"><a name="Tritonic-Tritoni"></a><!-- ws:end:WikiTextHeadingRule:36 -->Tritoni</h2> Commas: 225/224, 385/384, 27783/27500<br /> <br /> POTE generator: ~7/5 = 580.389<br /> <br /> Map: [<1 4 -3 -3 17|, <0 -5 11 12 -28|]<br /> EDOs: 31, 91, 122<br /> Badness: 0.0455<br /> <br /> <!-- ws:start:WikiTextHeadingRule:38:<h1> --><h1 id="toc19"><a name="Septimin"></a><!-- ws:end:WikiTextHeadingRule:38 -->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:40:<h2> --><h2 id="toc20"><a name="Septimin-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->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:42:<h2> --><h2 id="toc21"><a name="Septimin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->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:44:<h1> --><h1 id="toc22"><a name="Slender"></a><!-- ws:end:WikiTextHeadingRule:44 -->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:46:<h2> --><h2 id="toc23"><a name="Slender-11-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->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:48:<h2> --><h2 id="toc24"><a name="Slender-13-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->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:50:<h1> --><h1 id="toc25"><a name="Triton"></a><!-- ws:end:WikiTextHeadingRule:50 -->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:52:<h1> --><h1 id="toc26"><a name="Marvo"></a><!-- ws:end:WikiTextHeadingRule:52 -->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:54:<h2> --><h2 id="toc27"><a name="Marvo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->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<br /> <br /> <br /> <!-- ws:start:WikiTextHeadingRule:56:<h1> --><h1 id="toc28"><a name="Amavil"></a><!-- ws:end:WikiTextHeadingRule:56 -->Amavil</h1> Commas: 225/224, 17496/16807<br /> <br /> POTE generator: ~48/35 = 529.979<br /> <br /> Map: [<1 6 1 9|, <0 -10 3 -14|]<br /> Wedgie: <<10 -3 14 -28 -6 41||<br /> EDOs: 9, 34d, 43, 77d<br /> Badness: 0.1096<br /> <br /> <!-- ws:start:WikiTextHeadingRule:58:<h2> --><h2 id="toc29"><a name="Amavil-11-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->11-limit</h2> Commas: 99/98, 176/175, 864/847<br /> <br /> POTE generator: ~15/11 = 529.974<br /> <br /> Map: [<1 6 1 9 7|, <0 -10 3 -14 -8|]<br /> EDOs: 9, 34d, 43, 77de<br /> Badness: 0.0426<br /> <br /> <!-- ws:start:WikiTextHeadingRule:60:<h2> --><h2 id="toc30"><a name="Amavil-13-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->13-limit</h2> Commas: 78/77, 99/98, 144/143, 176/175<br /> <br /> POTE generator: ~15/11 = 529.951<br /> <br /> Map: [<1 6 1 9 7 9|, <0 -10 3 -14 -8 -12|]<br /> EDOs: 9, 34d, 43, 77de<br /> Badness: 0.0258</body></html>