Gamelismic clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 289173575 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 289235567 - 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>2012-01- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-03 09:39:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>289235567</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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==7-limit== | ==7-limit== | ||
[[Comma|Commas]]: | [[Comma|Commas]]: 1029/1024, 3136/3125 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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==11-limit== | ==11-limit== | ||
[[Comma|Commas]]: | [[Comma|Commas]]: 385/384, 441/440, 3136/3125 | ||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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[[Chords of hemithirds]] | [[Chords of hemithirds]] | ||
=Hemiseven= | |||
==7-limit== | |||
Commas: 1029/1024, 19683/19600 | |||
POTE generator: ~320/243 = 483.267 | |||
Map: [<1 4 14 2|, <0 -6 -29 2|] | |||
Wedgie: <<6 29 -2 32 -20 -86|| | |||
EDOs: 72, 149, 221, 514bd, 735bcd | |||
Badness: 0.0566 | |||
==11-limit== | |||
Commas: 385/384, 441/440, 19683/19600 | |||
POTE generator: ~320/243 = 483.276 | |||
Map: [<1 4 14 2 -5|, <0 -6 -29 2 21|] | |||
EDOs: 67c, 72, 149, 221e, 293de | |||
Badness: 0.0285 | |||
=Tritikleismic= | =Tritikleismic= | ||
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EDOs: 16</pre></div> | EDOs: 16</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>Gamelismic clan</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>Gamelismic clan</title></head><body><!-- ws:start:WikiTextTocRule:86:&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:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | <a href="#Miracle">Miracle</a><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- 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 --><!-- ws:start:WikiTextTocRule:95: --> | <a href="#Rodan">Rodan</a><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --> | <a href="#Valentine">Valentine</a><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --> | <a href="#Unidec">Unidec</a><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --> | <a href="#Hemithirds">Hemithirds</a><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --> | <a href="#Hemiseven">Hemiseven</a><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --> | <a href="#Tritikleismic">Tritikleismic</a><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --> | <a href="#Superkleismic">Superkleismic</a><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --> | <a href="#Gorgo">Gorgo</a><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --> | <a href="#Lemba">Lemba</a><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --> | <a href="#Gidorah">Gidorah</a><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --> | <a href="#Clyndro">Clyndro</a><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:130 --><br /> | ||
The 2.3.7-<a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&gt;. For any member of the clan, for the rank three <a class="wiki_link" href="/Gamelismic%20family#Gamelan">gamelan temperament</a> itself, and for the rank two 2.3.7 temperament <a class="wiki_link" href="/slendric">slendric</a>, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. <a class="wiki_link" href="/36edo">36edo</a> is a good tuning for gamelismic itself, though if the full 7-limit is desired, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/77edo">77edo</a> or <a class="wiki_link" href="/118edo">118edo</a> might be preferred.<br /> | The 2.3.7-<a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> comma for the gamelismic clan is the gamelisma, 1029/1024, with monzo |-10 1 0 3&gt;. For any member of the clan, for the rank three <a class="wiki_link" href="/Gamelismic%20family#Gamelan">gamelan temperament</a> itself, and for the rank two 2.3.7 temperament <a class="wiki_link" href="/slendric">slendric</a>, this means three 8/7 intervals give a fifth, 3/2. In fact, we find that 3/2 = (8/7)^3 * 1029/1024. From this it follows that gamelismic temperaments tend to flatten the both fifth and the 7/4, or if they do not, the other of the pair must be flattened even more. <a class="wiki_link" href="/36edo">36edo</a> is a good tuning for gamelismic itself, though if the full 7-limit is desired, <a class="wiki_link" href="/72edo">72edo</a>, <a class="wiki_link" href="/77edo">77edo</a> or <a class="wiki_link" href="/118edo">118edo</a> might be preferred.<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Hemithirds-7-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->7-limit</h2> | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Hemithirds-7-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->7-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: | <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 3136/3125<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Hemithirds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2> | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Hemithirds-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: | <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 3136/3125<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | <a class="wiki_link" href="/Minimax%20tuning">Minimax tuning</a>:<br /> | ||
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<a class="wiki_link" href="/Chords%20of%20hemithirds">Chords of hemithirds</a><br /> | <a class="wiki_link" href="/Chords%20of%20hemithirds">Chords of hemithirds</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="Hemiseven"></a><!-- ws:end:WikiTextHeadingRule:50 -->Hemiseven</h1> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Hemiseven-7-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->7-limit</h2> | |||
Commas: 1029/1024, 19683/19600<br /> | |||
<br /> | |||
POTE generator: ~320/243 = 483.267<br /> | |||
<br /> | |||
Map: [&lt;1 4 14 2|, &lt;0 -6 -29 2|]<br /> | |||
Wedgie: &lt;&lt;6 29 -2 32 -20 -86||<br /> | |||
EDOs: 72, 149, 221, 514bd, 735bcd<br /> | |||
Badness: 0.0566<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Hemiseven-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2> | |||
Commas: 385/384, 441/440, 19683/19600<br /> | |||
<br /> | |||
POTE generator: ~320/243 = 483.276<br /> | |||
<br /> | |||
Map: [&lt;1 4 14 2 -5|, &lt;0 -6 -29 2 21|]<br /> | |||
EDOs: 67c, 72, 149, 221e, 293de<br /> | |||
Badness: 0.0285<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="Tritikleismic"></a><!-- ws:end:WikiTextHeadingRule:56 -->Tritikleismic</h1> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Tritikleismic-7-limit"></a><!-- ws:end:WikiTextHeadingRule:58 -->7-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 15625/15552<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 1029/1024, 15625/15552<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br /> | <a class="wiki_link" href="/Eigenmonzo">Eigenmonzos</a>: 2, 9/7<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Tritikleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> | ||
<a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 4000/3993<br /> | <a class="wiki_link" href="/Comma">Commas</a>: 385/384, 441/440, 4000/3993<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br /> | <a class="wiki_link" href="/edo">EDOs</a>: <a class="wiki_link" href="/72edo">72</a>, <a class="wiki_link" href="/159edo">159</a>, <a class="wiki_link" href="/231edo">231</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Tritikleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->13-limit</h2> | ||
Commas: 325/324, 364/363, 441/440, 625/624<br /> | Commas: 325/324, 364/363, 441/440, 625/624<br /> | ||
<br /> | <br /> | ||
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EDOs: 15, 72, 87, 159<br /> | EDOs: 15, 72, 87, 159<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Superkleismic"></a><!-- ws:end:WikiTextHeadingRule:64 -->Superkleismic</h1> | ||
Commas: 1029/1024, 875/864<br /> | Commas: 1029/1024, 875/864<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0479<br /> | Badness: 0.0479<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Superkleismic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->11-limit</h2> | ||
Commas: 100/99, 245/242, 385/384<br /> | Commas: 100/99, 245/242, 385/384<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0257<br /> | Badness: 0.0257<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Superkleismic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:68 -->13-limit</h2> | ||
Commas: 100/99, 105/104, 245/243, 1188/1183<br /> | Commas: 100/99, 105/104, 245/243, 1188/1183<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h1&gt; --><h1 id="toc35"><a name="Gorgo"></a><!-- ws:end:WikiTextHeadingRule:70 -->Gorgo</h1> | ||
Commas: 36/35, 1029/1024<br /> | Commas: 36/35, 1029/1024<br /> | ||
<br /> | <br /> | ||
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EDOs: 5, 16, 21, 226, 247<br /> | EDOs: 5, 16, 21, 226, 247<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Gorgo-11-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->11-limit</h2> | ||
Commas: 36/35, 45/44, 1029/1024<br /> | Commas: 36/35, 45/44, 1029/1024<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0495<br /> | Badness: 0.0495<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:74:&lt;h2&gt; --><h2 id="toc37"><a name="Gorgo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:74 -->13-limit</h2> | ||
Commas: 27/26, 36/35, 45/55, 507/500<br /> | Commas: 27/26, 36/35, 45/55, 507/500<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0327<br /> | Badness: 0.0327<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:76:&lt;h2&gt; --><h2 id="toc38"><a name="Gorgo-Music"></a><!-- ws:end:WikiTextHeadingRule:76 -->Music</h2> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3" rel="nofollow">Gorgo Example</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3" rel="nofollow">Gorgo Example</a> by <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:78:&lt;h1&gt; --><h1 id="toc39"><a name="Lemba"></a><!-- ws:end:WikiTextHeadingRule:78 -->Lemba</h1> | ||
Commas: 50/49, 525/512<br /> | Commas: 50/49, 525/512<br /> | ||
<br /> | <br /> | ||
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EDOs: 10, 16, 26<br /> | EDOs: 10, 16, 26<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:80:&lt;h2&gt; --><h2 id="toc40"><a name="Lemba-Music"></a><!-- ws:end:WikiTextHeadingRule:80 -->Music</h2> | ||
By <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | By <a class="wiki_link" href="/Herman%20Miller">Herman Miller</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3" rel="nofollow">Lemba Galatsia</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/LembaGalatsia.mp3" rel="nofollow">Lemba Galatsia</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3" rel="nofollow">GPO Lemba</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/lemba-gpo-test.mp3" rel="nofollow">GPO Lemba</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:82:&lt;h1&gt; --><h1 id="toc41"><a name="Gidorah"></a><!-- ws:end:WikiTextHeadingRule:82 -->Gidorah</h1> | ||
Commas: 21/20, 144/125<br /> | Commas: 21/20, 144/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:84:&lt;h1&gt; --><h1 id="toc42"><a name="Clyndro"></a><!-- ws:end:WikiTextHeadingRule:84 -->Clyndro</h1> | ||
Commas: 1029/1024, 135/128<br /> | Commas: 1029/1024, 135/128<br /> | ||
<br /> | <br /> | ||