Archytas clan: Difference between revisions
Wikispaces>jdfreivald **Imported revision 370945992 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 474299112 - 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>2013-12-03 11:37:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>474299112</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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EDOs: 22, 49 | EDOs: 22, 49 | ||
Badness: 0.0250 | Badness: 0.0250 | ||
==13-limit== | |||
Commas: 64/63, 78/77, 91/90, 100/99 | |||
POTE generator: ~3/2 = 710.479 | |||
Map: [<1 0 -12 6 -22 -17|, <0 1 9 -2 16 13|] | |||
EDOs: 22, 27e, 49, 76bcde | |||
Badness: 0.0247 | |||
==Suprapyth== | ==Suprapyth== | ||
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Badness: 0.0327</pre></div> | Badness: 0.0327</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>Archytas 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>Archytas clan</title></head><body><!-- ws:start:WikiTextTocRule:70:&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:70 --><!-- ws:start:WikiTextTocRule:71: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --> | <a href="#Blacksmith">Blacksmith</a><!-- 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="#Superpyth">Superpyth</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: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --> | <a href="#Passion">Passion</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: --> | <a href="#Fervor">Fervor</a><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --> | <a href="#Quasisuper">Quasisuper</a><!-- 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="#Progress">Progress</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: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><br /> | ||
The <em>archytas clan</em> tempers out the <a class="wiki_link" href="/64_63">Archytas comma</a>, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to <a class="wiki_link" href="/81_80">81/80</a> in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br /> | The <em>archytas clan</em> tempers out the <a class="wiki_link" href="/64_63">Archytas comma</a>, 64/63. This means that four stacked 3/2 fifths equal a 9/7 major third. (Note the similarity in function to <a class="wiki_link" href="/81_80">81/80</a> in meantone, where four stacked 3/2 fifths equal a 5/4 major third.) This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:107:&lt;img src=&quot;/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg" alt="blacksmith10.jpg" title="blacksmith10.jpg" /><!-- ws:end:WikiTextLocalImageRule:107 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:12 -->Blackwood</h2> | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:12 -->Blackwood</h2> | ||
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Badness: 0.0250<br /> | Badness: 0.0250<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Superpyth-Suprapyth"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Superpyth-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h2> | ||
Commas: 64/63, 78/77, 91/90, 100/99<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 710.479<br /> | |||
<br /> | |||
Map: [&lt;1 0 -12 6 -22 -17|, &lt;0 1 9 -2 16 13|]<br /> | |||
EDOs: 22, 27e, 49, 76bcde<br /> | |||
Badness: 0.0247<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Superpyth-Suprapyth"></a><!-- ws:end:WikiTextHeadingRule:20 -->Suprapyth</h2> | |||
Commas: 55/54, 64/63, 99/98<br /> | Commas: 55/54, 64/63, 99/98<br /> | ||
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Badness: 0.0328<br /> | Badness: 0.0328<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Superpyth-Suprapyth-13-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->13-limit</h3> | ||
Commas: 55/54, 64/63, 65/63, 364/363<br /> | Commas: 55/54, 64/63, 65/63, 364/363<br /> | ||
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Badness: 0.0363<br /> | Badness: 0.0363<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Beatles"></a><!-- ws:end:WikiTextHeadingRule:24 -->Beatles</h1> | ||
Comma: 524288/492075<br /> | Comma: 524288/492075<br /> | ||
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Badness: 0.3585<br /> | Badness: 0.3585<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Beatles-7-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->7-limit</h2> | ||
Commas: 64/63, 686/675<br /> | Commas: 64/63, 686/675<br /> | ||
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Music: <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3" rel="nofollow">Beatles Improv</a> by Herman Miller<br /> | Music: <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3" rel="nofollow">Beatles Improv</a> by Herman Miller<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Beatles-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> | ||
Commas: 64/63, 100/99, 686/675<br /> | Commas: 64/63, 100/99, 686/675<br /> | ||
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Badness: 0.0456<br /> | Badness: 0.0456<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Beatles-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2> | ||
Commas: 64/63, 91/90, 100/99, 169/168<br /> | Commas: 64/63, 91/90, 100/99, 169/168<br /> | ||
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Badness: 0.0302<br /> | Badness: 0.0302<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Beatles-Ringo"></a><!-- ws:end:WikiTextHeadingRule:32 -->Ringo</h2> | ||
Commas: 56/55, 64/63, 540/539<br /> | Commas: 56/55, 64/63, 540/539<br /> | ||
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Badness: 0.0329<br /> | Badness: 0.0329<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Beatles-Ringo-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h3> | ||
Commas: 56/55, 64/63, 78/77, 91/90<br /> | Commas: 56/55, 64/63, 78/77, 91/90<br /> | ||
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Badness: 0.0226<br /> | Badness: 0.0226<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:36 -->Schism</h1> | ||
Commas: 64/63, 360/343<br /> | Commas: 64/63, 360/343<br /> | ||
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Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Schism-11-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->11-limit</h2> | ||
Commas: 45/44, 64/63, 99/98<br /> | Commas: 45/44, 64/63, 99/98<br /> | ||
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Badness: 0.0375<br /> | Badness: 0.0375<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Passion"></a><!-- ws:end:WikiTextHeadingRule:40 -->Passion</h1> | ||
Commas: 64/63, 3125/3087<br /> | Commas: 64/63, 3125/3087<br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Passion-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 64/63, 100/99, 1375/1372<br /> | Commas: 64/63, 100/99, 1375/1372<br /> | ||
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Badness: 0.0408<br /> | Badness: 0.0408<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Passion-13-limit"></a><!-- ws:end:WikiTextHeadingRule:44 -->13-limit</h2> | ||
Commas: 64/63 100/99 196/195 275/273<br /> | Commas: 64/63 100/99 196/195 275/273<br /> | ||
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Badness: 0.0309<br /> | Badness: 0.0309<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Fervor"></a><!-- ws:end:WikiTextHeadingRule:46 -->Fervor</h1> | ||
Comma: 67108864/61509375<br /> | Comma: 67108864/61509375<br /> | ||
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Badness: 0.8526<br /> | Badness: 0.8526<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Fervor-7-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->7-limit</h2> | ||
Commas: 64/63, 9604/9375<br /> | Commas: 64/63, 9604/9375<br /> | ||
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Badness: 0.1085<br /> | Badness: 0.1085<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Fervor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 1350/1331<br /> | Commas: 56/55, 64/63, 1350/1331<br /> | ||
<br /> | <br /> | ||
| Line 581: | Line 599: | ||
Badness: 0.0521<br /> | Badness: 0.0521<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="Fervor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:52 -->13-limit</h2> | ||
Commas: 56/55, 64/63, 78/77, 507/500<br /> | Commas: 56/55, 64/63, 78/77, 507/500<br /> | ||
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Badness: 0.0397<br /> | Badness: 0.0397<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h1&gt; --><h1 id="toc27"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:54 -->Quasisuper</h1> | ||
Commas: 64/63, 2430/2401<br /> | Commas: 64/63, 2430/2401<br /> | ||
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Badness: 0.0638<br /> | Badness: 0.0638<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Quasisuper-Quasisupra"></a><!-- ws:end:WikiTextHeadingRule:56 -->Quasisupra</h2> | ||
Commas: 64/63, 99/98, 121/120<br /> | Commas: 64/63, 99/98, 121/120<br /> | ||
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Badness: 0.0322<br /> | Badness: 0.0322<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="Quasisuper-Quasisoup"></a><!-- ws:end:WikiTextHeadingRule:58 -->Quasisoup</h2> | ||
Commas: 55/54, 64/63, 2430/2401<br /> | Commas: 55/54, 64/63, 2430/2401<br /> | ||
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Badness: 0.0835<br /> | Badness: 0.0835<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h1&gt; --><h1 id="toc30"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:60 -->Progress</h1> | ||
Comma: 32768/30375<br /> | Comma: 32768/30375<br /> | ||
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Badness: 0.2461<br /> | Badness: 0.2461<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Progress-7-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->7-limit</h2> | ||
Commas: 64/63, 392/375<br /> | Commas: 64/63, 392/375<br /> | ||
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Badness: 0.0664<br /> | Badness: 0.0664<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 77/75<br /> | Commas: 56/55, 64/63, 77/75<br /> | ||
<br /> | <br /> | ||
| Line 648: | Line 666: | ||
Badness: 0.0310<br /> | Badness: 0.0310<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Progress-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->13-limit</h2> | ||
Commas: 56/55, 64/63, 66/65, 77/75<br /> | Commas: 56/55, 64/63, 66/65, 77/75<br /> | ||
<br /> | <br /> | ||
| Line 657: | Line 675: | ||
Badness: 0.0262<br /> | Badness: 0.0262<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="Progress-Progressive"></a><!-- ws:end:WikiTextHeadingRule:68 -->Progressive</h2> | ||
Commas: 26/25, 56/55, 64/63, 77/75<br /> | Commas: 26/25, 56/55, 64/63, 77/75<br /> | ||
<br /> | <br /> | ||