Augmented family: Difference between revisions
Wikispaces>guest **Imported revision 357183434 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 457032608 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2013-10-05 13:12:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>457032608</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> | ||
| Line 85: | Line 85: | ||
EDOs: 12, 15, 27e, 69bcef | EDOs: 12, 15, 27e, 69bcef | ||
Badness: 0.0229 | Badness: 0.0229 | ||
===Agene=== | |||
Commas: 56/55, 64/63, 78/77, 100/99 | |||
POTE generator: ~3/2 = 709.677 | |||
Map: [<3 0 7 18 20 35|, <0 1 0 -2 -2 -5|] | |||
EDOs: 12f, 27e | |||
Badness: 0.0231 | |||
==Eugene== | ==Eugene== | ||
| Line 333: | Line 342: | ||
Badness: 0.0241</pre></div> | Badness: 0.0241</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>Augmented family</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>Augmented family</title></head><body><!-- ws:start:WikiTextTocRule:74:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 1em;"><a href="#August">August</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 2em;"><a href="#August-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 2em;"><a href="#August-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 2em;"><a href="#August-Augustus">Augustus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 1em;"><a href="#Augene">Augene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 2em;"><a href="#Augene-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-Ogene">Ogene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-Agene">Agene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 2em;"><a href="#Augene-Eugene">Eugene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 1em;"><a href="#Inflated">Inflated</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Inflated-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Deflated">Deflated</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 1em;"><a href="#Hexe">Hexe</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Hexe-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Hexe-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 1em;"><a href="#Hemiaug">Hemiaug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Hemiaug-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Hemiaug-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 1em;"><a href="#Triforce">Triforce</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 2em;"><a href="#Triforce-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 3em;"><a href="#Triforce-11-limit-Musical example:">Musical example:</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 2em;"><a href="#Triforce-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Triforce-Semitriforce">Semitriforce</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 3em;"><a href="#toc25"> </a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 1em;"><a href="#Hemiug">Hemiug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Hemiug-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><div style="margin-left: 2em;"><a href="#Hemiug-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><div style="margin-left: 1em;"><a href="#Oodako">Oodako</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><div style="margin-left: 2em;"><a href="#Oodako-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><div style="margin-left: 2em;"><a href="#Oodako-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><div style="margin-left: 1em;"><a href="#Hemisemiaug">Hemisemiaug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><div style="margin-left: 2em;"><a href="#Hemisemiaug-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><div style="margin-left: 1em;"><a href="#Niner">Niner</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><div style="margin-left: 2em;"><a href="#Niner-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><div style="margin-left: 2em;"><a href="#Niner-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --></div> | ||
<!-- ws:end:WikiTextTocRule:112 -->The 5-limit parent comma for the <strong>augmented family</strong> is 128/125, the <a class="wiki_link" href="/128_125">diesis</a>. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for <a class="wiki_link" href="/5-limit">5-limit</a> augmented, though a sharper fifth might be preferred to go with the sharp third.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> | ||
| Line 449: | Line 459: | ||
Badness: 0.0229<br /> | Badness: 0.0229<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="Augene-11-limit-Agene"></a><!-- ws:end:WikiTextHeadingRule:18 -->Agene</h3> | ||
Commas: 56/55, 64/63, 78/77, 100/99<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 709.677<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 18 20 35|, &lt;0 1 0 -2 -2 -5|]<br /> | |||
EDOs: 12f, 27e<br /> | |||
Badness: 0.0231<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Augene-Eugene"></a><!-- ws:end:WikiTextHeadingRule:20 -->Eugene</h2> | |||
Commas: 55/54, 64/63, 77/75<br /> | Commas: 55/54, 64/63, 77/75<br /> | ||
<br /> | <br /> | ||
| Line 461: | Line 480: | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3" rel="nofollow">Galticeran Sonatina</a> by <a class="wiki_link_ext" href="http://soundcloud.com/joelgranttaylor/galticeran_sonatina" rel="nofollow">Joel Taylor</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Inflated"></a><!-- ws:end:WikiTextHeadingRule:22 -->Inflated</h1> | ||
Commas: 28/27, 128/125<br /> | Commas: 28/27, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 471: | Line 490: | ||
Badness: 0.0547<br /> | Badness: 0.0547<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Inflated-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | ||
Commas: 28/27, 55/54, 128/125<br /> | Commas: 28/27, 55/54, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 480: | Line 499: | ||
Badness: 0.0312<br /> | Badness: 0.0312<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Deflated"></a><!-- ws:end:WikiTextHeadingRule:26 -->Deflated</h1> | ||
Commas: 21/20, 128/125<br /> | Commas: 21/20, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 490: | Line 509: | ||
Badness: 0.0591<br /> | Badness: 0.0591<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Hexe"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hexe</h1> | ||
Commas: 50/49, 128/125<br /> | Commas: 50/49, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 500: | Line 519: | ||
Badness: 0.0577<br /> | Badness: 0.0577<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Hexe-11-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->11-limit</h2> | ||
Commas: 50/49, 56/55, 125/121<br /> | Commas: 50/49, 56/55, 125/121<br /> | ||
<br /> | <br /> | ||
| Line 509: | Line 528: | ||
Badness: 0.0384<br /> | Badness: 0.0384<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Hexe-13-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->13-limit</h2> | ||
Commas: 50/49, 56/55, 66/65, 105/104<br /> | Commas: 50/49, 56/55, 66/65, 105/104<br /> | ||
<br /> | <br /> | ||
| Line 518: | Line 537: | ||
Badness: 0.0359<br /> | Badness: 0.0359<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:34 -->Hemiaug</h1> | ||
Commas: 128/125, 245/243<br /> | Commas: 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 528: | Line 547: | ||
Badness: 0.0705<br /> | Badness: 0.0705<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Hemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 245/243<br /> | Commas: 56/55, 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 537: | Line 556: | ||
Badness: 0.0382<br /> | Badness: 0.0382<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Hemiaug-13-limit"></a><!-- ws:end:WikiTextHeadingRule:38 -->13-limit</h2> | ||
Commas: 56/55, 91/90, 128/125, 245/243<br /> | Commas: 56/55, 91/90, 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 546: | Line 565: | ||
Badness: 0.0302<br /> | Badness: 0.0302<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Triforce"></a><!-- ws:end:WikiTextHeadingRule:40 -->Triforce</h1> | ||
Commas: 49/48, 128/125<br /> | Commas: 49/48, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 556: | Line 575: | ||
Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:113:&lt;img src=&quot;/file/view/triforce9.jpg/271381934/triforce9.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/triforce9.jpg/271381934/triforce9.jpg" alt="triforce9.jpg" title="triforce9.jpg" /><!-- ws:end:WikiTextLocalImageRule:113 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->11-limit</h2> | ||
Commas: 56/55, 77/75, 128/125<br /> | Commas: 56/55, 77/75, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 567: | Line 586: | ||
Badness: 0.0262<br /> | Badness: 0.0262<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h3&gt; --><h3 id="toc22"><a name="Triforce-11-limit-Musical example:"></a><!-- ws:end:WikiTextHeadingRule:44 -->Musical example:</h3> | ||
<a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15" rel="nofollow">The Triforce of Courage (tuned in 15edo)</a> by Igliashon Jones<br /> | <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/the-triforce-of-courage15" rel="nofollow">The Triforce of Courage (tuned in 15edo)</a> by Igliashon Jones<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:46 -->13-limit</h2> | ||
Commas: 49/48, 56/55, 66/65, 77/75<br /> | Commas: 49/48, 56/55, 66/65, 77/75<br /> | ||
<br /> | <br /> | ||
| Line 580: | Line 599: | ||
<a class="wiki_link" href="/triphi">Triforce(9) with L:s = phi</a><br /> | <a class="wiki_link" href="/triphi">Triforce(9) with L:s = phi</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Triforce-Semitriforce"></a><!-- ws:end:WikiTextHeadingRule:48 -->Semitriforce</h2> | ||
Commas: 49/48, 56/55, 77/75, 507/500<br /> | Commas: 49/48, 56/55, 77/75, 507/500<br /> | ||
<br /> | <br /> | ||
| Line 589: | Line 608: | ||
Badness: 0.0592<br /> | Badness: 0.0592<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h3&gt; --><h3 id="toc25"><!-- ws:end:WikiTextHeadingRule:50 --> </h3> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Hemiug"></a><!-- ws:end:WikiTextHeadingRule:52 -->Hemiug</h1> | ||
Commas: 128/125, 1323/1250<br /> | Commas: 128/125, 1323/1250<br /> | ||
<br /> | <br /> | ||
| Line 601: | Line 620: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Hemiug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 1323/1250<br /> | Commas: 56/55, 128/125, 1323/1250<br /> | ||
<br /> | <br /> | ||
| Line 610: | Line 629: | ||
Badness: 0.0681<br /> | Badness: 0.0681<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Hemiug-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->13-limit</h2> | ||
Commas: 56/55, 66/65, 105/104, 507/500<br /> | Commas: 56/55, 66/65, 105/104, 507/500<br /> | ||
<br /> | <br /> | ||
| Line 619: | Line 638: | ||
Badness: 0.0423<br /> | Badness: 0.0423<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="Oodako"></a><!-- ws:end:WikiTextHeadingRule:58 -->Oodako</h1> | ||
Commas: 128/125, 2401/2400<br /> | Commas: 128/125, 2401/2400<br /> | ||
<br /> | <br /> | ||
| Line 629: | Line 648: | ||
Badness: 0.1132<br /> | Badness: 0.1132<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Oodako-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 3773/3750<br /> | Commas: 56/55, 128/125, 3773/3750<br /> | ||
<br /> | <br /> | ||
| Line 638: | Line 657: | ||
Badness: 0.0592<br /> | Badness: 0.0592<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="Oodako-13-limit"></a><!-- ws:end:WikiTextHeadingRule:62 -->13-limit</h2> | ||
Commas: 56/55, 78/77, 128/125, 507/500<br /> | Commas: 56/55, 78/77, 128/125, 507/500<br /> | ||
<br /> | <br /> | ||
| Line 647: | Line 666: | ||
Badness: 0.0423<br /> | Badness: 0.0423<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h1&gt; --><h1 id="toc32"><a name="Hemisemiaug"></a><!-- ws:end:WikiTextHeadingRule:64 -->Hemisemiaug</h1> | ||
Commas: 128/125, 12005/11664<br /> | Commas: 128/125, 12005/11664<br /> | ||
<br /> | <br /> | ||
| Line 657: | Line 676: | ||
Badness: 0.2110<br /> | Badness: 0.2110<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Hemisemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 3773/3645<br /> | Commas: 56/55, 128/125, 3773/3645<br /> | ||
<br /> | <br /> | ||
| Line 666: | Line 685: | ||
Badness: 0.0807<br /> | Badness: 0.0807<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h1&gt; --><h1 id="toc34"><a name="Niner"></a><!-- ws:end:WikiTextHeadingRule:68 -->Niner</h1> | ||
Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads.<br /> | Niner gives 9 as the complexity of an otonal tetrad, tying it with augene as a temperament supported by 27edo. Niner[18], therefore, has nine such tetrads.<br /> | ||
<br /> | <br /> | ||
| Line 678: | Line 697: | ||
Badness: 0.0672<br /> | Badness: 0.0672<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:70:&lt;h2&gt; --><h2 id="toc35"><a name="Niner-11-limit"></a><!-- ws:end:WikiTextHeadingRule:70 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 540/539<br /> | Commas: 56/55, 128/125, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 687: | Line 706: | ||
Badness: 0.0349<br /> | Badness: 0.0349<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:72:&lt;h2&gt; --><h2 id="toc36"><a name="Niner-13-limit"></a><!-- ws:end:WikiTextHeadingRule:72 -->13-limit</h2> | ||
Commas: 56/55, 78/77, 91/90, 128/125<br /> | Commas: 56/55, 78/77, 91/90, 128/125<br /> | ||
<br /> | <br /> | ||