Augmented family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 332707266 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 336784810 - 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>2012-05- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-05-17 16:25:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>336784810</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: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[37edo|37d]], [[42edo|42d]], [[54edo|54cd]] | EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[37edo|37d]], [[42edo|42d]], [[54edo|54cd]] | ||
Badness: 0.0577 | Badness: 0.0577 | ||
==11-limit== | |||
Commas: 50/49, 56/55, 125/121 | |||
POTE generator: ~3/2 = 714.304 | |||
Map: [<6 0 14 17 21|, <0 1 0 0 0|] | |||
EDOs: 6, 12, 30de | |||
Badness: 0.0384 | |||
==13-limit== | |||
Commas: 50/49, 56/55, 66/65, 105/104 | |||
POTE generator: ~3/2 = 710.005 | |||
Map: [<6 0 14 17 21 13|, <0 1 0 0 0 1|] | |||
EDOs: 12f | |||
Badness: 0.0359 | |||
=Hemiaug= | =Hemiaug= | ||
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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:68:&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:68 --><!-- ws:start:WikiTextTocRule:69: --><div style="margin-left: 1em;"><a href="#Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><div style="margin-left: 1em;"><a href="#August">August</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><div style="margin-left: 2em;"><a href="#August-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><div style="margin-left: 2em;"><a href="#August-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><div style="margin-left: 2em;"><a href="#August-Augustus">Augustus</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><div style="margin-left: 1em;"><a href="#Augene">Augene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><div style="margin-left: 2em;"><a href="#Augene-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><div style="margin-left: 3em;"><a href="#Augene-11-limit-Ogene">Ogene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><div style="margin-left: 2em;"><a href="#Augene-Eugene">Eugene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><div style="margin-left: 1em;"><a href="#Inflated">Inflated</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><div style="margin-left: 2em;"><a href="#Inflated-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><div style="margin-left: 1em;"><a href="#Deflated">Deflated</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><div style="margin-left: 1em;"><a href="#Hexe">Hexe</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><div style="margin-left: 2em;"><a href="#Hexe-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><div style="margin-left: 2em;"><a href="#Hexe-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><div style="margin-left: 1em;"><a href="#Hemiaug">Hemiaug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><div style="margin-left: 2em;"><a href="#Hemiaug-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><div style="margin-left: 2em;"><a href="#Hemiaug-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><div style="margin-left: 1em;"><a href="#Triforce">Triforce</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><div style="margin-left: 2em;"><a href="#Triforce-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><div style="margin-left: 2em;"><a href="#Triforce-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><div style="margin-left: 2em;"><a href="#Triforce-Semitriforce">Semitriforce</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><div style="margin-left: 1em;"><a href="#Hemiug">Hemiug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><div style="margin-left: 2em;"><a href="#Hemiug-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><div style="margin-left: 2em;"><a href="#Hemiug-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><div style="margin-left: 1em;"><a href="#Oodako">Oodako</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><div style="margin-left: 2em;"><a href="#Oodako-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><div style="margin-left: 2em;"><a href="#Oodako-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><div style="margin-left: 1em;"><a href="#Hemisemiaug">Hemisemiaug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><div style="margin-left: 2em;"><a href="#Hemisemiaug-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><div style="margin-left: 1em;"><a href="#Niner">Niner</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><div style="margin-left: 2em;"><a href="#Niner-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><div style="margin-left: 2em;"><a href="#Niner-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --></div> | |||
<!-- ws:end:WikiTextTocRule:103 --><br /> | |||
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 /> | 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 /> | ||
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Badness: 0.0577<br /> | Badness: 0.0577<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Hexe-11-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->11-limit</h2> | ||
Commas: 50/49, 56/55, 125/121<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 714.304<br /> | |||
<br /> | |||
Map: [&lt;6 0 14 17 21|, &lt;0 1 0 0 0|]<br /> | |||
EDOs: 6, 12, 30de<br /> | |||
Badness: 0.0384<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Hexe-13-limit"></a><!-- ws:end:WikiTextHeadingRule:30 -->13-limit</h2> | |||
Commas: 50/49, 56/55, 66/65, 105/104<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 710.005<br /> | |||
<br /> | |||
Map: [&lt;6 0 14 17 21 13|, &lt;0 1 0 0 0 1|]<br /> | |||
EDOs: 12f<br /> | |||
Badness: 0.0359<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hemiaug</h1> | |||
Commas: 128/125, 245/243<br /> | Commas: 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 487: | Line 525: | ||
Badness: 0.0705<br /> | Badness: 0.0705<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Hemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 245/243<br /> | Commas: 56/55, 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 496: | Line 534: | ||
Badness: 0.0382<br /> | Badness: 0.0382<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Hemiaug-13-limit"></a><!-- ws:end:WikiTextHeadingRule:36 -->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 505: | Line 543: | ||
Badness: 0.0302<br /> | Badness: 0.0302<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="Triforce"></a><!-- ws:end:WikiTextHeadingRule:38 -->Triforce</h1> | ||
Commas: 49/48, 128/125<br /> | Commas: 49/48, 128/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:104:&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:104 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:40 -->11-limit</h2> | ||
Commas: 56/55, 77/75, 128/125<br /> | Commas: 56/55, 77/75, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 526: | Line 564: | ||
Badness: 0.0262<br /> | Badness: 0.0262<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:42 -->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 537: | Line 575: | ||
<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:44:&lt;h2&gt; --><h2 id="toc22"><a name="Triforce-Semitriforce"></a><!-- ws:end:WikiTextHeadingRule:44 -->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 546: | Line 584: | ||
Badness: 0.0592<br /> | Badness: 0.0592<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h1&gt; --><h1 id="toc23"><a name="Hemiug"></a><!-- ws:end:WikiTextHeadingRule:46 -->Hemiug</h1> | ||
Commas: 128/125, 1323/1250<br /> | Commas: 128/125, 1323/1250<br /> | ||
<br /> | <br /> | ||
| Line 557: | Line 595: | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="Hemiug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:48 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 1323/1250<br /> | Commas: 56/55, 128/125, 1323/1250<br /> | ||
<br /> | <br /> | ||
| Line 566: | Line 604: | ||
Badness: 0.0681<br /> | Badness: 0.0681<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="Hemiug-13-limit"></a><!-- ws:end:WikiTextHeadingRule:50 -->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 575: | Line 613: | ||
Badness: 0.0423<br /> | Badness: 0.0423<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h1&gt; --><h1 id="toc26"><a name="Oodako"></a><!-- ws:end:WikiTextHeadingRule:52 -->Oodako</h1> | ||
Commas: 128/125, 2401/2400<br /> | Commas: 128/125, 2401/2400<br /> | ||
<br /> | <br /> | ||
| Line 585: | Line 623: | ||
Badness: 0.1132<br /> | Badness: 0.1132<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h2&gt; --><h2 id="toc27"><a name="Oodako-11-limit"></a><!-- ws:end:WikiTextHeadingRule:54 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 3773/3750<br /> | Commas: 56/55, 128/125, 3773/3750<br /> | ||
<br /> | <br /> | ||
| Line 594: | Line 632: | ||
Badness: 0.0592<br /> | Badness: 0.0592<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h2&gt; --><h2 id="toc28"><a name="Oodako-13-limit"></a><!-- ws:end:WikiTextHeadingRule:56 -->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 603: | Line 641: | ||
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="Hemisemiaug"></a><!-- ws:end:WikiTextHeadingRule:58 -->Hemisemiaug</h1> | ||
Commas: 128/125, 12005/11664<br /> | Commas: 128/125, 12005/11664<br /> | ||
<br /> | <br /> | ||
| Line 613: | Line 651: | ||
Badness: 0.2110<br /> | Badness: 0.2110<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="Hemisemiaug-11-limit"></a><!-- ws:end:WikiTextHeadingRule:60 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 3773/3645<br /> | Commas: 56/55, 128/125, 3773/3645<br /> | ||
<br /> | <br /> | ||
| Line 622: | Line 660: | ||
Badness: 0.0807<br /> | Badness: 0.0807<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="Niner"></a><!-- ws:end:WikiTextHeadingRule:62 -->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 634: | Line 672: | ||
Badness: 0.0672<br /> | Badness: 0.0672<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="Niner-11-limit"></a><!-- ws:end:WikiTextHeadingRule:64 -->11-limit</h2> | ||
Commas: 56/55, 128/125, 540/539<br /> | Commas: 56/55, 128/125, 540/539<br /> | ||
<br /> | <br /> | ||
| Line 643: | Line 681: | ||
Badness: 0.0349<br /> | Badness: 0.0349<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h2&gt; --><h2 id="toc33"><a name="Niner-13-limit"></a><!-- ws:end:WikiTextHeadingRule:66 -->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 /> | ||