Augmented family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 274916038 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 277255722 - 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>2011-11- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-19 16:18:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>277255722</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: [[12edo|12]], [[27edo|27]], [[39edo|39d]], [[66edo|66cd]] | EDOs: [[12edo|12]], [[27edo|27]], [[39edo|39d]], [[66edo|66cd]] | ||
Badness: 0.0248 | Badness: 0.0248 | ||
===11-limit=== | |||
Commas: 56/55, 64/63, 100/99 | |||
POTE generator: ~3/2 = | |||
Map: [<3 0 7 18 20|, <0 1 0 -2 -2|] | |||
EDOs: 12, 15, 27e | |||
Badness: 0.0196 | |||
==Hexe== | ==Hexe== | ||
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[[triphi|Triforce(9) with L:s = phi]]</pre></div> | [[triphi|Triforce(9) with L:s = phi]]</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:22:&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:22 --><!-- ws:start:WikiTextTocRule:23: --><div style="margin-left: 2em;"><a href="#x-Seven limit children">Seven limit children</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><div style="margin-left: 2em;"><a href="#x-August">August</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><div style="margin-left: 3em;"><a href="#x-August-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><div style="margin-left: 3em;"><a href="#x-August-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><div style="margin-left: 2em;"><a href="#x-Augene">Augene</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><div style="margin-left: 3em;"><a href="#x-Augene-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 2em;"><a href="#x-Hexe">Hexe</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 2em;"><a href="#x-Hemiaug">Hemiaug</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#x-Triforce">Triforce</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 3em;"><a href="#x-Triforce-11-limit">11-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 3em;"><a href="#x-Triforce-13-limit">13-limit</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --></div> | ||
<!-- ws:end:WikiTextTocRule:34 -->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;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2> | ||
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Badness: 0.0248<br /> | Badness: 0.0248<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x-Augene-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h3> | ||
Commas: 56/55, 64/63, 100/99<br /> | |||
<br /> | |||
POTE generator: ~3/2 = <br /> | |||
<br /> | |||
Map: [&lt;3 0 7 18 20|, &lt;0 1 0 -2 -2|]<br /> | |||
EDOs: 12, 15, 27e<br /> | |||
Badness: 0.0196<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Hexe"></a><!-- ws:end:WikiTextHeadingRule:12 -->Hexe</h2> | |||
Commas: 50/49, 128/125<br /> | Commas: 50/49, 128/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0577<br /> | Badness: 0.0577<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hemiaug</h2> | ||
Commas: 128/125, 245/243<br /> | Commas: 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0705<br /> | Badness: 0.0705<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Triforce"></a><!-- ws:end:WikiTextHeadingRule:16 -->Triforce</h2> | ||
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:35:&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:35 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h3> | ||
Commas: 56/55, 77/75, 128/125<br /> | Commas: 56/55, 77/75, 128/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0262<br /> | Badness: 0.0262<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x-Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h3> | ||
Commas: 49/48, 56/55, 66/65, 77/75<br /> | Commas: 49/48, 56/55, 66/65, 77/75<br /> | ||
<br /> | <br /> | ||