Augmented family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 289128299 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 290292873 - 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>2012-01-07 20:31:32 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>290292873</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: 15, 48bc, 63bc, 78bc | EDOs: 15, 48bc, 63bc, 78bc | ||
Badness: 0.0547 | Badness: 0.0547 | ||
=Deflated= | |||
Commas: 21/20, 128/125 | |||
POTE generator: ~3/2 = 681.629 | |||
Map: [<3 0 7 13|, <0 1 0 -1|] | |||
Wedgie: <<3 0 -3 -7 -13 -7|| | |||
EDOs: 3, 9, 18bd, 21d, 30bd | |||
Badness: 0.0591 | |||
==11-limit== | ==11-limit== | ||
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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:28:&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:28 --><!-- ws:start:WikiTextTocRule:29: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#August">August</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Augene">Augene</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Inflated">Inflated</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Deflated">Deflated</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Hexe">Hexe</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Hemiaug">Hemiaug</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Triforce">Triforce</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:43 --><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: 0.0547<br /> | Badness: 0.0547<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Deflated"></a><!-- ws:end:WikiTextHeadingRule:14 -->Deflated</h1> | ||
Commas: 21/20, 128/125<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 681.629<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 13|, &lt;0 1 0 -1|]<br /> | |||
Wedgie: &lt;&lt;3 0 -3 -7 -13 -7||<br /> | |||
EDOs: 3, 9, 18bd, 21d, 30bd<br /> | |||
Badness: 0.0591<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Deflated-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> | |||
Commas: 28/27, 55/54, 128/125<br /> | Commas: 28/27, 55/54, 128/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0312<br /> | Badness: 0.0312<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Hexe"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hexe</h1> | ||
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:20:&lt;h1&gt; --><h1 id="toc10"><a name="Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:20 -->Hemiaug</h1> | ||
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:22:&lt;h1&gt; --><h1 id="toc11"><a name="Triforce"></a><!-- ws:end:WikiTextHeadingRule:22 -->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:44:&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:44 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2> | ||
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:26:&lt;h2&gt; --><h2 id="toc13"><a name="Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->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 /> | ||