Augmented family: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 192637528 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 192638858 - 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>2011-01-12 00:35:04 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-12 00:51:34 UTC</tt>.<br>
: The original revision id was <tt>192637528</tt>.<br>
: The original revision id was <tt>192638858</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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Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||
Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||
EDOs: [[12edo|12]], [[27edo|27]], [[66edo|66]]
EDOs: [[12edo|12]], [[27edo|27]], [[66edo|66]]
Badness: 0.0248</pre></div>
Badness: 0.0248
 
==Hexe==
Commas: 50/49, 128/125
 
[[POTE tuning|POTE generator]]: 710.963
 
Map: [&lt;6 0 14 17|, &lt;0 1 0 0|]
Wedgie: &lt;&lt;6 0 0 -14 -17 0||
EDOs: [[6edo|6]], [[12edo|12]], [[54edo|54]]
Badness: 0.0577
 
==Hemiaug==
Commas: 128/125, 245/243
 
[[POTE tuning|POTE generator]]: 445.118
 
Map: [&lt;3 1 7 -1|, &lt;0 2 0 5|]
Wedgie: &lt;&lt;6 0 15 -14 7 35||
EDOs: [[24edo|24]], [[27edo|27]]
Badness: 0.0705</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the augmented family is 128/125, the diesis. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. &lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the augmented family is 128/125, the diesis. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. &lt;br /&gt;
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Wedgie: &amp;lt;&amp;lt;3 0 -6 -7 -18 -14||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 0 -6 -7 -18 -14||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/66edo"&gt;66&lt;/a&gt;&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/66edo"&gt;66&lt;/a&gt;&lt;br /&gt;
Badness: 0.0248&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.0248&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Hexe"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hexe&lt;/h2&gt;
Commas: 50/49, 128/125&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 710.963&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;6 0 14 17|, &amp;lt;0 1 0 0|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 0 0 -14 -17 0||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/6edo"&gt;6&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/54edo"&gt;54&lt;/a&gt;&lt;br /&gt;
Badness: 0.0577&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Hemiaug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hemiaug&lt;/h2&gt;
Commas: 128/125, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 445.118&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;3 1 7 -1|, &amp;lt;0 2 0 5|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 0 15 -14 7 35||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;&lt;br /&gt;
Badness: 0.0705&lt;/body&gt;&lt;/html&gt;</pre></div>