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: | : 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> | : 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: <<3 0 -6 -7 -18 -14|| | Wedgie: <<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: [<6 0 14 17|, <0 1 0 0|] | |||
Wedgie: <<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: [<3 1 7 -1|, <0 2 0 5|] | |||
Wedgie: <<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"><html><head><title>Augmented family</title></head><body>The 5-limit parent comma for the augmented family is 128/125, the diesis. 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 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. <br /> | <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>The 5-limit parent comma for the augmented family is 128/125, the diesis. 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 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. <br /> | ||
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Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||<br /> | Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||<br /> | ||
EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/66edo">66</a><br /> | EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/66edo">66</a><br /> | ||
Badness: 0.0248</body></html></pre></div> | Badness: 0.0248<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Hexe"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexe</h2> | |||
Commas: 50/49, 128/125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.963<br /> | |||
<br /> | |||
Map: [&lt;6 0 14 17|, &lt;0 1 0 0|]<br /> | |||
Wedgie: &lt;&lt;6 0 0 -14 -17 0||<br /> | |||
EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/54edo">54</a><br /> | |||
Badness: 0.0577<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiaug</h2> | |||
Commas: 128/125, 245/243<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 445.118<br /> | |||
<br /> | |||
Map: [&lt;3 1 7 -1|, &lt;0 2 0 5|]<br /> | |||
Wedgie: &lt;&lt;6 0 15 -14 7 35||<br /> | |||
EDOs: <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/27edo">27</a><br /> | |||
Badness: 0.0705</body></html></pre></div> | |||