Augmented family: Difference between revisions
Wikispaces>xenwolf **Imported revision 147266047 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 192637528 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-12 00:35:04 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>192637528</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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==Seven limit children== | ==Seven limit children== | ||
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.</pre></div> | The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. | ||
==August== | |||
Commas: 36/35, 128/125 | |||
[[POTE tuning|POTE generator]]: 696.011 | |||
Map: [<3 0 7 -1|, <0 1 0 2|] | |||
Wedgie: <<3 0 6 -7 1 14|| | |||
EDOs: [[9edo|9]], [[12edo|12]], [[69edo|69]], [[81edo|81]] | |||
Badness: 0.0265 | |||
==Augene== | |||
Commas: 64/63, 126/125 | |||
[[POTE tuning|POTE generator]]: 709.257 | |||
Map: [<3 0 7 18|, <0 1 0 -2|] | |||
Wedgie: <<3 0 -6 -7 -18 -14|| | |||
EDOs: [[12edo|12]], [[27edo|27]], [[66edo|66]] | |||
Badness: 0.0248</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 /> | ||
<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> | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.</body></html></pre></div> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h2> | |||
Commas: 36/35, 128/125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.011<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 -1|, &lt;0 1 0 2|]<br /> | |||
Wedgie: &lt;&lt;3 0 6 -7 1 14||<br /> | |||
EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/69edo">69</a>, <a class="wiki_link" href="/81edo">81</a><br /> | |||
Badness: 0.0265<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Augene"></a><!-- ws:end:WikiTextHeadingRule:4 -->Augene</h2> | |||
Commas: 64/63, 126/125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 709.257<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 18|, &lt;0 1 0 -2|]<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 /> | |||
Badness: 0.0248</body></html></pre></div> |