Augmented family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 203847832 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 204205208 - 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>2011-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-22 22:35:12 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>204205208</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, | 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, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. | ||
==August== | ==August== | ||
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Wedgie: <<6 0 15 -14 7 35|| | Wedgie: <<6 0 15 -14 7 35|| | ||
EDOs: [[24edo|24]], [[27edo|27]] | EDOs: [[24edo|24]], [[27edo|27]] | ||
Badness: 0.0705</pre></div> | Badness: 0.0705 | ||
==Hemis== | |||
Commas: 49/48, 128/125 | |||
[[POTE tuning|POTE generator]]: ~7/6 = 247.049 | |||
Map: [<3 0 7 6|, <0 2 0 1|] | |||
Wedgie: <<6 0 3 -14 -12 7|| | |||
EDOs: 6, 9, 15, 24, 39, 102 | |||
Badness: 0.0202 | |||
===11-limit=== | |||
Commas: 56/55, 77/75, 128/125 | |||
[[POTE tuning|POTE generator]]: ~7/6 = 247.068 | |||
Map: [<3 0 7 6 8|, <0 2 0 1 1|] | |||
EDOs: 6, 9, 15, 24, 39, 63, 102 | |||
Badness: 0.0262 | |||
===13-limit=== | |||
Commas: 49/48, 56/55, 66/65, 77/75 | |||
[[POTE tuning|POTE generator]]: ~7/6 = 248.313 | |||
Map: [<3 0 7 6 8 4|, <0 2 0 1 1 3|] | |||
EDOs: 6, 9, 15, 24, 87 | |||
Badness: 0.0202</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, | 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, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h2> | ||
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Wedgie: &lt;&lt;6 0 15 -14 7 35||<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 /> | 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> | Badness: 0.0705<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Hemis"></a><!-- ws:end:WikiTextHeadingRule:14 -->Hemis</h2> | |||
Commas: 49/48, 128/125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 247.049<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 6|, &lt;0 2 0 1|]<br /> | |||
Wedgie: &lt;&lt;6 0 3 -14 -12 7||<br /> | |||
EDOs: 6, 9, 15, 24, 39, 102<br /> | |||
Badness: 0.0202<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="x-Hemis-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h3> | |||
Commas: 56/55, 77/75, 128/125<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 247.068<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 6 8|, &lt;0 2 0 1 1|]<br /> | |||
EDOs: 6, 9, 15, 24, 39, 63, 102<br /> | |||
Badness: 0.0262<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x-Hemis-13-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->13-limit</h3> | |||
Commas: 49/48, 56/55, 66/65, 77/75<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~7/6 = 248.313<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 6 8 4|, &lt;0 2 0 1 1 3|]<br /> | |||
EDOs: 6, 9, 15, 24, 87<br /> | |||
Badness: 0.0202</body></html></pre></div> | |||