Tetracot family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 197086990 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 204555638 - 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- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-23 23:14:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>204555638</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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Commas: 100/99, 144/143, 196/195, 243/242 | Commas: 100/99, 144/143, 196/195, 243/242 | ||
[[POTE tuning|POTE generator]]: 88.106 | [[POTE tuning|POTE generator]]: ~22/21 = 88.106 | ||
Map: [<1 1 1 2 2 4|, <0 8 18 11 20 -4|] | Map: [<1 1 1 2 2 4|, <0 8 18 11 20 -4|] | ||
EDOs: 41</pre></div> | EDOs: 13, 14, 27, 41, 68, 109 | ||
Badness: 0.0233</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>Tetracot family</title></head><body>The parent of the tetracot family is tetracot, the 5-limit temperament tempering out 20000/19683 = |5 -9 4&gt;, the minimal diesis or tetracot comma. The dual of this comma is the wedgie &lt;&lt;4 9 5||, which tells us 10/9 is a generator, and that four of them give 3/2. In fact, (10/9)^4 = 20000/19683 * 3/2. We also have (10/9)^9 = (20000/19683)^2 * 5/2. From this it is evident we should flatten the generator a bit, and <a class="wiki_link" href="/34edo">34edo</a> does this and makes for a recommendable tuning. Another possibility is to use (5/2)^(1/9) for a generator. The 13-note MOS gives enough space for eight triads, with the 20-note MOS supplying many more.<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>Tetracot family</title></head><body>The parent of the tetracot family is tetracot, the 5-limit temperament tempering out 20000/19683 = |5 -9 4&gt;, the minimal diesis or tetracot comma. The dual of this comma is the wedgie &lt;&lt;4 9 5||, which tells us 10/9 is a generator, and that four of them give 3/2. In fact, (10/9)^4 = 20000/19683 * 3/2. We also have (10/9)^9 = (20000/19683)^2 * 5/2. From this it is evident we should flatten the generator a bit, and <a class="wiki_link" href="/34edo">34edo</a> does this and makes for a recommendable tuning. Another possibility is to use (5/2)^(1/9) for a generator. The 13-note MOS gives enough space for eight triads, with the 20-note MOS supplying many more.<br /> | ||
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Commas: 100/99, 144/143, 196/195, 243/242<br /> | Commas: 100/99, 144/143, 196/195, 243/242<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 88.106<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~22/21 = 88.106<br /> | ||
<br /> | <br /> | ||
Map: [&lt;1 1 1 2 2 4|, &lt;0 8 18 11 20 -4|]<br /> | Map: [&lt;1 1 1 2 2 4|, &lt;0 8 18 11 20 -4|]<br /> | ||
EDOs: 41</body></html></pre></div> | EDOs: 13, 14, 27, 41, 68, 109<br /> | ||
Badness: 0.0233</body></html></pre></div> | |||