Tetracot family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 188430935 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 188803379 - 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>2010-12- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-16 17:21:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>188803379</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The parent of the tetracot family is tetracot, the 5-limit temperament tempering out 20000/19683 = |5 -9 4>, the minimal diesis or tetracot comma. The dual of this comma is the wedgie <<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 [[34edo]] 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. | <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;white-space: pre-wrap ! important" class="old-revision-html">The parent of the tetracot family is tetracot, the 5-limit temperament tempering out 20000/19683 = |5 -9 4>, the minimal diesis or tetracot comma. The dual of this comma is the wedgie <<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 [[34edo]] 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. | ||
[[POTE tuning|POTE generator]]: 176.160 | |||
Map: [<1 1 1|, <0 4 9|] | |||
EDOs: 27, 34, 75, 109 | |||
==Seven limit children== | ==Seven limit children== | ||
| Line 22: | Line 27: | ||
===Monkey=== | ===Monkey=== | ||
Commas: 5120/5103, 875/864 | Commas: 5120/5103, 875/864 | ||
[[POTE tuning|POTE generator]]: 175.659 | |||
Map: [<1 1 1 5|, <0 4 9 -15|] | Map: [<1 1 1 5|, <0 4 9 -15|] | ||
| Line 28: | Line 35: | ||
11-limit | 11-limit | ||
Commas: 243/242, 385/384, 100/99 | Commas: 243/242, 385/384, 100/99 | ||
[[POTE tuning|POTE generator]]: 175.570 | |||
Map: [<1 1 1 5 2|, <0 4 9 -15 10|] | Map: [<1 1 1 5 2|, <0 4 9 -15 10|] | ||
| Line 34: | Line 43: | ||
13-limit | 13-limit | ||
Commas: 100/99, 105/104, 144/143, 243/242 | Commas: 100/99, 105/104, 144/143, 243/242 | ||
[[POTE tuning|POTE generator]]: 175.622 | |||
Map: [<1 1 1 5 2 4|, <0 4 9 -15 10 -2|] | Map: [<1 1 1 5 2 4|, <0 4 9 -15 10 -2|] | ||
| Line 40: | Line 51: | ||
===Bunya=== | ===Bunya=== | ||
Commas: 225/224, 15625/15309 | Commas: 225/224, 15625/15309 | ||
[[POTE tuning|POTE generator]]: 175.741 | |||
Map: [<1 1 1 -1|, <0 4 9 26|] | Map: [<1 1 1 -1|, <0 4 9 26|] | ||
| Line 46: | Line 59: | ||
11-limit | 11-limit | ||
Commas: 100/99, 225/224, 1344/1331 | Commas: 100/99, 225/224, 1344/1331 | ||
[[POTE tuning|POTE generator]]: 175.777 | |||
Map: [<1 1 1 -1 2|, <0 4 9 26 10|] | Map: [<1 1 1 -1 2|, <0 4 9 26 10|] | ||
| Line 52: | Line 67: | ||
13-limit | 13-limit | ||
Commas: 100/99, 144/143, 225/224, 243/242 | Commas: 100/99, 144/143, 225/224, 243/242 | ||
[[POTE tuning|POTE generator]]: 175.886 | |||
Map: [<1 1 1 -1 2 4|, <0 4 9 26 10 -2|] | Map: [<1 1 1 -1 2 4|, <0 4 9 26 10 -2|] | ||
| Line 62: | Line 79: | ||
Commas: 245/243, 2401/2400 | Commas: 245/243, 2401/2400 | ||
[[POTE tuning|POTE generator]]: 88.076 | |||
Map: [<1 1 1 2|, <0 8 18 11|] | Map: [<1 1 1 2|, <0 8 18 11|] | ||
| Line 68: | Line 87: | ||
11-limit | 11-limit | ||
Commas: 100/99, 243/242, 245/242 | Commas: 100/99, 243/242, 245/242 | ||
[[POTE tuning|POTE generator]]: 87.975 | |||
Map: [<1 1 1 2 2|, <0 8 18 11 20|] | Map: [<1 1 1 2 2|, <0 8 18 11 20|] | ||
| Line 74: | Line 95: | ||
13-limit | 13-limit | ||
Commas: 100/99, 144/143, 196/195, 243/242 | Commas: 100/99, 144/143, 196/195, 243/242 | ||
[[POTE tuning|POTE generator]]: 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|] | ||
| Line 79: | Line 102: | ||
<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 /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 176.160<br /> | |||
<br /> | |||
Map: [&lt;1 1 1|, &lt;0 4 9|]<br /> | |||
EDOs: 27, 34, 75, 109<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> | ||
| Line 94: | Line 122: | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Monkey"></a><!-- ws:end:WikiTextHeadingRule:4 -->Monkey</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Seven limit children-Monkey"></a><!-- ws:end:WikiTextHeadingRule:4 -->Monkey</h3> | ||
Commas: 5120/5103, 875/864<br /> | Commas: 5120/5103, 875/864<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.659<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 5|, &lt;0 4 9 -15|]<br /> | Map: [&lt;1 1 1 5|, &lt;0 4 9 -15|]<br /> | ||
| Line 100: | Line 130: | ||
11-limit<br /> | 11-limit<br /> | ||
Commas: 243/242, 385/384, 100/99<br /> | Commas: 243/242, 385/384, 100/99<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.570<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 5 2|, &lt;0 4 9 -15 10|]<br /> | Map: [&lt;1 1 1 5 2|, &lt;0 4 9 -15 10|]<br /> | ||
| Line 106: | Line 138: | ||
13-limit <br /> | 13-limit <br /> | ||
Commas: 100/99, 105/104, 144/143, 243/242<br /> | Commas: 100/99, 105/104, 144/143, 243/242<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.622<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 5 2 4|, &lt;0 4 9 -15 10 -2|]<br /> | Map: [&lt;1 1 1 5 2 4|, &lt;0 4 9 -15 10 -2|]<br /> | ||
| Line 112: | Line 146: | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Bunya"></a><!-- ws:end:WikiTextHeadingRule:6 -->Bunya</h3> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Seven limit children-Bunya"></a><!-- ws:end:WikiTextHeadingRule:6 -->Bunya</h3> | ||
Commas: 225/224, 15625/15309<br /> | Commas: 225/224, 15625/15309<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.741<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 -1|, &lt;0 4 9 26|]<br /> | Map: [&lt;1 1 1 -1|, &lt;0 4 9 26|]<br /> | ||
| Line 118: | Line 154: | ||
11-limit<br /> | 11-limit<br /> | ||
Commas: 100/99, 225/224, 1344/1331<br /> | Commas: 100/99, 225/224, 1344/1331<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.777<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 -1 2|, &lt;0 4 9 26 10|]<br /> | Map: [&lt;1 1 1 -1 2|, &lt;0 4 9 26 10|]<br /> | ||
| Line 124: | Line 162: | ||
13-limit<br /> | 13-limit<br /> | ||
Commas: 100/99, 144/143, 225/224, 243/242<br /> | Commas: 100/99, 144/143, 225/224, 243/242<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 175.886<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 -1 2 4|, &lt;0 4 9 26 10 -2|]<br /> | Map: [&lt;1 1 1 -1 2 4|, &lt;0 4 9 26 10 -2|]<br /> | ||
| Line 134: | Line 174: | ||
<br /> | <br /> | ||
Commas: 245/243, 2401/2400<br /> | Commas: 245/243, 2401/2400<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 88.076<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 2|, &lt;0 8 18 11|]<br /> | Map: [&lt;1 1 1 2|, &lt;0 8 18 11|]<br /> | ||
| Line 140: | Line 182: | ||
11-limit<br /> | 11-limit<br /> | ||
Commas: 100/99, 243/242, 245/242<br /> | Commas: 100/99, 243/242, 245/242<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 87.975<br /> | |||
<br /> | <br /> | ||
Map: [&lt;1 1 1 2 2|, &lt;0 8 18 11 20|]<br /> | Map: [&lt;1 1 1 2 2|, &lt;0 8 18 11 20|]<br /> | ||
| Line 146: | Line 190: | ||
13-limit<br /> | 13-limit<br /> | ||
Commas: 100/99, 144/143, 196/195, 243/242<br /> | Commas: 100/99, 144/143, 196/195, 243/242<br /> | ||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 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: 41</body></html></pre></div> | ||