Tetracot family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~spt3125~~|~~spt3125~~]] and made on <tt>2013-12-~~03 21~~:19:01 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-04 02:01:49 UTC</tt>.<br>

: The original revision id was <tt>~~474467034~~</tt>.<br>

: The original revision id was <tt>474514676</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>

<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">[[toc]]

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.

The name comes from members of the Araucaria family of conifers, which have four cotyledons (though sometimes these are fused).

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<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 <strong>tetracot family</strong> is <strong>tetracot</strong>, the 5-limit temperament <a class="wiki_link" href="/tempering%20out">tempering out</a> 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><div id="toc"><h1 class="nopad">Table of Contents</h1><div style="margin-left: 1em;"><a href="#Tetracot">Tetracot</a></div>

<div style="margin-left: 2em;"><a href="#Tetracot-Seven limit children">Seven limit children</a></div>

<div style="margin-left: 3em;"><a href="#Tetracot-Seven limit children-Monkey and Bunya">Monkey and Bunya</a></div>

<div style="margin-left: 1em;"><a href="#Monkey">Monkey</a></div>

<div style="margin-left: 2em;"><a href="#Monkey-11-limit">11-limit</a></div>

<div style="margin-left: 2em;"><a href="#Monkey-13-limit">13-limit</a></div>

<div style="margin-left: 1em;"><a href="#Bunya">Bunya</a></div>

<div style="margin-left: 2em;"><a href="#Bunya-11-limit">11-limit</a></div>

<div style="margin-left: 2em;"><a href="#Bunya-13-limit">13-limit</a></div>

<div style="margin-left: 1em;"><a href="#Modus">Modus</a></div>

<div style="margin-left: 2em;"><a href="#Modus-11-limit">11-limit</a></div>

<div style="margin-left: 2em;"><a href="#Modus-13-limit">13-limit</a></div>

<div style="margin-left: 3em;"><a href="#Modus-13-limit-Musical Examples">Musical Examples</a></div>

<div style="margin-left: 1em;"><a href="#Ponens">Ponens</a></div>

<div style="margin-left: 2em;"><a href="#Ponens-13-limit">13-limit</a></div>

<div style="margin-left: 1em;"><a href="#Wollemia">Wollemia</a></div>

<div style="margin-left: 2em;"><a href="#Wollemia-11-limit">11-limit</a></div>

<div style="margin-left: 2em;"><a href="#Wollemia-13-limit">13-limit</a></div>

<div style="margin-left: 1em;"><a href="#Octacot">Octacot</a></div>

<div style="margin-left: 2em;"><a href="#Octacot-11-limit">11-limit</a></div>

<div style="margin-left: 2em;"><a href="#Octacot-13-limit">13-limit</a></div>

<div style="margin-left: 2em;"><a href="#Octacot-Octocat">Octocat</a></div>

<div style="margin-left: 2em;"><a href="#Octacot-Octopod">Octopod</a></div>

<div style="margin-left: 1em;"><a href="#Dificot">Dificot</a></div>

<div style="margin-left: 1em;"><a href="#Duodecicot">Duodecicot</a></div>

</div>

The parent of the <strong>tetracot family</strong> is <strong>tetracot</strong>, the 5-limit temperament <a class="wiki_link" href="/tempering%20out">tempering out</a> 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 />

The name comes from members of the Araucaria family of conifers, which have four cotyledons (though sometimes these are fused).<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:spt3125|spt3125]] and made on <tt>2013-12-03 21:19:01 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2013-12-04 02:01:49 UTC</tt>.<br>
-: The original revision id was <tt>474467034</tt>.<br>
+: The original revision id was <tt>474514676</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>
 <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&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 [[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">[[toc]]
+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 [[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.
 The name comes from members of the Araucaria family of conifers, which have four cotyledons (though sometimes these are fused).
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-<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tetracot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The parent of the &lt;strong&gt;tetracot family&lt;/strong&gt; is &lt;strong&gt;tetracot&lt;/strong&gt;, the 5-limit temperament &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; 20000/19683 = |5 -9 4&amp;gt;, the minimal diesis or tetracot comma. The dual of this comma is the wedgie &amp;lt;&amp;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 &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; 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.&lt;br /&gt;
+<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tetracot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:50:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Tetracot"&gt;Tetracot&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tetracot-Seven limit children"&gt;Seven limit children&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Tetracot-Seven limit children-Monkey and Bunya"&gt;Monkey and Bunya&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Monkey"&gt;Monkey&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Monkey-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Monkey-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Bunya"&gt;Bunya&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bunya-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Bunya-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Modus"&gt;Modus&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Modus-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Modus-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Modus-13-limit-Musical Examples"&gt;Musical Examples&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Ponens"&gt;Ponens&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Ponens-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Wollemia"&gt;Wollemia&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wollemia-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wollemia-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Octacot"&gt;Octacot&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octacot-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octacot-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octacot-Octocat"&gt;Octocat&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Octacot-Octopod"&gt;Octopod&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Dificot"&gt;Dificot&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Duodecicot"&gt;Duodecicot&lt;/a&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;/div&gt;
+&lt;!-- ws:end:WikiTextTocRule:76 --&gt;The parent of the &lt;strong&gt;tetracot family&lt;/strong&gt; is &lt;strong&gt;tetracot&lt;/strong&gt;, the 5-limit temperament &lt;a class="wiki_link" href="/tempering%20out"&gt;tempering out&lt;/a&gt; 20000/19683 = |5 -9 4&amp;gt;, the minimal diesis or tetracot comma. The dual of this comma is the wedgie &amp;lt;&amp;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 &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; 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.&lt;br /&gt;
 &lt;br /&gt;
 The name comes from members of the Araucaria family of conifers, which have four cotyledons (though sometimes these are fused).&lt;br /&gt;