Tetracot family: Difference between revisions

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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

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Map: [&lt;1 1 1 5 2 4|, &lt;0 4 9 -15 10 -2|]

EDOs: 7, 34, 41

===Octacot===

Octacot cuts the Gordian knot of deciding between the monkey and bunya mappings for 7 by cutting the generator in half and splitting the difference. It adds 245/243 to the normal comma list, and also tempers out 2401/2400. It has wedgie &lt;&lt;8 18 11 10 -5 -25|| and may also be described as 41&amp;68. [[68edo]] or [[109edo]] can be used as tunings, as can (5/2)^(1/18), which gives just major thirds. Another tuning is [[150edo]], which has a generator, 11/150, of exactly 88 cents. This relates octacot to the [[88cET]] non-octave temperament, which like [[Carlos Alpha]] arguably makes more sense viewed as part of a rank two temperament with octaves rather than rank one without them.  

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Tetracot family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The parent of the tetracot family is tetracot, the 5-limit temperament tempering out 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;

EDOs: 7, 34, 41&lt;br /&gt;

&lt;br /&gt;

Octacot cuts the Gordian knot of deciding between the monkey and bunya mappings for 7 by cutting the generator in half and splitting the difference. It adds 245/243 to the normal comma list, and also tempers out 2401/2400. It has wedgie &amp;lt;&amp;lt;8 18 11 10 -5 -25|| and may also be described as 41&amp;amp;68. &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; or &lt;a class="wiki_link" href="/109edo"&gt;109edo&lt;/a&gt; can be used as tunings, as can (5/2)^(1/18), which gives just major thirds. Another tuning is &lt;a class="wiki_link" href="/150edo"&gt;150edo&lt;/a&gt;, which has a generator, 11/150, of exactly 88 cents. This relates octacot to the &lt;a class="wiki_link" href="/88cET"&gt;88cET&lt;/a&gt; non-octave temperament, which like &lt;a class="wiki_link" href="/Carlos%20Alpha"&gt;Carlos Alpha&lt;/a&gt; arguably makes more sense viewed as part of a rank two temperament with octaves rather than rank one without them. &lt;br /&gt;

&lt;br /&gt;