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:phylingual|phylingual]] and made on <tt>2012-06-19 20:57:44 UTC</tt>.<br>

: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-19 21:03:54 UTC</tt>.<br>

: The original revision id was <tt>~~346578204~~</tt>.<br>

: The original revision id was <tt>346579252</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>

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EDOs: 14c, 27, 34, 75, 109, 470b, 579b

==~~Musical Examples~~==

== ==

* [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Tetracot Perc-Sitar]] by Dustin Schallert, in [[27edo]]

* [[http://soundcloud.com/dustin-schallert/tetracot-jam|Tetracot Jam]] by Dustin Schallert in [[27edo]]

==Seven limit children==

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EDOs: 7, 27e, 34d, 61de

Badness: 0.0238

==Musical Examples==

[[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Tetracot Perc-Sitar]] by Dustin Schallert, in [[27edo]]

[[http://soundcloud.com/dustin-schallert/tetracot-jam|Tetracot Jam]] by Dustin Schallert in [[27edo]]

=Ponens=

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Badness: 0.1198</pre></div>

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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> | <a href="#Monkey">Monkey</a> | <a href="#Bunya">Bunya</a> | <a href="#Modus">Modus</a> | <a href="#Ponens">Ponens</a> | <a href="#Wollemia">Wollemia</a> | <a href="#Octacot">Octacot</a> | <a href="#Dificot">Dificot</a> | <a href="#Duodecicot">Duodecicot</a>

<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> | <a href="#Monkey">Monkey</a> | <a href="#Bunya">Bunya</a> | <a href="#Modus">Modus</a> | <a href="#Ponens">Ponens</a> | <a href="#Wollemia">Wollemia</a> | <a href="#Octacot">Octacot</a> | <a href="#Dificot">Dificot</a> | <a href="#Duodecicot">Duodecicot</a>

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 />

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 />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 176.160<br />

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EDOs: 14c, 27, 34, 75, 109, 470b, 579b<br />

<br />

<h2 id="toc0"~~><a name="x-Musical Examples"></a~~>~~Musical Examples~~</h2>

<h2 id="toc0"> </h2>

<ul><li><a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow">Tetracot Perc-Sitar</a> by Dustin Schallert, in <a class="wiki_link" href="/27edo">27edo</a></li><li><a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow">Tetracot Jam</a> by Dustin Schallert in <a class="wiki_link" href="/27edo">27edo</a></li></ul><br />

<br />

<h2 id="toc1"><a name="x-Seven limit children"></a>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. Adding 875/864, the keema, gives monkey, and 179200/177147 (or equivalently 225/224) gives bunya (the names come from members of the Araucaria family of conifers, which have four cotyledons, though sometimes these are fused.) Adding 245/243 gives octacot, which splits the generator in half.<br />

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Badness: 0.0238<br />

<br />

<h1 id="~~toc12~~"><a name="Ponens"></a>Ponens</h1>

<h2 id="toc12"><a name="Modus-Musical Examples"></a>Musical Examples</h2>

<a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow">Tetracot Perc-Sitar</a> by Dustin Schallert, in <a class="wiki_link" href="/27edo">27edo</a><br />

<a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow">Tetracot Jam</a> by Dustin Schallert in <a class="wiki_link" href="/27edo">27edo</a><br />

<br />

<h1 id="toc13"><a name="Ponens"></a>Ponens</h1>

The error of 11 is about the same as that of Modus, but flat instead of sharp, and much more abundant. Since the other primes are all sharp, however, this leads to a much larger error for other intervals involving 11.<br />

<br />

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Badness: 0.0631<br />

<br />

<h2 id="~~toc13~~"><a name="Ponens-13-limit"></a>13-limit</h2>

<h2 id="toc14"><a name="Ponens-13-limit"></a>13-limit</h2>

Commas: 55/54, 64/63, 66/65, 143/140<br />

<br />

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Badness: 0.039<br />

<br />

<h1 id="~~toc14~~"><a name="Wollemia"></a>Wollemia</h1>

<h1 id="toc15"><a name="Wollemia"></a>Wollemia</h1>

Commas: 126/125, 2240/2187<br />

<br />

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Badness: 0.0705<br />

<br />

<h2 id="~~toc15~~"><a name="Wollemia-11-limit"></a>11-limit</h2>

<h2 id="toc16"><a name="Wollemia-11-limit"></a>11-limit</h2>

Commas: 56/55, 100/99, 243/242<br />

<br />

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Badness: 0.0376<br />

<br />

<h2 id="~~toc16~~"><a name="Wollemia-13-limit"></a>13-limit</h2>

<h2 id="toc17"><a name="Wollemia-13-limit"></a>13-limit</h2>

Commas: 56/55, 91/90, 100/99, 352/351<br />

<br />

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Badness: 0.0312<br />

<br />

<h1 id="~~toc17~~"><a name="Octacot"></a>Octacot</h1>

<h1 id="toc18"><a name="Octacot"></a>Octacot</h1>

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. <a class="wiki_link" href="/68edo">68edo</a> or <a class="wiki_link" href="/109edo">109edo</a> can be used as tunings, as can (5/2)^(1/18), which gives just major thirds. Another tuning is <a class="wiki_link" href="/150edo">150edo</a>, which has a generator, 11/150, of exactly 88 cents. This relates octacot to the <a class="wiki_link" href="/88cET">88cET</a> non-octave temperament, which like <a class="wiki_link" href="/Carlos%20Alpha">Carlos Alpha</a> arguably makes more sense viewed as part of a rank two temperament with octaves rather than rank one without them.<br />

<br />

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EDOs: 14c, 27, 41, 68, 109<br />

<br />

<h2 id="~~toc18~~"><a name="Octacot-11-limit"></a>11-limit</h2>

<h2 id="toc19"><a name="Octacot-11-limit"></a>11-limit</h2>

Commas: 100/99, 243/242, 245/242<br />

<br />

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See also: <a class="wiki_link" href="/Chords%20of%20octacot">Chords of octacot</a><br />

<br />

<h2 id="~~toc19~~"><a name="Octacot-13-limit"></a>13-limit</h2>

<h2 id="toc20"><a name="Octacot-13-limit"></a>13-limit</h2>

Commas: 100/99, 144/143, 196/195, 243/242<br />

<br />

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Badness: 0.0233<br />

<br />

<h2 id="~~toc20~~"><a name="Octacot-Octocat"></a>Octocat</h2>

<h2 id="toc21"><a name="Octacot-Octocat"></a>Octocat</h2>

Commas: 78/77, 91/90, 100/99, 245/242<br />

<br />

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Badness: 0.0276<br />

<br />

<h2 id="~~toc21~~"><a name="Octacot-Octopod"></a>Octopod</h2>

<h2 id="toc22"><a name="Octacot-Octopod"></a>Octopod</h2>

Commas: 100/99 105/104 243/242 245/242<br />

<br />

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Badness: 0.0283<br />

<br />

<h1 id="~~toc22~~"><a name="Dificot"></a>Dificot</h1>

<h1 id="toc23"><a name="Dificot"></a>Dificot</h1>

Commas: 100/99, 243/242, 245/242, 343/338<br />

<br />

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Badness: 0.0519<br />

<br />

<h1 id="~~toc23~~"><a name="Duodecicot"></a>Duodecicot</h1>

<h1 id="toc24"><a name="Duodecicot"></a>Duodecicot</h1>

Commas: 3087/3125, 10976/10935<br />

<br />

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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:phylingual|phylingual]] and made on <tt>2012-06-19 20:57:44 UTC</tt>.<br>
+: This revision was by author [[User:phylingual|phylingual]] and made on <tt>2012-06-19 21:03:54 UTC</tt>.<br>
-: The original revision id was <tt>346578204</tt>.<br>
+: The original revision id was <tt>346579252</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>
@@ Line 14: / Line 14: @@
 EDOs: 14c, 27, 34, 75, 109, 470b, 579b
-==Musical Examples==
+== ==
-* [[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Tetracot Perc-Sitar]] by Dustin Schallert, in [[27edo]]
-* [[http://soundcloud.com/dustin-schallert/tetracot-jam|Tetracot Jam]] by Dustin Schallert in [[27edo]]
 ==Seven limit children==
@@ Line 110: / Line 108: @@
 EDOs: 7, 27e, 34d, 61de
 Badness: 0.0238
+==Musical Examples==
+[[http://soundcloud.com/dustin-schallert/tetracot-perc-sitar|Tetracot Perc-Sitar]] by Dustin Schallert, in [[27edo]]
+[[http://soundcloud.com/dustin-schallert/tetracot-jam|Tetracot Jam]] by Dustin Schallert in [[27edo]]
 =Ponens=
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 Badness: 0.1198</pre></div>
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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;&lt;!-- ws:start:WikiTextTocRule:48:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Monkey"&gt;Monkey&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt; | &lt;a href="#Bunya"&gt;Bunya&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Modus"&gt;Modus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Ponens"&gt;Ponens&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt; | &lt;a href="#Wollemia"&gt;Wollemia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Octacot"&gt;Octacot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Dificot"&gt;Dificot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Duodecicot"&gt;Duodecicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&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@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt; | &lt;a href="#Monkey"&gt;Monkey&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt; | &lt;a href="#Bunya"&gt;Bunya&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Modus"&gt;Modus&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Ponens"&gt;Ponens&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Wollemia"&gt;Wollemia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Octacot"&gt;Octacot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt; | &lt;a href="#Dificot"&gt;Dificot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt; | &lt;a href="#Duodecicot"&gt;Duodecicot&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:73 --&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;!-- 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;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 176.160&lt;br /&gt;
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 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Musical Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Musical Examples&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; &lt;/h2&gt;
-  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow"&gt;Tetracot Perc-Sitar&lt;/a&gt; by Dustin Schallert, in &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow"&gt;Tetracot Jam&lt;/a&gt; by Dustin Schallert in &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+  &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Seven limit children"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Seven limit children&lt;/h2&gt;
   The second comma of the &lt;a class="wiki_link" href="/Normal%20lists"&gt;normal comma list&lt;/a&gt; defines which 7-limit family member we are looking at. Adding 875/864, the keema, gives monkey, and 179200/177147 (or equivalently 225/224) gives bunya (the names come from members of the Araucaria family of conifers, which have four cotyledons, though sometimes these are fused.) Adding 245/243 gives octacot, which splits the generator in half.&lt;br /&gt;
@@ Line 330: / Line 332: @@
 Badness: 0.0238&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Ponens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Ponens&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Modus-Musical Examples"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Musical Examples&lt;/h2&gt;
+ &lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-perc-sitar" rel="nofollow"&gt;Tetracot Perc-Sitar&lt;/a&gt; by Dustin Schallert, in &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://soundcloud.com/dustin-schallert/tetracot-jam" rel="nofollow"&gt;Tetracot Jam&lt;/a&gt; by Dustin Schallert in &lt;a class="wiki_link" href="/27edo"&gt;27edo&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Ponens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Ponens&lt;/h1&gt;
   The error of 11 is about the same as that of Modus, but flat instead of sharp, and much more abundant. Since the other primes are all sharp, however, this leads to a much larger error for other intervals involving 11.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 341: / Line 347: @@
 Badness: 0.0631&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Ponens-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Ponens-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
   Commas: 55/54, 64/63, 66/65, 143/140&lt;br /&gt;
 &lt;br /&gt;
@@ Line 350: / Line 356: @@
 Badness: 0.039&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Wollemia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Wollemia&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Wollemia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Wollemia&lt;/h1&gt;
   Commas: 126/125, 2240/2187&lt;br /&gt;
 &lt;br /&gt;
@@ Line 360: / Line 366: @@
 Badness: 0.0705&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Wollemia-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Wollemia-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
   Commas: 56/55, 100/99, 243/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 369: / Line 375: @@
 Badness: 0.0376&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Wollemia-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Wollemia-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
   Commas: 56/55, 91/90, 100/99, 352/351&lt;br /&gt;
 &lt;br /&gt;
@@ Line 378: / Line 384: @@
 Badness: 0.0312&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Octacot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Octacot&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Octacot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Octacot&lt;/h1&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;
@@ Line 390: / Line 396: @@
 EDOs: 14c, 27, 41, 68, 109&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Octacot-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Octacot-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;11-limit&lt;/h2&gt;
   Commas: 100/99, 243/242, 245/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 400: / Line 406: @@
 See also: &lt;a class="wiki_link" href="/Chords%20of%20octacot"&gt;Chords of octacot&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Octacot-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Octacot-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;13-limit&lt;/h2&gt;
   Commas: 100/99, 144/143, 196/195, 243/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 409: / Line 415: @@
 Badness: 0.0233&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Octacot-Octocat"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Octocat&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Octacot-Octocat"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Octocat&lt;/h2&gt;
   Commas: 78/77, 91/90, 100/99, 245/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 418: / Line 424: @@
 Badness: 0.0276&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Octacot-Octopod"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Octopod&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Octacot-Octopod"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Octopod&lt;/h2&gt;
   Commas: 100/99 105/104 243/242 245/242&lt;br /&gt;
 &lt;br /&gt;
@@ Line 427: / Line 433: @@
 Badness: 0.0283&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Dificot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Dificot&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Dificot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Dificot&lt;/h1&gt;
   Commas: 100/99, 243/242, 245/242, 343/338&lt;br /&gt;
 &lt;br /&gt;
@@ Line 436: / Line 442: @@
 Badness: 0.0519&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Duodecicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Duodecicot&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Duodecicot"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Duodecicot&lt;/h1&gt;
   Commas: 3087/3125, 10976/10935&lt;br /&gt;
 &lt;br /&gt;

Tetracot family: Difference between revisions

Wikispaces>phylingual