Trienstonic clan: 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:genewardsmith|genewardsmith]] and made on <tt>2011-02-~~26 17~~:42:43 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-18 19:35:16 UTC</tt>.<br>

: The original revision id was <tt>~~205295050~~</tt>.<br>

: The original revision id was <tt>229795855</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">Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.

<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|flat]]

==Father==

Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.

=Father=

Commas: 16/15, 28/27

7-limit minimax

[<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|]

~~Eigenmonzos~~: 2, 7/5

[[Eigenmonzo subgroup]]: 2.7/5

9-limit ~~minimax~~

9-limit eigenmonzo subgroup: 2.9/5

~~[<1 0 0 0|, <4 0 -1 0|, <0 0 1 0|, <10 0 -3 0|]~~

~~Eigenmonzos~~: 2, 5/4

[[POTE tuning|POTE generator]]: 742.002

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EDOs: 5, 8, 13, 21, 55, 76

==Octokaidecal==

=Uncle=

Commas: 28/27, 256/245

7-limit eigenmonzo subgroup: 2.5/3

9-limit eigenmonzo subgroup: 2.9/5

=Octokaidecal=

Commas: 28/27, 50/49

7-limit eigenmonzo subgroup: 2.5

9-limit eigenmonzo subgroup: 2.5

[[POTE tuning|POTE generator]]: 728.874

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EDOs: 10, 18, 28

==Opossum==

=Opossum=

Commas: 28/27, 126/125

7-limit eigenmonzo subgroup: 2.7

9-limit eigenmonzo subgroup: 2.7

[[POTE tuning|POTE generator]]: ~10/9 = 159.691

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Badness: 0.0407

===11-limit===

==11-limit==

Commas: 28/27, 55/54, 77/75

11-limit eigenmonzo subgroup: 2.7

[[POTE tuning|POTE generator]]: ~10/9 = 159.807

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Badness: 0.0223

===13-limit===

==13-limit==

Commas: 28/27, 40/39, 55/54, 66/65

13-limit eigenmonzo subgroup: 2.7

15-limit eigenmonzo subgroup: 2.7

[[POTE tuning|POTE generator]]: ~10/9 = 158.805

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Badness: 0.0194</pre></div>

<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>Trienstonic clan</title></head><body>Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.<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>Trienstonic clan</title></head><body><a href="#Father">Father</a> | <a href="#Uncle">Uncle</a> | <a href="#Octokaidecal">Octokaidecal</a> | <a href="#Opossum">Opossum</a>

<br />

Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.<br />

<br />

<h2 id="toc0"><a name="x-Father"></a>Father</h2>

<h1 id="toc0"><a name="Father"></a>Father</h1>

Commas: 16/15, 28/27<br />

<br />

7-limit minimax<br />

[&lt;1 0 0 0|, &lt;3/2 0 -1/4 1/4|, &lt;5/2 0 1/4 -1/4|, &lt;5/2 0 -3/4 3/4|]<br />

~~Eigenmonzos~~: 2, 7/5<br />

<a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>: 2.7/5<br />

<br />

9-limit ~~minimax<br />~~

9-limit eigenmonzo subgroup: 2.9/5<br />

~~[&lt;1 0 0 0|, &lt;4 0 -1 0|, &lt;0 0 1 0|, &lt;10 0 -3 0|]<br />~~

~~Eigenmonzos~~: 2, 5/4<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 742.002<br />

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EDOs: 5, 8, 13, 21, 55, 76<br />

<br />

<h2 id="toc1"><a name="x-Octokaidecal"></a>Octokaidecal</h2>

<h1 id="toc1"><a name="Uncle"></a>Uncle</h1>

Commas: 28/27, 256/245<br />

<br />

7-limit eigenmonzo subgroup: 2.5/3<br />

9-limit eigenmonzo subgroup: 2.9/5<br />

<br />

<h1 id="toc2"><a name="Octokaidecal"></a>Octokaidecal</h1>

Commas: 28/27, 50/49<br />

<br />

7-limit eigenmonzo subgroup: 2.5<br />

9-limit eigenmonzo subgroup: 2.5<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 728.874<br />

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EDOs: 10, 18, 28<br />

<br />

<h2 id="~~toc2~~"><a name="x-Opossum"></a>Opossum</h2>

<h1 id="toc3"><a name="Opossum"></a>Opossum</h1>

Commas: 28/27, 126/125<br />

<br />

7-limit eigenmonzo subgroup: 2.7<br />

9-limit eigenmonzo subgroup: 2.7<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 159.691<br />

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Badness: 0.0407<br />

<br />

<h3 id="~~toc3~~"><a name="x-Opossum-11-limit"></a>11-limit</h3>

<h2 id="toc4"><a name="Opossum-11-limit"></a>11-limit</h2>

Commas: 28/27, 55/54, 77/75<br />

<br />

11-limit eigenmonzo subgroup: 2.7<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 159.807<br />

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Badness: 0.0223<br />

<br />

<h3 id="~~toc4~~"><a name="x-Opossum-13-limit"></a>13-limit</h3>

<h2 id="toc5"><a name="Opossum-13-limit"></a>13-limit</h2>

Commas: 28/27, 40/39, 55/54, 66/65<br />

<br />

13-limit eigenmonzo subgroup: 2.7<br />

15-limit eigenmonzo subgroup: 2.7<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~10/9 = 158.805<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:genewardsmith|genewardsmith]] and made on <tt>2011-02-26 17:42:43 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-18 19:35:16 UTC</tt>.<br>
-: The original revision id was <tt>205295050</tt>.<br>
+: The original revision id was <tt>229795855</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">Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.
+<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|flat]]
-==Father==
+Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.
+=Father=
 Commas: 16/15, 28/27
 -limit minimax
 [&lt;1 0 0 0|, &lt;3/2 0 -1/4 1/4|, &lt;5/2 0 1/4 -1/4|, &lt;5/2 0 -3/4 3/4|]
-Eigenmonzos: 2, 7/5
+[[Eigenmonzo subgroup]]: 2.7/5
--limit minimax
+-limit eigenmonzo subgroup: 2.9/5
-[&lt;1 0 0 0|, &lt;4 0 -1 0|, &lt;0 0 1 0|, &lt;10 0 -3 0|]
-Eigenmonzos: 2, 5/4
 [[POTE tuning|POTE generator]]: 742.002
@@ Line 25: / Line 25: @@
 EDOs: 5, 8, 13, 21, 55, 76
-==Octokaidecal==
+=Uncle=
+Commas: 28/27, 256/245
+-limit eigenmonzo subgroup: 2.5/3
+-limit eigenmonzo subgroup: 2.9/5
+=Octokaidecal=
 Commas: 28/27, 50/49
+-limit eigenmonzo subgroup: 2.5
+-limit eigenmonzo subgroup: 2.5
 [[POTE tuning|POTE generator]]: 728.874
@@ Line 34: / Line 44: @@
 EDOs: 10, 18, 28
-==Opossum==
+=Opossum=
 Commas: 28/27, 126/125
+-limit eigenmonzo subgroup: 2.7
+-limit eigenmonzo subgroup: 2.7
 [[POTE tuning|POTE generator]]: ~10/9 = 159.691
@@ Line 44: / Line 57: @@
 Badness: 0.0407
-===11-limit===
+==11-limit==
 Commas: 28/27, 55/54, 77/75
+-limit eigenmonzo subgroup: 2.7
 [[POTE tuning|POTE generator]]: ~10/9 = 159.807
@@ Line 53: / Line 68: @@
 Badness: 0.0223
-===13-limit===
+==13-limit==
 Commas: 28/27, 40/39, 55/54, 66/65
+-limit eigenmonzo subgroup: 2.7
+-limit eigenmonzo subgroup: 2.7
 [[POTE tuning|POTE generator]]: ~10/9 = 158.805
@@ Line 62: / Line 80: @@
 Badness: 0.0194</pre></div>
 <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;Trienstonic clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.&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;Trienstonic clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Father"&gt;Father&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Uncle"&gt;Uncle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Octokaidecal"&gt;Octokaidecal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Opossum"&gt;Opossum&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
+&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;br /&gt;
+Adding 16/15 to the trienstonic comma of 28/27 leads to father temperament, adding 256/245 gives uncle, adding 50/49 gives octokaidecal and adding 126/125 gives opossum. Other members of the clan discussed elsewhere are sharptone, sharp, and blacksmith.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Father"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Father&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Father"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Father&lt;/h1&gt;
 Commas: 16/15, 28/27&lt;br /&gt;
 &lt;br /&gt;
 -limit minimax&lt;br /&gt;
 [&amp;lt;1 0 0 0|, &amp;lt;3/2 0 -1/4 1/4|, &amp;lt;5/2 0 1/4 -1/4|, &amp;lt;5/2 0 -3/4 3/4|]&lt;br /&gt;
-Eigenmonzos: 2, 7/5&lt;br /&gt;
+&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.7/5&lt;br /&gt;
 &lt;br /&gt;
--limit minimax&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.9/5&lt;br /&gt;
-[&amp;lt;1 0 0 0|, &amp;lt;4 0 -1 0|, &amp;lt;0 0 1 0|, &amp;lt;10 0 -3 0|]&lt;br /&gt;
-Eigenmonzos: 2, 5/4&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 742.002&lt;br /&gt;
@@ Line 81: / Line 99: @@
 EDOs: 5, 8, 13, 21, 55, 76&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-Octokaidecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Octokaidecal&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Uncle"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Uncle&lt;/h1&gt;
+Commas: 28/27, 256/245&lt;br /&gt;
+&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.5/3&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.9/5&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Octokaidecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Octokaidecal&lt;/h1&gt;
 Commas: 28/27, 50/49&lt;br /&gt;
+&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.5&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.5&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 728.874&lt;br /&gt;
@@ Line 90: / Line 118: @@
 EDOs: 10, 18, 28&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Opossum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Opossum&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Opossum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Opossum&lt;/h1&gt;
 Commas: 28/27, 126/125&lt;br /&gt;
+&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 159.691&lt;br /&gt;
@@ Line 100: / Line 131: @@
 Badness: 0.0407&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Opossum-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Opossum-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h2&gt;
 Commas: 28/27, 55/54, 77/75&lt;br /&gt;
+&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 159.807&lt;br /&gt;
@@ Line 109: / Line 142: @@
 Badness: 0.0223&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Opossum-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Opossum-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h2&gt;
 Commas: 28/27, 40/39, 55/54, 66/65&lt;br /&gt;
+&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
+-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~10/9 = 158.805&lt;br /&gt;