Trienstonic clan: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
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>2012-05-28 16:54:22 UTC</tt>.<br>
: The original revision id was <tt>340220246</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">[[toc|flat]]
 
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.
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.


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7-limit minimax
7-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|]
[&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|]
[[Eigenmonzo subgroup]]: 2.7/5
 
[[Eigenmonzo_subgroup|Eigenmonzo subgroup]]: 2.7/5


9-limit eigenmonzo subgroup: 2.9/5
9-limit eigenmonzo subgroup: 2.9/5


[[POTE tuning|POTE generator]]: 742.002
[[POTE_tuning|POTE generator]]: 742.002


Map: [&lt;1 0 4 -2|, &lt;0 1 -1 3|]
Map: [&lt;1 0 4 -2|, &lt;0 1 -1 3|]
Wedgie: &lt;&lt;1 -1 3 -4 2 10||
Wedgie: &lt;&lt;1 -1 3 -4 2 10||
EDOs: 5, 8d, 13cd, 21bcd
EDOs: 5, 8d, 13cd, 21bcd
Badness: 0.0213
Badness: 0.0213


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7-limit eigenmonzo subgroup: 2.5/3
7-limit eigenmonzo subgroup: 2.5/3
9-limit eigenmonzo subgroup: 2.9/5
9-limit eigenmonzo subgroup: 2.9/5


Map: [&lt;1 0 12 -2|, &lt;0 1 -6 3|]
Map: [&lt;1 0 12 -2|, &lt;0 1 -6 3|]
Wedgie: &lt;&lt;1 -6 3 -12 2 24||
Wedgie: &lt;&lt;1 -6 3 -12 2 24||
EDOs: 13d, 18, 23bc, 41bcd
EDOs: 13d, 18, 23bc, 41bcd
Badness: 0.0727
Badness: 0.0727


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7-limit eigenmonzo subgroup: 2.5
7-limit eigenmonzo subgroup: 2.5
9-limit eigenmonzo subgroup: 2.5
9-limit eigenmonzo subgroup: 2.5


[[POTE tuning|POTE generator]]: 728.874
[[POTE_tuning|POTE generator]]: 728.874


Map: [&lt;2 0 -5 -4|, &lt;0 1 3 3|]
Map: [&lt;2 0 -5 -4|, &lt;0 1 3 3|]
Wedgie: &lt;&lt;2 6 6 5 4 -2||
Wedgie: &lt;&lt;2 6 6 5 4 -2||
EDOs: 10, 18, 28b
EDOs: 10, 18, 28b
Badness: 0.0367
Badness: 0.0367


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Map: [&lt;2 0 -5 -4 7|, &lt;0 1 3 3 0|]
Map: [&lt;2 0 -5 -4 7|, &lt;0 1 3 3 0|]
EDOs: 10, 18e
EDOs: 10, 18e
Badness: 0.0302
Badness: 0.0302


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7-limit eigenmonzo subgroup: 2.7
7-limit eigenmonzo subgroup: 2.7
9-limit eigenmonzo subgroup: 2.7
9-limit eigenmonzo subgroup: 2.7


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


Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -9|]
Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -9|]
Wedgie: &lt;&lt;3 5 9 1 6 7||
Wedgie: &lt;&lt;3 5 9 1 6 7||
EDOs: 7d, 8d, 15
EDOs: 7d, 8d, 15
Badness: 0.0407
Badness: 0.0407


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11-limit eigenmonzo subgroup: 2.7
11-limit eigenmonzo subgroup: 2.7


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


Map: [&lt;1 2 3 4 4|, &lt;0 -3 -5 -9 -4|]
Map: [&lt;1 2 3 4 4|, &lt;0 -3 -5 -9 -4|]
EDOs: 7d, 8d, 15
EDOs: 7d, 8d, 15
Badness: 0.0223
Badness: 0.0223


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13-limit eigenmonzo subgroup: 2.7
13-limit eigenmonzo subgroup: 2.7
15-limit eigenmonzo subgroup: 2.7
15-limit eigenmonzo subgroup: 2.7


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


Map: [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|]
Map: [&lt;1 2 3 4 4 4|, &lt;0 -3 -5 -9 -4 -2|]
EDOs: 7d, 8d, 15, 38bcef
EDOs: 7d, 8d, 15, 38bcef
Badness: 0.0194
Badness: 0.0194


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Map: [&lt;1 0 7 -2|, &lt;0 1 -3 3|]
Map: [&lt;1 0 7 -2|, &lt;0 1 -3 3|]
Wedgie: &lt;&lt;1 -3 3 -7 2 15||
Wedgie: &lt;&lt;1 -3 3 -7 2 15||
EDOs: 2d, 5c, 19ccdd
EDOs: 2d, 5c, 19ccdd
Badness: 0.0585
Badness: 0.0585


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Map: [&lt;1 0 -3|, &lt;0 3 10|]
Map: [&lt;1 0 -3|, &lt;0 3 10|]
EDOs: 15, 47b, 62b
EDOs: 15, 47b, 62b
Badness: 0.2958
Badness: 0.2958


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Map: [&lt;1 0 -3 -2|, &lt;0 3 10 9|]
Map: [&lt;1 0 -3 -2|, &lt;0 3 10 9|]
Wedgie: &lt;&lt;3 10 9 9 6 -7||
Wedgie: &lt;&lt;3 10 9 9 6 -7||
EDOs: 15
EDOs: 15
Badness: 0.0779
Badness: 0.0779


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Map: [&lt;1 0 -3 -2 -4|, &lt;0 3 10 9 14|]
Map: [&lt;1 0 -3 -2 -4|, &lt;0 3 10 9 14|]
EDOs: 15
EDOs: 15
Badness: 0.0432
Badness: 0.0432


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Map: [&lt;1 0 -3 -2 -4 0|, &lt;0 3 10 9 14 7|]
Map: [&lt;1 0 -3 -2 -4 0|, &lt;0 3 10 9 14 7|]
EDOs: 15
EDOs: 15
Badness: 0.0327
Badness: 0.0327


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Map: [&lt;15 24 35 42 52 0|, &lt;0 0 0 0 0 1|]
Map: [&lt;15 24 35 42 52 0|, &lt;0 0 0 0 0 1|]
EDOs: 15, 30, 45bc
EDOs: 15, 30, 45bc
Badness: 0.0289
Badness: 0.0289
</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;&lt;!-- ws:start:WikiTextTocRule:26:&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:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;a href="#Father"&gt;Father&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Uncle"&gt;Uncle&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Octokaidecal"&gt;Octokaidecal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Opossum"&gt;Opossum&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Wallaby"&gt;Wallaby&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Kangaroo"&gt;Kangaroo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt; | &lt;a href="#Quindecic"&gt;Quindecic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&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;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;
7-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;
&lt;a class="wiki_link" href="/Eigenmonzo%20subgroup"&gt;Eigenmonzo subgroup&lt;/a&gt;: 2.7/5&lt;br /&gt;
&lt;br /&gt;
9-limit eigenmonzo subgroup: 2.9/5&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;
&lt;br /&gt;
Map: [&amp;lt;1 0 4 -2|, &amp;lt;0 1 -1 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -1 3 -4 2 10||&lt;br /&gt;
EDOs: 5, 8d, 13cd, 21bcd&lt;br /&gt;
Badness: 0.0213&lt;br /&gt;
&lt;br /&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;
7-limit eigenmonzo subgroup: 2.5/3&lt;br /&gt;
9-limit eigenmonzo subgroup: 2.9/5&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 12 -2|, &amp;lt;0 1 -6 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -6 3 -12 2 24||&lt;br /&gt;
EDOs: 13d, 18, 23bc, 41bcd&lt;br /&gt;
Badness: 0.0727&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;
7-limit eigenmonzo subgroup: 2.5&lt;br /&gt;
9-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;
&lt;br /&gt;
Map: [&amp;lt;2 0 -5 -4|, &amp;lt;0 1 3 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 6 6 5 4 -2||&lt;br /&gt;
EDOs: 10, 18, 28b&lt;br /&gt;
Badness: 0.0367&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Octokaidecal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit&lt;/h2&gt;
Commas: 28/27, 50/49, 55/54&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 732.330&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 -5 -4 7|, &amp;lt;0 1 3 3 0|]&lt;br /&gt;
EDOs: 10, 18e&lt;br /&gt;
Badness: 0.0302&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Opossum"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Opossum&lt;/h1&gt;
Commas: 28/27, 126/125&lt;br /&gt;
&lt;br /&gt;
7-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
9-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;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 4|, &amp;lt;0 -3 -5 -9|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 5 9 1 6 7||&lt;br /&gt;
EDOs: 7d, 8d, 15&lt;br /&gt;
Badness: 0.0407&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Opossum-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
Commas: 28/27, 55/54, 77/75&lt;br /&gt;
&lt;br /&gt;
11-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;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 4 4|, &amp;lt;0 -3 -5 -9 -4|]&lt;br /&gt;
EDOs: 7d, 8d, 15&lt;br /&gt;
Badness: 0.0223&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Opossum-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 28/27, 40/39, 55/54, 66/65&lt;br /&gt;
&lt;br /&gt;
13-limit eigenmonzo subgroup: 2.7&lt;br /&gt;
15-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;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 4 4 4|, &amp;lt;0 -3 -5 -9 -4 -2|]&lt;br /&gt;
EDOs: 7d, 8d, 15, 38bcef&lt;br /&gt;
Badness: 0.0194&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Wallaby"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Wallaby&lt;/h1&gt;
Commas: 28/27, 35/32&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 691.351&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 7 -2|, &amp;lt;0 1 -3 3|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -3 3 -7 2 15||&lt;br /&gt;
EDOs: 2d, 5c, 19ccdd&lt;br /&gt;
Badness: 0.0585&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Kangaroo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Kangaroo&lt;/h1&gt;
Comma: 64000/59049&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 561.195&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -3|, &amp;lt;0 3 10|]&lt;br /&gt;
EDOs: 15, 47b, 62b&lt;br /&gt;
Badness: 0.2958&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Kangaroo-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;7-limit&lt;/h2&gt;
Commas: 28/27, 1029/1000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 560.328&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -3 -2|, &amp;lt;0 3 10 9|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 10 9 9 6 -7||&lt;br /&gt;
EDOs: 15&lt;br /&gt;
Badness: 0.0779&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Kangaroo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11-limit&lt;/h2&gt;
Commas: 28/27, 77/75, 245/242&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 560.155&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -3 -2 -4|, &amp;lt;0 3 10 9 14|]&lt;br /&gt;
EDOs: 15&lt;br /&gt;
Badness: 0.0432&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Kangaroo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
Commas: 28/27, 40/39, 77/75, 147/143&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 559.770&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -3 -2 -4 0|, &amp;lt;0 3 10 9 14 7|]&lt;br /&gt;
EDOs: 15&lt;br /&gt;
Badness: 0.0327&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="Quindecic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Quindecic&lt;/h1&gt;
Commas: 28/27, 49/48, 55/54, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~13/8 = 852.924&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;15 24 35 42 52 0|, &amp;lt;0 0 0 0 0 1|]&lt;br /&gt;
EDOs: 15, 30, 45bc&lt;br /&gt;
Badness: 0.0289&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

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|]

Eigenmonzo subgroup: 2.7/5

9-limit eigenmonzo subgroup: 2.9/5

POTE generator: 742.002

Map: [<1 0 4 -2|, <0 1 -1 3|]

Wedgie: <<1 -1 3 -4 2 10||

EDOs: 5, 8d, 13cd, 21bcd

Badness: 0.0213

Uncle

Commas: 28/27, 256/245

7-limit eigenmonzo subgroup: 2.5/3

9-limit eigenmonzo subgroup: 2.9/5

Map: [<1 0 12 -2|, <0 1 -6 3|]

Wedgie: <<1 -6 3 -12 2 24||

EDOs: 13d, 18, 23bc, 41bcd

Badness: 0.0727

Octokaidecal

Commas: 28/27, 50/49

7-limit eigenmonzo subgroup: 2.5

9-limit eigenmonzo subgroup: 2.5

POTE generator: 728.874

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

Wedgie: <<2 6 6 5 4 -2||

EDOs: 10, 18, 28b

Badness: 0.0367

11-limit

Commas: 28/27, 50/49, 55/54

POTE generator: ~3/2 = 732.330

Map: [<2 0 -5 -4 7|, <0 1 3 3 0|]

EDOs: 10, 18e

Badness: 0.0302

Opossum

Commas: 28/27, 126/125

7-limit eigenmonzo subgroup: 2.7

9-limit eigenmonzo subgroup: 2.7

POTE generator: ~10/9 = 159.691

Map: [<1 2 3 4|, <0 -3 -5 -9|]

Wedgie: <<3 5 9 1 6 7||

EDOs: 7d, 8d, 15

Badness: 0.0407

11-limit

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

11-limit eigenmonzo subgroup: 2.7

POTE generator: ~10/9 = 159.807

Map: [<1 2 3 4 4|, <0 -3 -5 -9 -4|]

EDOs: 7d, 8d, 15

Badness: 0.0223

13-limit

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

13-limit eigenmonzo subgroup: 2.7

15-limit eigenmonzo subgroup: 2.7

POTE generator: ~10/9 = 158.805

Map: [<1 2 3 4 4 4|, <0 -3 -5 -9 -4 -2|]

EDOs: 7d, 8d, 15, 38bcef

Badness: 0.0194

Wallaby

Commas: 28/27, 35/32

POTE generator: ~3/2 = 691.351

Map: [<1 0 7 -2|, <0 1 -3 3|]

Wedgie: <<1 -3 3 -7 2 15||

EDOs: 2d, 5c, 19ccdd

Badness: 0.0585

Kangaroo

Comma: 64000/59049

POTE generator: ~27/20 = 561.195

Map: [<1 0 -3|, <0 3 10|]

EDOs: 15, 47b, 62b

Badness: 0.2958

7-limit

Commas: 28/27, 1029/1000

POTE generator: ~7/5 = 560.328

Map: [<1 0 -3 -2|, <0 3 10 9|]

Wedgie: <<3 10 9 9 6 -7||

EDOs: 15

Badness: 0.0779

11-limit

Commas: 28/27, 77/75, 245/242

POTE generator: ~7/5 = 560.155

Map: [<1 0 -3 -2 -4|, <0 3 10 9 14|]

EDOs: 15

Badness: 0.0432

13-limit

Commas: 28/27, 40/39, 77/75, 147/143

POTE generator: ~7/5 = 559.770

Map: [<1 0 -3 -2 -4 0|, <0 3 10 9 14 7|]

EDOs: 15

Badness: 0.0327

Quindecic

Commas: 28/27, 49/48, 55/54, 77/75

POTE generator: ~13/8 = 852.924

Map: [<15 24 35 42 52 0|, <0 0 0 0 0 1|]

EDOs: 15, 30, 45bc

Badness: 0.0289

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