Valinorsmic 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>2014-01-07 11:34:22 UTC</tt>.<br>
: The original revision id was <tt>481096984</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]]
 
 
The valinorsmic rank three temperaments temper out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)
The valinorsmic rank three temperaments temper out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)


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Map: [&lt;1 0 0 0 -4|, &lt;0 1 0 0 0|, &lt;0 0 1 0 2|, &lt;0 0 0 1 1|]
Map: [&lt;1 0 0 0 -4|, &lt;0 1 0 0 0|, &lt;0 0 1 0 2|, &lt;0 0 0 1 1|]
EDOs: 22, 31, 46, 53, 58, 80, 111
EDOs: 22, 31, 46, 53, 58, 80, 111


Line 21: Line 13:


Map: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
Map: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
EDOs: 15, 31, 46, 77, 80, 111
EDOs: 15, 31, 46, 77, 80, 111
Badness: 0.000679
Badness: 0.000679


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Map: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
Map: [&lt;1 0 0 12 8|, &lt;0 1 0 3 3|, &lt;0 0 1 -6 -4|]
EDOs: 31, 46, 77, 80, 111
EDOs: 31, 46, 77, 80, 111
Badness: 0.001147
Badness: 0.001147


Line 35: Line 31:


Map: [&lt;2 0 11 0 14|, &lt;0 1 -2 0 -4|, &lt;0 0 0 1 1|]
Map: [&lt;2 0 11 0 14|, &lt;0 1 -2 0 -4|, &lt;0 0 0 1 1|]
EDOs: 12, 22, 46, 58, 80, 126
EDOs: 12, 22, 46, 58, 80, 126
Badness: 0.000728
Badness: 0.000728


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Map: [&lt;2 0 11 0 14 24|, &lt;0 1 -2 0 -4 -7|, &lt;0 0 0 1 1 1|]
Map: [&lt;2 0 11 0 14 24|, &lt;0 1 -2 0 -4 -7|, &lt;0 0 0 1 1 1|]
EDOs: 22, 46, 58, 80, 138cde, 242cde, 322bcde
EDOs: 22, 46, 58, 80, 138cde, 242cde, 322bcde
Badness: 0.000970
Badness: 0.000970


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Map: [&lt;1 1 0 6 2|, &lt;0 2 0 5 5|, &lt;0 0 1 -2 0|]
Map: [&lt;1 1 0 6 2|, &lt;0 2 0 5 5|, &lt;0 0 1 -2 0|]
EDOs: 7, 24, 31, 58, 89
EDOs: 7, 24, 31, 58, 89
Badness: 0.000751
Badness: 0.000751


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Map: [&lt;1 1 0 6 2 4|, &lt;0 2 0 5 5 -1|, &lt;0 0 1 -2 0 0|]
Map: [&lt;1 1 0 6 2 4|, &lt;0 2 0 5 5 -1|, &lt;0 0 1 -2 0 0|]
EDOs: 7, 24, 31, 58
EDOs: 7, 24, 31, 58
Badness: 0.000923
Badness: 0.000923


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Map: [&lt;1 0 0 1, -3|, &lt;0 1 0 7 7|, &lt;0 0 1 -4 -2|]
Map: [&lt;1 0 0 1, -3|, &lt;0 1 0 7 7|, &lt;0 0 1 -4 -2|]
EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd
Badness: 0.00123
Badness: 0.00123


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Map: [&lt;1 0 0 1, -3 2|, &lt;0 1 0 7 7 4|, &lt;0 0 1 -4 -2 -2|]
Map: [&lt;1 0 0 1, -3 2|, &lt;0 1 0 7 7 4|, &lt;0 0 1 -4 -2 -2|]
EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf
Badness: 0.000932</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.000932
<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;Valinorismic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:18:&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:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;a href="#Rank four valinorsmic temperament"&gt;Rank four valinorsmic temperament&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Manwe"&gt;Manwe&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Varda"&gt;Varda&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Mandos"&gt;Mandos&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Ulmo"&gt;Ulmo&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
&lt;br /&gt;
The valinorsmic rank three temperaments temper out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)&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="Rank four valinorsmic temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Rank four valinorsmic temperament&lt;/h1&gt;
Comma: 176/175&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 0 -4|, &amp;lt;0 1 0 0 0|, &amp;lt;0 0 1 0 2|, &amp;lt;0 0 0 1 1|]&lt;br /&gt;
EDOs: 22, 31, 46, 53, 58, 80, 111&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="Manwe"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Manwe&lt;/h1&gt;
Commas: 176/175, 1331/1323&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 12 8|, &amp;lt;0 1 0 3 3|, &amp;lt;0 0 1 -6 -4|]&lt;br /&gt;
EDOs: 15, 31, 46, 77, 80, 111&lt;br /&gt;
Badness: 0.000679&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="Manwe-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
Commas: 176/175, 1331/1323, 351/350&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 12 8|, &amp;lt;0 1 0 3 3|, &amp;lt;0 0 1 -6 -4|]&lt;br /&gt;
EDOs: 31, 46, 77, 80, 111&lt;br /&gt;
Badness: 0.001147&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Varda"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Varda&lt;/h1&gt;
Commas: 176/175, 896/891&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 11 0 14|, &amp;lt;0 1 -2 0 -4|, &amp;lt;0 0 0 1 1|]&lt;br /&gt;
EDOs: 12, 22, 46, 58, 80, 126&lt;br /&gt;
Badness: 0.000728&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Varda-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Commas: 176/175, 352/351, 364/363&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 0 11 0 14 24|, &amp;lt;0 1 -2 0 -4 -7|, &amp;lt;0 0 0 1 1 1|]&lt;br /&gt;
EDOs: 22, 46, 58, 80, 138cde, 242cde, 322bcde&lt;br /&gt;
Badness: 0.000970&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Mandos"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Mandos&lt;/h1&gt;
Commas: 176/175, 243/242&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 6 2|, &amp;lt;0 2 0 5 5|, &amp;lt;0 0 1 -2 0|]&lt;br /&gt;
EDOs: 7, 24, 31, 58, 89&lt;br /&gt;
Badness: 0.000751&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="Mandos-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 144/143, 176/175, 243/242&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 6 2 4|, &amp;lt;0 2 0 5 5 -1|, &amp;lt;0 0 1 -2 0 0|]&lt;br /&gt;
EDOs: 7, 24, 31, 58&lt;br /&gt;
Badness: 0.000923&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="Ulmo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Ulmo&lt;/h1&gt;
Commas: 176/175, 2200/2187&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 1, -3|, &amp;lt;0 1 0 7 7|, &amp;lt;0 0 1 -4 -2|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd&lt;br /&gt;
Badness: 0.00123&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Ulmo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 176/175, 325/324&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 1, -3 2|, &amp;lt;0 1 0 7 7 4|, &amp;lt;0 0 1 -4 -2 -2|]&lt;br /&gt;
EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf&lt;br /&gt;
Badness: 0.000932&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The valinorsmic rank three temperaments temper out the valinorsma, 176/175, which equates 48/35 with 15/11 (rather than 11/8, which is what the keenanisma 385/384 does.)

Rank four valinorsmic temperament

Comma: 176/175

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

EDOs: 22, 31, 46, 53, 58, 80, 111

Manwe

Commas: 176/175, 1331/1323

Map: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]

EDOs: 15, 31, 46, 77, 80, 111

Badness: 0.000679

13-limit

Commas: 176/175, 1331/1323, 351/350

Map: [<1 0 0 12 8|, <0 1 0 3 3|, <0 0 1 -6 -4|]

EDOs: 31, 46, 77, 80, 111

Badness: 0.001147

Varda

Commas: 176/175, 896/891

Map: [<2 0 11 0 14|, <0 1 -2 0 -4|, <0 0 0 1 1|]

EDOs: 12, 22, 46, 58, 80, 126

Badness: 0.000728

13-limit

Commas: 176/175, 352/351, 364/363

Map: [<2 0 11 0 14 24|, <0 1 -2 0 -4 -7|, <0 0 0 1 1 1|]

EDOs: 22, 46, 58, 80, 138cde, 242cde, 322bcde

Badness: 0.000970

Mandos

Commas: 176/175, 243/242

Map: [<1 1 0 6 2|, <0 2 0 5 5|, <0 0 1 -2 0|]

EDOs: 7, 24, 31, 58, 89

Badness: 0.000751

13-limit

Commas: 144/143, 176/175, 243/242

Map: [<1 1 0 6 2 4|, <0 2 0 5 5 -1|, <0 0 1 -2 0 0|]

EDOs: 7, 24, 31, 58

Badness: 0.000923

Ulmo

Commas: 176/175, 2200/2187

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

EDOs: 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd

Badness: 0.00123

13-limit

Commas: 169/168, 176/175, 325/324

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

EDOs: 7, 39, 46, 53, 80, 133d, 179, 312cdf

Badness: 0.000932

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