Didymus rank-3 family: Difference between revisions

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~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~

These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

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

__FORCETOC__

~~: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-31 13:54:44 UTC</tt>.<br>~~

~~: The original revision id was <tt>288922277</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">These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

~~[[toc|flat]]~~

=Euterpe=

Commas: 81/80, 99/98

Minimax tuning

[|1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>,

|0 0 0 1 0>, |-1 0 -1/2 2 0>]

Eigenmonzos: 2, 5, 7

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

EDOs: 5, 12, 26, 31, 88

Badness: 0.000536

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Minimax tuning

[|1 0 0 0 0>, |1 0 0 0 1/6>, |0 0 0 0 2/3>,

|1 -1 0 1 1/6>, |0 0 0 0 1>]

Eigenmonzos: 2, 7/3, 11

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

EDOs: 7, 12, 19, 26, 45

Badness: 0.000530

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Map: [<1 0 -4 -13 0|, <0 1 4 10 0], <0 0 0 0 1|]

EDOs: 12, 19, 31, 81

Badness: 0.000558

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||1 0 0 0 0>, |1 0 1/4 0 0>, |0 0 1 0 0>,

|0 0 0 1 0>, |-4 0 2 1 0>]

Eigenmonzos: 2, 5, 7

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

EDOs: 7, 12, 24, 31, 105, 129

Badness: 0.000738

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Lattice basis: 11/9 length 0.2536 8/7 length 2.807

Angle(11/9, 8/7) = 90 degrees

Map to lattice: [<0 2 8 0 5|, <0 0 0 -1 0|]

Map: [<1 1 0 0 2|, <0 2 8 0 5|, <0 0 0 1 0|]

EDOs: 7, 14c, 24, 31, 100de, 131bde, 162bde

Badness: 0.000842

[[~~Spectrum of a temperament~~|Spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5

Scale: [[urania24]]

[[Spectrum_of_a_temperament|Spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5

Scale: [[urania24|urania24]]

=Terpsichore=

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

EDOs: 19, 31, 81, 112b

Badness: 0.000850

Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11~~</pre></div>~~

~~<h4>Original HTML content~~:~~</h4>~~

Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11

<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>Didymus rank three family</title></head><body>These are the rank three temperaments tempering out the didymus ~~comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.<br />~~

[[Category:didymus]]

~~<br />~~

[[Category:family]]

<a href="#Euterpe">Euterpe</a> | <a href="#Calliope">Calliope</a> | <a href="#Erato">Erato</a> | <a href="#Clio">Clio</a> | <a href="#Polyhymnia">Polyhymnia</a> | <a href="#Thalia">Thalia</a> | <a href="#Melpomene">Melpomene</a> | <a href="#Urania">Urania</a> | <a href="#Terpsichore">Terpsichore</a>

[[Category:rank_3]]

~~<br />~~

[[Category:theory]]

~~<h1 id="toc0"><a name="Euterpe"></a>Euterpe</h1>~~

~~Commas: 81/80, 99/98<br />~~

~~<br />~~

~~Minimax tuning<br />~~

~~[|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;, <br />~~

~~|0 0 0 1 0&gt;, |-1 0 -1/2 2 0&gt;~~]~~<br />~~

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

~~<br />~~

~~Map: [&lt;1 0 -4 0 1|, &lt;0 1 4 0 -2|, &lt;0 0 0 1 2|~~]~~<br />~~

~~EDOs: 5, 12, 26, 31, 88<br />~~

~~Badness: 0.000536<br />~~

~~<br />~~

~~<h1 id="toc1"><a name="Calliope"></a>Calliope</h1>~~

~~Commas: 81/80, 45/44<br />~~

~~<br />~~

~~Minimax tuning<br />~~

[~~|1 0 0 0 0&gt;, |1 0 0 0 1/6&gt;, |0 0 0 0 2/3&gt;, <br />~~

~~|1 -1 0 1 1/6&gt;, |0 0 0 0 1&gt;]<br />~~

~~Eigenmonzos: 2, 7/3, 11<br />~~

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 0 -6|, &lt;0 1 4 0 6|, &lt;0 0 0 1 0|]<br />~~

~~EDOs~~: ~~7, 12, 19, 26, 45<br />~~

~~Badness: 0.000530<br />~~

~~<br />~~

~~<h1 id="toc2"><a name="Erato"></a>Erato</h1>~~

~~Commas: 81/80, 126/125<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 -13 0|, &lt;0 1 4 10 0~~]~~, &lt;0 0 0 0 1|~~]~~<br />~~

~~EDOs~~: ~~12, 19, 31, 81<br />~~

~~Badness: 0.000558<br />~~

~~<br />~~

~~<h1 id="toc3"><a name="Clio"></a>Clio</h1>~~

~~Commas: 81/80, 176/175<br />~~

~~<br />~~

~~Minimax tuning<br />~~

~~||1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;, <br />~~

~~|0 0 0 1 0&gt;, |-4 0 2 1 0&gt;~~]~~<br />~~

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

~~<br />~~

~~Map:~~ [~~&lt;1 0 -4 0 -12|, &lt;0 1 4 0 8|, &lt;0 0 0 1 1|]<br />~~

~~EDOs: 7, 12, 24, 31, 105, 129<br />~~

~~Badness: 0.000738<br />~~

~~<br />~~

~~<h1 id="toc4"><a name="Polyhymnia"></a>Polyhymnia</h1>~~

~~Commas: 81/80, 385/384<br />~~

~~<br />~~

~~<h1 id="toc5"><a name="Thalia"></a>Thalia</h1>~~

~~Commas: 81/80, 55/54<br />~~

~~<br />~~

~~<h1 id="toc6"><a name="Melpomene"></a>Melpomene</h1>~~

~~Commas: 81/80, 56/55<br />~~

~~<br />~~

~~<h1 id="toc7"><a name="Urania"></a>Urania</h1>~~

~~Commas: 81/80, 121/120<br />~~

~~<br />~~

~~Lattice basis: 11/9 length 0.2536 8/7 length 2.807<br />~~

~~Angle(11/9, 8/7) = 90 degrees<br />~~

~~Map to lattice:~~ [~~&lt;0 2 8 0 5|, &lt;0 0 0 -1 0|]<br />~~

~~<br />~~

~~Map~~: ~~[&lt;1 1 0 0 2|, &lt;0 2 8 0 5|, &lt;0 0 0 1 0|~~]~~<br />~~

~~EDOs: 7, 14c, 24, 31, 100de, 131bde, 162bde<br />~~

~~Badness: 0.000842<br />~~

~~<a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5<br />~~

~~Scale: <a class="wiki_link" href="/urania24">urania24</a><br />~~

~~<br />~~

~~<h1 id="toc8"><a name="Terpsichore"></a>Terpsichore</h1>~~

~~Commas: 81/80, 540/539<br />~~

~~<br />~~

~~Map: [&lt;1 0 -4 0 -2|, &lt;0 1 4 0 7|, &lt;0 0 0 1 -2|~~]~~<br />~~

~~EDOs: 19, 31, 81, 112b<br />~~

~~Badness: 0.000850<br />~~

~~Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11</body></html></pre></div>~~

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+__FORCETOC__
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-31 13:54:44 UTC</tt>.<br>
-: The original revision id was <tt>288922277</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">These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.
-[[toc|flat]]
 =Euterpe=
 Commas: 81/80, 99/98
 Minimax tuning
 [|1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;,
 |0 0 0 1 0&gt;, |-1 0 -1/2 2 0&gt;]
 Eigenmonzos: 2, 5, 7
 Map: [&lt;1 0 -4 0 1|, &lt;0 1 4 0 -2|, &lt;0 0 0 1 2|]
 EDOs: 5, 12, 26, 31, 88
 Badness: 0.000536
@@ Line 26: / Line 21: @@
 Minimax tuning
 [|1 0 0 0 0&gt;, |1 0 0 0 1/6&gt;, |0 0 0 0 2/3&gt;,
 |1 -1 0 1 1/6&gt;, |0 0 0 0 1&gt;]
 Eigenmonzos: 2, 7/3, 11
 Map: [&lt;1 0 -4 0 -6|, &lt;0 1 4 0 6|, &lt;0 0 0 1 0|]
 EDOs: 7, 12, 19, 26, 45
 Badness: 0.000530
@@ Line 38: / Line 37: @@
 Map: [&lt;1 0 -4 -13 0|, &lt;0 1 4 10 0], &lt;0 0 0 0 1|]
 EDOs: 12, 19, 31, 81
 Badness: 0.000558
@@ Line 47: / Line 48: @@
 ||1 0 0 0 0&gt;, |1 0 1/4 0 0&gt;, |0 0 1 0 0&gt;,
 |0 0 0 1 0&gt;, |-4 0 2 1 0&gt;]
 Eigenmonzos: 2, 5, 7
 Map: [&lt;1 0 -4 0 -12|, &lt;0 1 4 0 8|, &lt;0 0 0 1 1|]
 EDOs: 7, 12, 24, 31, 105, 129
 Badness: 0.000738
@@ Line 66: / Line 70: @@
 Lattice basis: 11/9 length 0.2536 8/7 length 2.807
 Angle(11/9, 8/7) = 90 degrees
 Map to lattice: [&lt;0 2 8 0 5|, &lt;0 0 0 -1 0|]
 Map: [&lt;1 1 0 0 2|, &lt;0 2 8 0 5|, &lt;0 0 0 1 0|]
 EDOs: 7, 14c, 24, 31, 100de, 131bde, 162bde
 Badness: 0.000842
-[[Spectrum of a temperament|Spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5
-Scale: [[urania24]]
+[[Spectrum_of_a_temperament|Spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5
+Scale: [[urania24|urania24]]
 =Terpsichore=
@@ Line 79: / Line 89: @@
 Map: [&lt;1 0 -4 0 -2|, &lt;0 1 4 0 7|, &lt;0 0 0 1 -2|]
 EDOs: 19, 31, 81, 112b
 Badness: 0.000850
-Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11</pre></div>
-<h4>Original HTML content:</h4>
+Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11
-<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;Didymus rank three family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These are the rank three temperaments tempering out the didymus comma, 81/80. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.&lt;br /&gt;
+[[Category:didymus]]
-&lt;br /&gt;
+[[Category:family]]
-&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="#Euterpe"&gt;Euterpe&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt; | &lt;a href="#Calliope"&gt;Calliope&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt; | &lt;a href="#Erato"&gt;Erato&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt; | &lt;a href="#Clio"&gt;Clio&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt; | &lt;a href="#Polyhymnia"&gt;Polyhymnia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Thalia"&gt;Thalia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#Melpomene"&gt;Melpomene&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Urania"&gt;Urania&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt; | &lt;a href="#Terpsichore"&gt;Terpsichore&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;
+[[Category:rank_3]]
-&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;br /&gt;
+[[Category:theory]]
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Euterpe"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Euterpe&lt;/h1&gt;
-Commas: 81/80, 99/98&lt;br /&gt;
-&lt;br /&gt;
-Minimax tuning&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |1 0 1/4 0 0&amp;gt;, |0 0 1 0 0&amp;gt;, &lt;br /&gt;
-|0 0 0 1 0&amp;gt;, |-1 0 -1/2 2 0&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 5, 7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 0 1|, &amp;lt;0 1 4 0 -2|, &amp;lt;0 0 0 1 2|]&lt;br /&gt;
-EDOs: 5, 12, 26, 31, 88&lt;br /&gt;
-Badness: 0.000536&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="Calliope"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Calliope&lt;/h1&gt;
-Commas: 81/80, 45/44&lt;br /&gt;
-&lt;br /&gt;
-Minimax tuning&lt;br /&gt;
-[|1 0 0 0 0&amp;gt;, |1 0 0 0 1/6&amp;gt;, |0 0 0 0 2/3&amp;gt;, &lt;br /&gt;
-|1 -1 0 1 1/6&amp;gt;, |0 0 0 0 1&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 7/3, 11&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 0 -6|, &amp;lt;0 1 4 0 6|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
-EDOs: 7, 12, 19, 26, 45&lt;br /&gt;
-Badness: 0.000530&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="Erato"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Erato&lt;/h1&gt;
-Commas: 81/80, 126/125&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 -13 0|, &amp;lt;0 1 4 10 0], &amp;lt;0 0 0 0 1|]&lt;br /&gt;
-EDOs: 12, 19, 31, 81&lt;br /&gt;
-Badness: 0.000558&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="Clio"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Clio&lt;/h1&gt;
-Commas: 81/80, 176/175&lt;br /&gt;
-&lt;br /&gt;
-Minimax tuning&lt;br /&gt;
-||1 0 0 0 0&amp;gt;, |1 0 1/4 0 0&amp;gt;, |0 0 1 0 0&amp;gt;, &lt;br /&gt;
-|0 0 0 1 0&amp;gt;, |-4 0 2 1 0&amp;gt;]&lt;br /&gt;
-Eigenmonzos: 2, 5, 7&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 0 -12|, &amp;lt;0 1 4 0 8|, &amp;lt;0 0 0 1 1|]&lt;br /&gt;
-EDOs: 7, 12, 24, 31, 105, 129&lt;br /&gt;
-Badness: 0.000738&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="Polyhymnia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Polyhymnia&lt;/h1&gt;
-Commas: 81/80, 385/384&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="Thalia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Thalia&lt;/h1&gt;
-Commas: 81/80, 55/54&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Melpomene"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Melpomene&lt;/h1&gt;
-Commas: 81/80, 56/55&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="Urania"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Urania&lt;/h1&gt;
-Commas: 81/80, 121/120&lt;br /&gt;
-&lt;br /&gt;
-Lattice basis: 11/9 length 0.2536 8/7 length 2.807&lt;br /&gt;
-Angle(11/9, 8/7) = 90 degrees&lt;br /&gt;
-Map to lattice: [&amp;lt;0 2 8 0 5|, &amp;lt;0 0 0 -1 0|]&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 0 2|, &amp;lt;0 2 8 0 5|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
-EDOs: 7, 14c, 24, 31, 100de, 131bde, 162bde&lt;br /&gt;
-Badness: 0.000842&lt;br /&gt;
-&lt;a class="wiki_link" href="/Spectrum%20of%20a%20temperament"&gt;Spectrum&lt;/a&gt;: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5&lt;br /&gt;
-Scale: &lt;a class="wiki_link" href="/urania24"&gt;urania24&lt;/a&gt;&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="Terpsichore"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Terpsichore&lt;/h1&gt;
-Commas: 81/80, 540/539&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 0 -4 0 -2|, &amp;lt;0 1 4 0 7|, &amp;lt;0 0 0 1 -2|]&lt;br /&gt;
-EDOs: 19, 31, 81, 112b&lt;br /&gt;
-Badness: 0.000850&lt;br /&gt;
-Spectrum: 4/3, 10/9, 9/8, 6/5, 9/7, 7/5, 7/6, 5/4, 8/7, 11/9, 12/11, 11/8, 11/10, 14/11&lt;/body&gt;&lt;/html&gt;</pre></div>