Orwellismic family: 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>
The orwellismic family of [[rank_three_temperaments|rank three temperaments]] tempers out the orwellisma, 1728/1715.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-10 17:24:25 UTC</tt>.<br>
: The original revision id was <tt>319229134</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]]


The orwellismic family of [[rank three temperaments]] tempers out the orwellisma, 1728/1715.
[[Comma|Comma]]: 1728/1715


[[Comma]]: 1728/1715
[[7-limit|7-]] and [[9-limit|9-limit]] [[minimax|minimax]]


[[7-limit|7-]] and [[9-limit]] [[minimax]]
[&lt;1 0 0 0|, &lt;0 1 0 0|, &lt;3/2 3/4 3/4 -3/4|,  
[&lt;1 0 0 0|, &lt;0 1 0 0|, &lt;3/2 3/4 3/4 -3/4|,  
&lt;3/2 3/4 -1/4 1/4|]
&lt;3/2 3/4 -1/4 1/4|]
[[Eigenmonzo]]s: 2, 4/3, 7/5
 
[[Eigenmonzo|Eigenmonzo]]s: 2, 4/3, 7/5


Lattice basis: 7/6 0.7526 3/2 1.3931
Lattice basis: 7/6 0.7526 3/2 1.3931
Angle(7/6, 3/2) = 97.5081
Angle(7/6, 3/2) = 97.5081
Map to lattice: [&lt;0 0 -3 1|, &lt;0 1 0 1|]
Map to lattice: [&lt;0 0 -3 1|, &lt;0 1 0 1|]


[[Map]]: [&lt;1 0 0 2|, &lt;0 1 0 1|, &lt;0 0 3 -1|]
[[Map|Map]]: [&lt;1 0 0 2|, &lt;0 1 0 1|, &lt;0 0 3 -1|]
[[Generator]]s: 2, 3, 12/7
 
[[generator|Generator]]s: 2, 3, 12/7
 
Edos: [[9edo|9]], [[14edo|14]], [[17edo|17]], [[18edo|18]], [[22edo|22]], [[26edo|26]], [[27edo|27]], [[31edo|31]], [[49edo|49]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[84edo|84]], [[111edo|111]], [[142edo|142]], [[164edo|164d]], [[306edo|306d]], [[417edo|417cd]]
Edos: [[9edo|9]], [[14edo|14]], [[17edo|17]], [[18edo|18]], [[22edo|22]], [[26edo|26]], [[27edo|27]], [[31edo|31]], [[49edo|49]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[84edo|84]], [[111edo|111]], [[142edo|142]], [[164edo|164d]], [[306edo|306d]], [[417edo|417cd]]
[[Badness]]: 0.000187


[[Projection pair]]: 5 1728/343 to 2.3.7
[[Badness|Badness]]: 0.000187
 
[[Projection_pair|Projection pair]]: 5 1728/343 to 2.3.7


[[Scale]]s: [[orwellismic9]]
[[scale|Scale]]s: [[Orwellismic9|orwellismic9]]


=Orwellian=
=Orwellian=
Line 34: Line 34:


Map: [&lt;1 0 0 2 5|, &lt;0 1 0 1 0| &lt;0 0 3 -1 -2|]
Map: [&lt;1 0 0 2 5|, &lt;0 1 0 1 0| &lt;0 0 3 -1 -2|]
EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee
EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee
Badness: 0.000715
Badness: 0.000715


=Guanyin=
=Guanyin=
[[Comma]]s: 176/175, 540/539
[[Comma|Comma]]s: 176/175, 540/539
 
[[11-limit|11-limit]] [[minimax|minimax]]


[[11-limit]] [[minimax]]
[&lt;1 0 0 0 0|, &lt;-2/9 0 -5/9 5/9 4/9|, &lt;4/3 0 1/3 -1/3 1/3|,  
[&lt;1 0 0 0 0|, &lt;-2/9 0 -5/9 5/9 4/9|, &lt;4/3 0 1/3 -1/3 1/3|,  
&lt;4/3 0 -2/3 2/3 1/3|, &lt;0 0 0 0 1|]
&lt;4/3 0 -2/3 2/3 1/3|, &lt;0 0 0 0 1|]
[[Eigenmonzo]]s: 2, 11/8, 7/5
 
[[Eigenmonzo|Eigenmonzo]]s: 2, 11/8, 7/5


Lattice basis: 7/6 0.5167 3/2 1.3055
Lattice basis: 7/6 0.5167 3/2 1.3055
Angle(7/6, 3/2) = 79.0940
Angle(7/6, 3/2) = 79.0940
Map to lattice: [&lt;0 0 -3 1 -5|, &lt;0 1 0 1 1|]
Map to lattice: [&lt;0 0 -3 1 -5|, &lt;0 1 0 1 1|]


[[Map]]: [&lt;1 0 0 2 -2|, &lt;0 1 0 1 1|, &lt;0 0 3 -1 5|]
[[Map|Map]]: [&lt;1 0 0 2 -2|, &lt;0 1 0 1 1|, &lt;0 0 3 -1 5|]
[[Generator]]s: 2, 3, 12/7
 
[[generator|Generator]]s: 2, 3, 12/7
 
EDOs: [[9edo|9]], [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cd]], [[391edo|391cd]]
EDOs: [[9edo|9]], [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cd]], [[391edo|391cd]]
[[Badness]]: 0.000411


[[Projection pair]]s: 5 1728/343 11 186624/16807 to 2.3.7
[[Badness|Badness]]: 0.000411
 
[[Projection_pair|Projection pair]]s: 5 1728/343 11 186624/16807 to 2.3.7
 
[[scale|Scale]]s: [[guanyin22|guanyin22]]


[[Scale]]s: [[guanyin22]]
Music:  
Music:  
[[http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297|Trio for SoftSaturn, NebulaSing and TromBonehead]]  [[http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3|play]] by [[Gene Ward Smith]]


==[[13-limit]]==
[http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297 Trio for SoftSaturn, NebulaSing and TromBonehead]  [http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]
[[Comma]]s: 176/175, 351/350, 540/539
 
==[[13-limit|13-limit]]==
[[Comma|Comma]]s: 176/175, 351/350, 540/539
 
[[Map|Map]]: [&lt;1 0 0 2 -2 3|, &lt;0 1 0 1 1 -2|, &lt;0 0 3 -1 5 5|]


[[Map]]: [&lt;1 0 0 2 -2 3|, &lt;0 1 0 1 1 -2|, &lt;0 0 3 -1 5 5|]
EDOs: [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cdf]], [[391edo|391cdf]]
EDOs: [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cdf]], [[391edo|391cdf]]
[[Badness]]: 0.000758
 
[[Badness|Badness]]: 0.000758


Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7
Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7


==Georgian==
==Georgian==
[[Comma]]s: 144/143, 176/175, 196/195
[[Comma|Comma]]s: 144/143, 176/175, 196/195
 
[[Map|Map]]: [&lt;1 0 0 2 -2 6|, &lt;0 1 0 1 1 1|, &lt;0 0 3 -1 5 -5|]


[[Map]]: [&lt;1 0 0 2 -2 6|, &lt;0 1 0 1 1 1|, &lt;0 0 3 -1 5 -5|]
EDOs: [[9edo|9]], [[31edo|31]], [[46edo|46f]], [[48edo|48c]], [[58edo|58]]
EDOs: [[9edo|9]], [[31edo|31]], [[46edo|46f]], [[48edo|48c]], [[58edo|58]]
[[Badness]]: 0.000904
 
[[Badness|Badness]]: 0.000904


Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7
Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7
 
[[Category:family]]
</pre></div>
[[Category:guanyin]]
<h4>Original HTML content:</h4>
[[Category:listen]]
<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;Orwellismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Orwellian"&gt;Orwellian&lt;/a&gt;&lt;/div&gt;
[[Category:orwell]]
&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Guanyin"&gt;Guanyin&lt;/a&gt;&lt;/div&gt;
[[Category:orwellismic]]
&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Guanyin-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Guanyin-Georgian"&gt;Georgian&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
The orwellismic family of &lt;a class="wiki_link" href="/rank%20three%20temperaments"&gt;rank three temperaments&lt;/a&gt; tempers out the orwellisma, 1728/1715.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;: 1728/1715&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/7-limit"&gt;7-&lt;/a&gt; and &lt;a class="wiki_link" href="/9-limit"&gt;9-limit&lt;/a&gt; &lt;a class="wiki_link" href="/minimax"&gt;minimax&lt;/a&gt;&lt;br /&gt;
[&amp;lt;1 0 0 0|, &amp;lt;0 1 0 0|, &amp;lt;3/2 3/4 3/4 -3/4|, &lt;br /&gt;
&amp;lt;3/2 3/4 -1/4 1/4|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 4/3, 7/5&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 7/6 0.7526 3/2 1.3931&lt;br /&gt;
Angle(7/6, 3/2) = 97.5081&lt;br /&gt;
Map to lattice: [&amp;lt;0 0 -3 1|, &amp;lt;0 1 0 1|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 0 2|, &amp;lt;0 1 0 1|, &amp;lt;0 0 3 -1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 3, 12/7&lt;br /&gt;
Edos: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/14edo"&gt;14&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/49edo"&gt;49&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, &lt;a class="wiki_link" href="/84edo"&gt;84&lt;/a&gt;, &lt;a class="wiki_link" href="/111edo"&gt;111&lt;/a&gt;, &lt;a class="wiki_link" href="/142edo"&gt;142&lt;/a&gt;, &lt;a class="wiki_link" href="/164edo"&gt;164d&lt;/a&gt;, &lt;a class="wiki_link" href="/306edo"&gt;306d&lt;/a&gt;, &lt;a class="wiki_link" href="/417edo"&gt;417cd&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.000187&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;: 5 1728/343 to 2.3.7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Scale"&gt;Scale&lt;/a&gt;s: &lt;a class="wiki_link" href="/orwellismic9"&gt;orwellismic9&lt;/a&gt;&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="Orwellian"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Orwellian&lt;/h1&gt;
Commas: 99/98, 385/384&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 0 2 5|, &amp;lt;0 1 0 1 0| &amp;lt;0 0 3 -1 -2|]&lt;br /&gt;
EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee&lt;br /&gt;
Badness: 0.000715&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="Guanyin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Guanyin&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 176/175, 540/539&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; &lt;a class="wiki_link" href="/minimax"&gt;minimax&lt;/a&gt;&lt;br /&gt;
[&amp;lt;1 0 0 0 0|, &amp;lt;-2/9 0 -5/9 5/9 4/9|, &amp;lt;4/3 0 1/3 -1/3 1/3|, &lt;br /&gt;
&amp;lt;4/3 0 -2/3 2/3 1/3|, &amp;lt;0 0 0 0 1|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Eigenmonzo"&gt;Eigenmonzo&lt;/a&gt;s: 2, 11/8, 7/5&lt;br /&gt;
&lt;br /&gt;
Lattice basis: 7/6 0.5167 3/2 1.3055&lt;br /&gt;
Angle(7/6, 3/2) = 79.0940&lt;br /&gt;
Map to lattice: [&amp;lt;0 0 -3 1 -5|, &amp;lt;0 1 0 1 1|]&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 0 2 -2|, &amp;lt;0 1 0 1 1|, &amp;lt;0 0 3 -1 5|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 3, 12/7&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, &lt;a class="wiki_link" href="/111edo"&gt;111&lt;/a&gt;, &lt;a class="wiki_link" href="/280edo"&gt;280cd&lt;/a&gt;, &lt;a class="wiki_link" href="/391edo"&gt;391cd&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.000411&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Projection%20pair"&gt;Projection pair&lt;/a&gt;s: 5 1728/343 11 186624/16807 to 2.3.7&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Scale"&gt;Scale&lt;/a&gt;s: &lt;a class="wiki_link" href="/guanyin22"&gt;guanyin22&lt;/a&gt;&lt;br /&gt;
Music: &lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297" rel="nofollow"&gt;Trio for SoftSaturn, NebulaSing and TromBonehead&lt;/a&gt;  &lt;a class="wiki_link_ext" href="http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&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="Guanyin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 176/175, 351/350, 540/539&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 0 2 -2 3|, &amp;lt;0 1 0 1 1 -2|, &amp;lt;0 0 3 -1 5 5|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/80edo"&gt;80&lt;/a&gt;, &lt;a class="wiki_link" href="/111edo"&gt;111&lt;/a&gt;, &lt;a class="wiki_link" href="/280edo"&gt;280cdf&lt;/a&gt;, &lt;a class="wiki_link" href="/391edo"&gt;391cdf&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.000758&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7&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="Guanyin-Georgian"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Georgian&lt;/h2&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 144/143, 176/175, 196/195&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 0 0 2 -2 6|, &amp;lt;0 1 0 1 1 1|, &amp;lt;0 0 3 -1 5 -5|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/46edo"&gt;46f&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48c&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.000904&lt;br /&gt;
&lt;br /&gt;
Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 00:00, 17 July 2018

The orwellismic family of rank three temperaments tempers out the orwellisma, 1728/1715.

Comma: 1728/1715

7- and 9-limit minimax

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

<3/2 3/4 -1/4 1/4|]

Eigenmonzos: 2, 4/3, 7/5

Lattice basis: 7/6 0.7526 3/2 1.3931

Angle(7/6, 3/2) = 97.5081

Map to lattice: [<0 0 -3 1|, <0 1 0 1|]

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

Generators: 2, 3, 12/7

Edos: 9, 14, 17, 18, 22, 26, 27, 31, 49, 53, 58, 80, 84, 111, 142, 164d, 306d, 417cd

Badness: 0.000187

Projection pair: 5 1728/343 to 2.3.7

Scales: orwellismic9

Orwellian

Commas: 99/98, 385/384

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

EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee

Badness: 0.000715

Guanyin

Commas: 176/175, 540/539

11-limit minimax

[<1 0 0 0 0|, <-2/9 0 -5/9 5/9 4/9|, <4/3 0 1/3 -1/3 1/3|,

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

Eigenmonzos: 2, 11/8, 7/5

Lattice basis: 7/6 0.5167 3/2 1.3055

Angle(7/6, 3/2) = 79.0940

Map to lattice: [<0 0 -3 1 -5|, <0 1 0 1 1|]

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

Generators: 2, 3, 12/7

EDOs: 9, 22, 31, 53, 58, 80, 111, 280cd, 391cd

Badness: 0.000411

Projection pairs: 5 1728/343 11 186624/16807 to 2.3.7

Scales: guanyin22

Music:

Trio for SoftSaturn, NebulaSing and TromBonehead play by Gene Ward Smith

13-limit

Commas: 176/175, 351/350, 540/539

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

EDOs: 22, 31, 53, 58, 80, 111, 280cdf, 391cdf

Badness: 0.000758

Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7

Georgian

Commas: 144/143, 176/175, 196/195

Map: [<1 0 0 2 -2 6|, <0 1 0 1 1 1|, <0 0 3 -1 5 -5|]

EDOs: 9, 31, 46f, 48c, 58

Badness: 0.000904

Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7

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