Orwellismic family
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[[toc]] The orwellismic family of [[rank three temperaments]] tempers out the orwellisma, 1728/1715. [[Comma]]: 1728/1715 [[7-limit|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|] [[Eigenmonzo]]s: 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|] [[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]] [[Badness]]: 0.000187 [[Projection pair]]: 5 1728/343 to 2.3.7 [[Scale]]s: [[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= [[Comma]]s: 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|] [[Eigenmonzo]]s: 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|] [[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]] [[Badness]]: 0.000411 [[Projection pair]]s: 5 1728/343 11 186624/16807 to 2.3.7 [[Scale]]s: [[guanyin22]] 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]]== [[Comma]]s: 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: [[22edo|22]], [[31edo|31]], [[53edo|53]], [[58edo|58]], [[80edo|80]], [[111edo|111]], [[280edo|280cdf]], [[391edo|391cdf]] [[Badness]]: 0.000758 Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7 ==Georgian== [[Comma]]s: 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: [[9edo|9]], [[31edo|31]], [[46edo|46f]], [[48edo|48c]], [[58edo|58]] [[Badness]]: 0.000904 Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7
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<html><head><title>Orwellismic family</title></head><body><!-- ws:start:WikiTextTocRule:8:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><div style="margin-left: 1em;"><a href="#Orwellian">Orwellian</a></div> <!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --><div style="margin-left: 1em;"><a href="#Guanyin">Guanyin</a></div> <!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><div style="margin-left: 2em;"><a href="#Guanyin-13-limit">13-limit</a></div> <!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><div style="margin-left: 2em;"><a href="#Guanyin-Georgian">Georgian</a></div> <!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --></div> <!-- ws:end:WikiTextTocRule:13 --><br /> The orwellismic family of <a class="wiki_link" href="/rank%20three%20temperaments">rank three temperaments</a> tempers out the orwellisma, 1728/1715.<br /> <br /> <a class="wiki_link" href="/Comma">Comma</a>: 1728/1715<br /> <br /> <a class="wiki_link" href="/7-limit">7-</a> and <a class="wiki_link" href="/9-limit">9-limit</a> <a class="wiki_link" href="/minimax">minimax</a><br /> [<1 0 0 0|, <0 1 0 0|, <3/2 3/4 3/4 -3/4|, <br /> <3/2 3/4 -1/4 1/4|]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 4/3, 7/5<br /> <br /> Lattice basis: 7/6 0.7526 3/2 1.3931<br /> Angle(7/6, 3/2) = 97.5081<br /> Map to lattice: [<0 0 -3 1|, <0 1 0 1|]<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 0 0 2|, <0 1 0 1|, <0 0 3 -1|]<br /> <a class="wiki_link" href="/Generator">Generator</a>s: 2, 3, 12/7<br /> Edos: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/14edo">14</a>, <a class="wiki_link" href="/17edo">17</a>, <a class="wiki_link" href="/18edo">18</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/26edo">26</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/80edo">80</a>, <a class="wiki_link" href="/84edo">84</a>, <a class="wiki_link" href="/111edo">111</a>, <a class="wiki_link" href="/142edo">142</a>, <a class="wiki_link" href="/164edo">164d</a>, <a class="wiki_link" href="/306edo">306d</a>, <a class="wiki_link" href="/417edo">417cd</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.000187<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>: 5 1728/343 to 2.3.7<br /> <br /> <a class="wiki_link" href="/Scale">Scale</a>s: <a class="wiki_link" href="/orwellismic9">orwellismic9</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Orwellian"></a><!-- ws:end:WikiTextHeadingRule:0 -->Orwellian</h1> Commas: 99/98, 385/384<br /> <br /> Map: [<1 0 0 2 5|, <0 1 0 1 0| <0 0 3 -1 -2|]<br /> EDOs: 22, 31, 53, 84e, 163e, 194e, 247cde, 278bdee<br /> Badness: 0.000715<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Guanyin"></a><!-- ws:end:WikiTextHeadingRule:2 -->Guanyin</h1> <a class="wiki_link" href="/Comma">Comma</a>s: 176/175, 540/539<br /> <br /> <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/minimax">minimax</a><br /> [<1 0 0 0 0|, <-2/9 0 -5/9 5/9 4/9|, <4/3 0 1/3 -1/3 1/3|, <br /> <4/3 0 -2/3 2/3 1/3|, <0 0 0 0 1|]<br /> <a class="wiki_link" href="/Eigenmonzo">Eigenmonzo</a>s: 2, 11/8, 7/5<br /> <br /> Lattice basis: 7/6 0.5167 3/2 1.3055<br /> Angle(7/6, 3/2) = 79.0940<br /> Map to lattice: [<0 0 -3 1 -5|, <0 1 0 1 1|]<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 0 0 2 -2|, <0 1 0 1 1|, <0 0 3 -1 5|]<br /> <a class="wiki_link" href="/Generator">Generator</a>s: 2, 3, 12/7<br /> EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/80edo">80</a>, <a class="wiki_link" href="/111edo">111</a>, <a class="wiki_link" href="/280edo">280cd</a>, <a class="wiki_link" href="/391edo">391cd</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.000411<br /> <br /> <a class="wiki_link" href="/Projection%20pair">Projection pair</a>s: 5 1728/343 11 186624/16807 to 2.3.7<br /> <br /> <a class="wiki_link" href="/Scale">Scale</a>s: <a class="wiki_link" href="/guanyin22">guanyin22</a><br /> Music: <br /> <a class="wiki_link_ext" href="http://www.archive.org/details/TrioForSoftsaturnNebulasingAndTrombonehead_297" rel="nofollow">Trio for SoftSaturn, NebulaSing and TromBonehead</a> <a class="wiki_link_ext" href="http://www.archive.org/download/TrioForSoftsaturnNebulasingAndTrombonehead_297/trio-gorts.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Gene%20Ward%20Smith">Gene Ward Smith</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Guanyin-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 --><a class="wiki_link" href="/13-limit">13-limit</a></h2> <a class="wiki_link" href="/Comma">Comma</a>s: 176/175, 351/350, 540/539<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 0 0 2 -2 3|, <0 1 0 1 1 -2|, <0 0 3 -1 5 5|]<br /> EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/53edo">53</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/80edo">80</a>, <a class="wiki_link" href="/111edo">111</a>, <a class="wiki_link" href="/280edo">280cdf</a>, <a class="wiki_link" href="/391edo">391cdf</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.000758<br /> <br /> Projection pairs: 5 1728/343 11 186624/16807 221184/16897 to 2.3.7<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Guanyin-Georgian"></a><!-- ws:end:WikiTextHeadingRule:6 -->Georgian</h2> <a class="wiki_link" href="/Comma">Comma</a>s: 144/143, 176/175, 196/195<br /> <br /> <a class="wiki_link" href="/Map">Map</a>: [<1 0 0 2 -2 6|, <0 1 0 1 1 1|, <0 0 3 -1 5 -5|]<br /> EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/31edo">31</a>, <a class="wiki_link" href="/46edo">46f</a>, <a class="wiki_link" href="/48edo">48c</a>, <a class="wiki_link" href="/58edo">58</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.000904<br /> <br /> Projection pairs: 5 1728/343 11 186624/16807 16807/1296 to 2.3.7</body></html>