|
|
| Line 1: |
Line 1: |
| <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]]
| |
| [<1 0 0 0|, <0 1 0 0|, <3/2 3/4 3/4 -3/4|, | | [<1 0 0 0|, <0 1 0 0|, <3/2 3/4 3/4 -3/4|, |
| | |
| <3/2 3/4 -1/4 1/4|] | | <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: [<0 0 -3 1|, <0 1 0 1|] | | Map to lattice: [<0 0 -3 1|, <0 1 0 1|] |
|
| |
|
| [[Map]]: [<1 0 0 2|, <0 1 0 1|, <0 0 3 -1|] | | [[Map|Map]]: [<1 0 0 2|, <0 1 0 1|, <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: [<1 0 0 2 5|, <0 1 0 1 0| <0 0 3 -1 -2|] | | 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 | | 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]]
| |
| [<1 0 0 0 0|, <-2/9 0 -5/9 5/9 4/9|, <4/3 0 1/3 -1/3 1/3|, | | [<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|] | | <4/3 0 -2/3 2/3 1/3|, <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: [<0 0 -3 1 -5|, <0 1 0 1 1|] | | 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|] | | [[Map|Map]]: [<1 0 0 2 -2|, <0 1 0 1 1|, <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]]: [<1 0 0 2 -2 3|, <0 1 0 1 1 -2|, <0 0 3 -1 5 5|] |
|
| |
|
| [[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]] | | 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]]: [<1 0 0 2 -2 6|, <0 1 0 1 1 1|, <0 0 3 -1 5 -5|] |
|
| |
|
| [[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]] | | 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"><html><head><title>Orwellismic family</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><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>
| | [[Category:orwell]] |
| <!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --><div style="margin-left: 1em;"><a href="#Guanyin">Guanyin</a></div>
| | [[Category:orwellismic]] |
| <!-- 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 />
| |
| [&lt;1 0 0 0|, &lt;0 1 0 0|, &lt;3/2 3/4 3/4 -3/4|, <br />
| |
| &lt;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: [&lt;0 0 -3 1|, &lt;0 1 0 1|]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 0 2|, &lt;0 1 0 1|, &lt;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:&lt;h1&gt; --><h1 id="toc0"><a name="Orwellian"></a><!-- ws:end:WikiTextHeadingRule:0 -->Orwellian</h1>
| |
| Commas: 99/98, 385/384<br />
| |
| <br />
| |
| Map: [&lt;1 0 0 2 5|, &lt;0 1 0 1 0| &lt;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:&lt;h1&gt; --><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 />
| |
| [&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|, <br />
| |
| &lt;4/3 0 -2/3 2/3 1/3|, &lt;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: [&lt;0 0 -3 1 -5|, &lt;0 1 0 1 1|]<br />
| |
| <br />
| |
| <a class="wiki_link" href="/Map">Map</a>: [&lt;1 0 0 2 -2|, &lt;0 1 0 1 1|, &lt;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:&lt;h2&gt; --><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>: [&lt;1 0 0 2 -2 3|, &lt;0 1 0 1 1 -2|, &lt;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:&lt;h2&gt; --><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>: [&lt;1 0 0 2 -2 6|, &lt;0 1 0 1 1 1|, &lt;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></pre></div>
| |
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
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