Subgroup temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 376169174 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 376252188 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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>2012-10-24 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-10-24 23:37:50 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>376252188</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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[[Lp tuning#L2 tuning|L2 error]]: 2.457 cents | [[Lp tuning#L2 tuning|L2 error]]: 2.457 cents | ||
==Hemif== | ==Hemif (11 limit)== | ||
Commas: 243/242, 896/891 | Commas: 243/242, 896/891 | ||
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=2.3.7.11.13= | =2.3.7.11.13= | ||
==Hemif (13 limit)== | |||
Subgroup: 2.3.7.11.13 | |||
Commas: 144/143, 243/242, 364/363 | |||
Related temperament: [[xenharmonic/Breedsmic temperaments|Hemififths]], namo | |||
[[Tp tuning|POT2 generator]]: ~11/9 = 351.691 | |||
[[Gencom]]: [2 11/9; 144/143 243/242 364/363] | |||
Gencom map: [<1 1 0 -1 2 4|, <0 2 0 13 5 -1|] | |||
Map: [<1 1 -1 2 4|, <0 2 13 5 -1|] | |||
EDOs: 7, 10, 17, 24, 41, 58 | |||
[[Tp tuning#T2 tuning|T2 error]]: 1.756 cents | |||
==Parapyth (Rank 3)== | ==Parapyth (Rank 3)== | ||
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[[Lp tuning#L2 tuning|L2 error]]: 1.317</pre></div> | [[Lp tuning#L2 tuning|L2 error]]: 1.317</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Subgroup temperaments</title></head><body><!-- ws:start:WikiTextTocRule:70:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#x2.3.11">2.3.11</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --> | <a href="#x2.3.7.11.13">2.3.7.11.13</a><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --> | <a href="#x2.5.7.11">2.5.7.11</a><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --> | <a href="#x2.9.15.7.11.13">2.9.15.7.11.13</a><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --> | <a href="#x2.9.21">2.9.21</a><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --> | <a href="#x2.3.7/5.11/5.13/5">2.3.7/5.11/5.13/5</a><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --> | <a href="#x2.3.7.11/5.13">2.3.7.11/5.13</a><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:106 --><br /> | ||
Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on <a class="wiki_link" href="/Chromatic%20pairs">Chromatic pairs</a>.<br /> | Below are some subgroups and temperaments for them. Obviously, no attempt has been made at completeness; attention is focused on subgroups containing interesting chords. The reader may also want to consult the page on <a class="wiki_link" href="/Chromatic%20pairs">Chromatic pairs</a>.<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.457 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.457 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x2.3.7.11-Hemif"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemif</h2> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="x2.3.7.11-Hemif (11 limit)"></a><!-- ws:end:WikiTextHeadingRule:28 -->Hemif (11 limit)</h2> | ||
Commas: 243/242, 896/891<br /> | Commas: 243/242, 896/891<br /> | ||
<br /> | <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="x2.3.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:30 -->2.3.7.11.13</h1> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="x2.3.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:30 -->2.3.7.11.13</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x2.3.7.11.13-Parapyth (Rank 3)"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="x2.3.7.11.13-Hemif (13 limit)"></a><!-- ws:end:WikiTextHeadingRule:32 -->Hemif (13 limit)</h2> | ||
Subgroup: 2.3.7.11.13<br /> | |||
Commas: 144/143, 243/242, 364/363<br /> | |||
Related temperament: <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Breedsmic%20temperaments">Hemififths</a>, namo<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Tp%20tuning">POT2 generator</a>: ~11/9 = 351.691<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Gencom">Gencom</a>: [2 11/9; 144/143 243/242 364/363]<br /> | |||
Gencom map: [&lt;1 1 0 -1 2 4|, &lt;0 2 0 13 5 -1|]<br /> | |||
<br /> | |||
Map: [&lt;1 1 -1 2 4|, &lt;0 2 13 5 -1|]<br /> | |||
EDOs: 7, 10, 17, 24, 41, 58<br /> | |||
<a class="wiki_link" href="/Tp%20tuning#T2 tuning">T2 error</a>: 1.756 cents<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="x2.3.7.11.13-Parapyth (Rank 3)"></a><!-- ws:end:WikiTextHeadingRule:34 -->Parapyth (Rank 3)</h2> | |||
Commas: 352/351, 364/363<br /> | Commas: 352/351, 364/363<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.928 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.928 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="x2.3.7.11.13-Leapfrog"></a><!-- ws:end:WikiTextHeadingRule:36 -->Leapfrog</h2> | ||
Commas: 169/168, 352/351, 364/363<br /> | Commas: 169/168, 352/351, 364/363<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.847 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.847 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h1&gt; --><h1 id="toc19"><a name="x2.5.7.11"></a><!-- ws:end:WikiTextHeadingRule:38 -->2.5.7.11</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h2&gt; --><h2 id="toc20"><a name="x2.5.7.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:40 -->Larry</h2> | ||
Commas: 243/242, 4000/3993<br /> | Commas: 243/242, 4000/3993<br /> | ||
Related temperaments: <a class="wiki_link" href="/Gravity%20family#Gravity">gravity</a>, <a class="wiki_link" href="/Gravity%20family#Harry">harry</a><br /> | Related temperaments: <a class="wiki_link" href="/Gravity%20family#Gravity">gravity</a>, <a class="wiki_link" href="/Gravity%20family#Harry">harry</a><br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6765 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6765 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:42 -->2.9.7.11</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:44 -->Machine</h2> | ||
Commas: 64/63, 99/98<br /> | Commas: 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.421 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 4.421 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:46 -->Apparatus</h2> | ||
Commas: 41503/41472, 322102/321489<br /> | Commas: 41503/41472, 322102/321489<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.1505 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.1505 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h2&gt; --><h2 id="toc24"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:48 -->Mechanism</h2> | ||
Commas: 896/891, 26411/26244<br /> | Commas: 896/891, 26411/26244<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9531 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.9531 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h1&gt; --><h1 id="toc25"><a name="x2.9.15.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:50 -->2.9.15.7.11.13</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h2&gt; --><h2 id="toc26"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)"></a><!-- ws:end:WikiTextHeadingRule:52 -->Stacks (aka 2magic)</h2> | ||
Commas: 100/99, 105/104, 144/143, 196/195<br /> | Commas: 100/99, 105/104, 144/143, 196/195<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.772 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 3.772 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:54:&lt;h3&gt; --><h3 id="toc27"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"></a><!-- ws:end:WikiTextHeadingRule:54 -->2.9.15.7.11 stacks</h3> | ||
Commas: 100/99, 225/224, 245/243<br /> | Commas: 100/99, 225/224, 245/243<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.741 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.741 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h3&gt; --><h3 id="toc28"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7 stacks"></a><!-- ws:end:WikiTextHeadingRule:56 -->2.9.15.7 stacks</h3> | ||
Commas: 225/224, 245/243<br /> | Commas: 225/224, 245/243<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.149 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 2.149 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h1&gt; --><h1 id="toc29"><a name="x2.9.21"></a><!-- ws:end:WikiTextHeadingRule:58 -->2.9.21</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:60:&lt;h2&gt; --><h2 id="toc30"><a name="x2.9.21-A-team"></a><!-- ws:end:WikiTextHeadingRule:60 -->A-team</h2> | ||
Commas: 1029/1024<br /> | Commas: 1029/1024<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6403<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6403<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h1&gt; --><h1 id="toc31"><a name="x2.3.7/5.11/5.13/5"></a><!-- ws:end:WikiTextHeadingRule:62 -->2.3.7/5.11/5.13/5</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:64:&lt;h2&gt; --><h2 id="toc32"><a name="x2.3.7/5.11/5.13/5-Historical"></a><!-- ws:end:WikiTextHeadingRule:64 -->Historical</h2> | ||
Subgroup: 2.3.7/5.11/5.13/5<br /> | Subgroup: 2.3.7/5.11/5.13/5<br /> | ||
Commas: 364/363, 441/440, 1001/1000<br /> | Commas: 364/363, 441/440, 1001/1000<br /> | ||
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<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6274 cents<br /> | <a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 0.6274 cents<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:66:&lt;h1&gt; --><h1 id="toc33"><a name="x2.3.7.11/5.13"></a><!-- ws:end:WikiTextHeadingRule:66 -->2.3.7.11/5.13</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:68:&lt;h2&gt; --><h2 id="toc34"><a name="x2.3.7.11/5.13-Hypnosis"></a><!-- ws:end:WikiTextHeadingRule:68 -->Hypnosis</h2> | ||
<br /> | <br /> | ||
Subgroup: 2.3.7.11/5.13<br /> | Subgroup: 2.3.7.11/5.13<br /> | ||