Subgroup temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 376098326 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 376169174 - 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 17:38:07 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>376169174</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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EDOs: 17, 41, 46, 58, 87, 104 | EDOs: 17, 41, 46, 58, 87, 104 | ||
[[Lp tuning#L2 tuning|L2 error]]: 0.928 cents | [[Lp tuning#L2 tuning|L2 error]]: 0.928 cents | ||
==Leapfrog== | |||
Commas: 169/168, 352/351, 364/363 | |||
[[Lp tuning|POL2 generator]]: ~3/2 = 704.745 cents | |||
Gencom: [2 3/2; 169/169 352/351 364/363] | |||
Gencom mapping: [<1 1 0 -6 -3 -1|, <0 1 0 15 11 8|] | |||
Sval map: [<1 0 -21 -14 -9|, <0 1 15 11 8|] | |||
EDOs: 17, 46, 63 | |||
[[Lp tuning#L2 tuning|L2 error]]: 1.847 cents | |||
=2.5.7.11= | =2.5.7.11= | ||
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Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|] | Sval map: [<1 0 -3 8 0|, <0 3 11 -13 7|] | ||
EDOs: 17, 36, 118e, 125e, 161e, 197e | EDOs: 17, 36, 118e, 125e, 161e, 197e | ||
[[Lp tuning#L2 tuning|L2 error]]: 1.317 | [[Lp tuning#L2 tuning|L2 error]]: 1.317</pre></div> | ||
</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:68:&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:68 --><!-- ws:start:WikiTextTocRule:69: --><a href="#x2.3.7">2.3.7</a><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#x2.3.11">2.3.11</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --> | <a href="#x2.3.5.11">2.3.5.11</a><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#x2.3.7.11">2.3.7.11</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#x2.3.7.11.13">2.3.7.11.13</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#x2.5.7.11">2.5.7.11</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --><!-- ws:end:WikiTextTocRule:88 --><!-- ws:start:WikiTextTocRule:89: --> | <a href="#x2.9.7.11">2.9.7.11</a><!-- ws:end:WikiTextTocRule:89 --><!-- ws:start:WikiTextTocRule:90: --><!-- ws:end:WikiTextTocRule:90 --><!-- ws:start:WikiTextTocRule:91: --><!-- ws:end:WikiTextTocRule:91 --><!-- ws:start:WikiTextTocRule:92: --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --> | <a href="#x2.9.15.7.11.13">2.9.15.7.11.13</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --> | <a href="#x2.9.21">2.9.21</a><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --> | <a href="#x2.3.7/5.11/5.13/5">2.3.7/5.11/5.13/5</a><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --> | <a href="#x2.3.7.11/5.13">2.3.7.11/5.13</a><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --> | ||
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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 /> | ||
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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:34:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="x2.3.7.11.13-Leapfrog"></a><!-- ws:end:WikiTextHeadingRule:34 -->Leapfrog</h2> | ||
Commas: 169/168, 352/351, 364/363<br /> | |||
<br /> | |||
<a class="wiki_link" href="/Lp%20tuning">POL2 generator</a>: ~3/2 = 704.745 cents<br /> | |||
<br /> | |||
Gencom: [2 3/2; 169/169 352/351 364/363]<br /> | |||
Gencom mapping: [&lt;1 1 0 -6 -3 -1|, &lt;0 1 0 15 11 8|]<br /> | |||
<br /> | |||
Sval map: [&lt;1 0 -21 -14 -9|, &lt;0 1 15 11 8|]<br /> | |||
EDOs: 17, 46, 63<br /> | |||
<a class="wiki_link" href="/Lp%20tuning#L2 tuning">L2 error</a>: 1.847 cents<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h1&gt; --><h1 id="toc18"><a name="x2.5.7.11"></a><!-- ws:end:WikiTextHeadingRule:36 -->2.5.7.11</h1> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="x2.5.7.11-Larry"></a><!-- ws:end:WikiTextHeadingRule:38 -->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:40:&lt;h1&gt; --><h1 id="toc20"><a name="x2.9.7.11"></a><!-- ws:end:WikiTextHeadingRule:40 -->2.9.7.11</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="x2.9.7.11-Machine"></a><!-- ws:end:WikiTextHeadingRule:42 -->Machine</h2> | ||
Commas: 64/63, 99/98<br /> | Commas: 64/63, 99/98<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:44:&lt;h2&gt; --><h2 id="toc22"><a name="x2.9.7.11-Apparatus"></a><!-- ws:end:WikiTextHeadingRule:44 -->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:46:&lt;h2&gt; --><h2 id="toc23"><a name="x2.9.7.11-Mechanism"></a><!-- ws:end:WikiTextHeadingRule:46 -->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:48:&lt;h1&gt; --><h1 id="toc24"><a name="x2.9.15.7.11.13"></a><!-- ws:end:WikiTextHeadingRule:48 -->2.9.15.7.11.13</h1> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:50:&lt;h2&gt; --><h2 id="toc25"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)"></a><!-- ws:end:WikiTextHeadingRule:50 -->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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:52:&lt;h3&gt; --><h3 id="toc26"><a name="x2.9.15.7.11.13-Stacks (aka 2magic)-2.9.15.7.11 stacks"></a><!-- ws:end:WikiTextHeadingRule:52 -->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 /> | ||
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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 /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="x2.9.21"></a><!-- ws:end:WikiTextHeadingRule:56 -->2.9.21</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:58:&lt;h2&gt; --><h2 id="toc29"><a name="x2.9.21-A-team"></a><!-- ws:end:WikiTextHeadingRule:58 -->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:60:&lt;h1&gt; --><h1 id="toc30"><a name="x2.3.7/5.11/5.13/5"></a><!-- ws:end:WikiTextHeadingRule:60 -->2.3.7/5.11/5.13/5</h1> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:62:&lt;h2&gt; --><h2 id="toc31"><a name="x2.3.7/5.11/5.13/5-Historical"></a><!-- ws:end:WikiTextHeadingRule:62 -->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:64:&lt;h1&gt; --><h1 id="toc32"><a name="x2.3.7.11/5.13"></a><!-- ws:end:WikiTextHeadingRule:64 -->2.3.7.11/5.13</h1> | ||
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Subgroup: 2.3.7.11/5.13<br /> | Subgroup: 2.3.7.11/5.13<br /> | ||