Chromatic pairs: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 218475982 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 218485022 - 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>2011-04-08 10:43:21 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-08 11:07:24 UTC</tt>.<br>
: The original revision id was <tt>218475982</tt>.<br>
: The original revision id was <tt>218485022</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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[[roulette13|Thirteen note chromatic scale]]
[[roulette13|Thirteen note chromatic scale]]
[[roulette19|Nineteen note mega chromatic scale]]
[[roulette19|Nineteen note mega chromatic scale]]
=Garibaldi=
Group: 2.3.5.7
Commas: 225/224, 3125/3087
Val name: 12&amp;29
POTE generator: ~3/2 = 702.085
Map: [&lt;1 0 15 25|, &lt;0 1 -8 -14|]
EDOs: 7, 12, 17, 29, 41, 53, 94
Error: 2.834
[[garibaldi12|Twelve note albitonic scale]]
[[garibaldi17|Seventeen note chromatic scale]]


=Baldy=
=Baldy=
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[[silver10|Ten note albitonic scale]]
[[silver10|Ten note albitonic scale]]
[[silver17|Seventeen note chromatic scale]]
[[silver17|Seventeen note chromatic scale]]
=Meantone=
Group: 2.3.5.7
Commas: 81/80, 126/125
Val name: 12&amp;19
POTE generator: 696.495
Map: [&lt;1 0 -4 -13|, &lt;0 1 4 10|]
EDOs: 5, 7, 12, 19, 31, 81, 112, 143
Error: 3.585
[[meantone5|Five note haplotonic scale]]
[[meantone7|Seven note albitonic scale]]
[[meantone12|Twelve note chromatic scale]]


=Indium=
=Indium=
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Group: 2.3.5.7.11
Group: 2.3.5.7.11
Commas: 100/99, 225/224, 245/243
Commas: 100/99, 225/224, 245/243
Val name: 19&amp;22


POTE generator: ~5/4 = 380.696
POTE generator: ~5/4 = 380.696
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Error: 5.584
Error: 5.584


[[orwell9|nine note albitonic scale]]
[[orwell9|Nine note albitonic scale]]
[[orwell13|Thirteen note chromatic scale]]
[[orwell13|Thirteen note chromatic scale]]


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</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Chromatic pairs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:58:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;a href="#Terrain"&gt;Terrain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt; | &lt;a href="#Bridgetown"&gt;Bridgetown&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Cata"&gt;Cata&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Tridec"&gt;Tridec&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt; | &lt;a href="#Pepperoni"&gt;Pepperoni&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Nestoria"&gt;Nestoria&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Huntington"&gt;Huntington&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Roulette"&gt;Roulette&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Baldy"&gt;Baldy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt; | &lt;a href="#Bossier"&gt;Bossier&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Radon"&gt;Radon&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Silver"&gt;Silver&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Indium"&gt;Indium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Magic"&gt;Magic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt; | &lt;a href="#Hemif"&gt;Hemif&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt; | &lt;a href="#Skwares"&gt;Skwares&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Greeley"&gt;Greeley&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Semidim"&gt;Semidim&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt; | &lt;a href="#Orwell"&gt;Orwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#Mohaha"&gt;Mohaha&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt; | &lt;a href="#Tutone"&gt;Tutone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt; | &lt;a href="#Score"&gt;Score&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt; | &lt;a href="#Supra"&gt;Supra&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt; | &lt;a href="#Augment"&gt;Augment&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;
<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;Chromatic pairs&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:62:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;a href="#Terrain"&gt;Terrain&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt; | &lt;a href="#Bridgetown"&gt;Bridgetown&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Cata"&gt;Cata&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Tridec"&gt;Tridec&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Pepperoni"&gt;Pepperoni&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Nestoria"&gt;Nestoria&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt; | &lt;a href="#Huntington"&gt;Huntington&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Roulette"&gt;Roulette&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Baldy"&gt;Baldy&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt; | &lt;a href="#Bossier"&gt;Bossier&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt; | &lt;a href="#Radon"&gt;Radon&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Silver"&gt;Silver&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Meantone"&gt;Meantone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt; | &lt;a href="#Indium"&gt;Indium&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt; | &lt;a href="#Magic"&gt;Magic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt; | &lt;a href="#Hemif"&gt;Hemif&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&gt; | &lt;a href="#Skwares"&gt;Skwares&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt; | &lt;a href="#Greeley"&gt;Greeley&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt; | &lt;a href="#Semidim"&gt;Semidim&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt; | &lt;a href="#Orwell"&gt;Orwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&gt; | &lt;a href="#Mohaha"&gt;Mohaha&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:85 --&gt;&lt;!-- ws:start:WikiTextTocRule:86: --&gt;&lt;!-- ws:end:WikiTextTocRule:86 --&gt;&lt;!-- ws:start:WikiTextTocRule:87: --&gt; | &lt;a href="#Tutone"&gt;Tutone&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt; | &lt;a href="#Score"&gt;Score&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt; | &lt;a href="#Supra"&gt;Supra&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;&lt;!-- ws:end:WikiTextTocRule:91 --&gt;&lt;!-- ws:start:WikiTextTocRule:92: --&gt;&lt;!-- ws:end:WikiTextTocRule:92 --&gt;&lt;!-- ws:start:WikiTextTocRule:93: --&gt; | &lt;a href="#Augment"&gt;Augment&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:93 --&gt;&lt;!-- ws:start:WikiTextTocRule:94: --&gt;
&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:94 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of MOS in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with &lt;a class="wiki_link" href="/Target%20tunings"&gt;tuning target&lt;/a&gt; the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.&lt;br /&gt;
By a &lt;em&gt;chromatic pair&lt;/em&gt; is meant a pair of MOS in some rank two temperament (which may often be a &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup temperament&lt;/a&gt;) in which the smaller of the pair is analogous to Meantone[7], the diatonic scale, and the larger to Meantone[12], the chromatic scale. Because on a standard keyboard the smaller scale is given by the white keys, the smaller scale of the pair is called &amp;quot;albitonic&amp;quot; from the Latin word for &amp;quot;white&amp;quot;. Also included at times are &amp;quot;haplotonic&amp;quot; scales, which are the analogs of Meantone[5]. The pair temperaments are listed in order of increasing unweighted rms error with &lt;a class="wiki_link" href="/Target%20tunings"&gt;tuning target&lt;/a&gt; the ratios between subgroup generators; this gives a measure more reflective of the errors than Tenney-Euclidean error will give.&lt;br /&gt;
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&lt;a class="wiki_link" href="/roulette19"&gt;Nineteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/roulette19"&gt;Nineteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Baldy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Baldy&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Garibaldi"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Garibaldi&lt;/h1&gt;
Group: 2.3.5.7&lt;br /&gt;
Commas: 225/224, 3125/3087&lt;br /&gt;
Val name: 12&amp;amp;29&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 702.085&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 15 25|, &amp;lt;0 1 -8 -14|]&lt;br /&gt;
EDOs: 7, 12, 17, 29, 41, 53, 94&lt;br /&gt;
Error: 2.834&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/garibaldi12"&gt;Twelve note albitonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/garibaldi17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Baldy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Baldy&lt;/h1&gt;
Subgroup: 2.9.5.7.13&lt;br /&gt;
Subgroup: 2.9.5.7.13&lt;br /&gt;
Commas: 225/224, 325/324, 640/637&lt;br /&gt;
Commas: 225/224, 325/324, 640/637&lt;br /&gt;
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&lt;a class="wiki_link" href="/baldy17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/baldy17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Bossier"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Bossier&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Bossier"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Bossier&lt;/h1&gt;
Subgroup: 2.7.11.13&lt;br /&gt;
Subgroup: 2.7.11.13&lt;br /&gt;
Commas: 1573/1569, 15488/15379&lt;br /&gt;
Commas: 1573/1569, 15488/15379&lt;br /&gt;
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&lt;a class="wiki_link" href="/bossier14"&gt;Fourteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/bossier14"&gt;Fourteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Radon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Radon&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Radon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Radon&lt;/h1&gt;
Subgroup: 2.3.7.11&lt;br /&gt;
Subgroup: 2.3.7.11&lt;br /&gt;
Commas: 896/891, 1029/1024&lt;br /&gt;
Commas: 896/891, 1029/1024&lt;br /&gt;
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&lt;a class="wiki_link" href="/radon16"&gt;Sixteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/radon16"&gt;Sixteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Silver"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Silver&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Silver"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Silver&lt;/h1&gt;
Subgroup: 2.5.7.13.17&lt;br /&gt;
Subgroup: 2.5.7.13.17&lt;br /&gt;
Commas: 170/169, 640/637, 5525/5488&lt;br /&gt;
Commas: 170/169, 640/637, 5525/5488&lt;br /&gt;
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&lt;a class="wiki_link" href="/silver17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/silver17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Indium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Indium&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Meantone&lt;/h1&gt;
Group: 2.3.5.7&lt;br /&gt;
Commas: 81/80, 126/125&lt;br /&gt;
Val name: 12&amp;amp;19&lt;br /&gt;
&lt;br /&gt;
POTE generator: 696.495&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 -4 -13|, &amp;lt;0 1 4 10|]&lt;br /&gt;
EDOs: 5, 7, 12, 19, 31, 81, 112, 143&lt;br /&gt;
Error: 3.585&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/meantone5"&gt;Five note haplotonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/meantone7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/meantone12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Indium"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Indium&lt;/h1&gt;
Subgroup: 2.5/3.7/3.11/3&lt;br /&gt;
Subgroup: 2.5/3.7/3.11/3&lt;br /&gt;
Commas: 3025/3024, 3125/3087&lt;br /&gt;
Commas: 3025/3024, 3125/3087&lt;br /&gt;
Line 657: Line 716:
&lt;a class="wiki_link" href="/indium17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/indium17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc14"&gt;&lt;a name="Magic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Magic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Magic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Magic&lt;/h1&gt;
Group: 2.3.5.7.11&lt;br /&gt;
Group: 2.3.5.7.11&lt;br /&gt;
Commas: 100/99, 225/224, 245/243&lt;br /&gt;
Commas: 100/99, 225/224, 245/243&lt;br /&gt;
Val name: 19&amp;amp;22&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 380.696&lt;br /&gt;
POTE generator: ~5/4 = 380.696&lt;br /&gt;
Line 672: Line 732:
&lt;a class="wiki_link" href="/magic16"&gt;Sixteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/magic16"&gt;Sixteen note mega chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Hemif"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Hemif&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Hemif"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Hemif&lt;/h1&gt;
Subgroup: 2.3.7.11.13&lt;br /&gt;
Subgroup: 2.3.7.11.13&lt;br /&gt;
Commas: 144/143, 243/242, 364/363&lt;br /&gt;
Commas: 144/143, 243/242, 364/363&lt;br /&gt;
Line 687: Line 747:
&lt;a class="wiki_link" href="/hemif17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/hemif17"&gt;Seventeen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Skwares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Skwares&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Skwares"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Skwares&lt;/h1&gt;
Subgroup: 2.3.7.11&lt;br /&gt;
Subgroup: 2.3.7.11&lt;br /&gt;
Commas: 99/98, 243/242&lt;br /&gt;
Commas: 99/98, 243/242&lt;br /&gt;
Line 702: Line 762:
&lt;a class="wiki_link" href="/skwares14"&gt;Fourteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/skwares14"&gt;Fourteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc17"&gt;&lt;a name="Greeley"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Greeley&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Greeley"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Greeley&lt;/h1&gt;
Subgroup: 2.5/3.7/3.11/3&lt;br /&gt;
Subgroup: 2.5/3.7/3.11/3&lt;br /&gt;
Commas: 121/120, 126/125&lt;br /&gt;
Commas: 121/120, 126/125&lt;br /&gt;
Line 715: Line 775:
&lt;a class="wiki_link" href="/greeley15"&gt;Fifteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/greeley15"&gt;Fifteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Semidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Semidim&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Semidim"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Semidim&lt;/h1&gt;
Subgroup: 2.5/3.7/3.11/3.13/3&lt;br /&gt;
Subgroup: 2.5/3.7/3.11/3.13/3&lt;br /&gt;
Commas: 121/120, 169/168, 275/273&lt;br /&gt;
Commas: 121/120, 169/168, 275/273&lt;br /&gt;
Line 729: Line 789:
&lt;a class="wiki_link" href="/semidim13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/semidim13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Orwell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Orwell&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Orwell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Orwell&lt;/h1&gt;
Group: 2.3.5.7.11&lt;br /&gt;
Group: 2.3.5.7.11&lt;br /&gt;
Commas: 99/98, 121/120, 176/175&lt;br /&gt;
Commas: 99/98, 121/120, 176/175&lt;br /&gt;
Line 740: Line 800:
Error: 5.584&lt;br /&gt;
Error: 5.584&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/orwell9"&gt;nine note albitonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/orwell9"&gt;Nine note albitonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/orwell13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/orwell13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc20"&gt;&lt;a name="Mohaha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Mohaha&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Mohaha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Mohaha&lt;/h1&gt;
Subgroup: 2.3.5.11&lt;br /&gt;
Subgroup: 2.3.5.11&lt;br /&gt;
Commas: 81/80, 121/120&lt;br /&gt;
Commas: 81/80, 121/120&lt;br /&gt;
Line 757: Line 817:
&lt;a class="wiki_link" href="/mohaha10"&gt;Ten note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/mohaha10"&gt;Ten note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Mohaha-Mohoho"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Mohoho&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Mohaha-Mohoho"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Mohoho&lt;/h2&gt;
Subgroup: 2.3.5.11.13&lt;br /&gt;
Subgroup: 2.3.5.11.13&lt;br /&gt;
Commas: 66/65, 81/80, 121/120&lt;br /&gt;
Commas: 66/65, 81/80, 121/120&lt;br /&gt;
Line 767: Line 827:
Error: 9.556 cents&lt;br /&gt;
Error: 9.556 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Tutone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Tutone&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Tutone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Tutone&lt;/h1&gt;
Subgroup: 2.9.5.7.11&lt;br /&gt;
Subgroup: 2.9.5.7.11&lt;br /&gt;
Commas: 81/80, 99/98, 126/125&lt;br /&gt;
Commas: 81/80, 99/98, 126/125&lt;br /&gt;
Line 782: Line 842:
&lt;a class="wiki_link" href="/tutone13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/tutone13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Tutone-Leantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Leantone&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Tutone-Leantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Leantone&lt;/h2&gt;
Subgroup: 2.9.5.7.11&lt;br /&gt;
Subgroup: 2.9.5.7.11&lt;br /&gt;
Commas: 45/44, 56/55, 81/80&lt;br /&gt;
Commas: 45/44, 56/55, 81/80&lt;br /&gt;
Line 797: Line 857:
&lt;a class="wiki_link" href="/leantone13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/leantone13"&gt;Thirteen note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc24"&gt;&lt;a name="Score"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Score&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Score"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Score&lt;/h1&gt;
Subgroup: 2.7.11.13&lt;br /&gt;
Subgroup: 2.7.11.13&lt;br /&gt;
Commas: 343/338, 847/832&lt;br /&gt;
Commas: 343/338, 847/832&lt;br /&gt;
Line 812: Line 872:
&lt;a class="wiki_link" href="/score11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/score11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc25"&gt;&lt;a name="Supra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Supra&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Supra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Supra&lt;/h1&gt;
Subgroup: 2.3.7.11&lt;br /&gt;
Subgroup: 2.3.7.11&lt;br /&gt;
Commas: 64/63, 99/98&lt;br /&gt;
Commas: 64/63, 99/98&lt;br /&gt;
Line 826: Line 886:
&lt;a class="wiki_link" href="/supra12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/supra12"&gt;Twelve note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Supra-Supraphon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Supraphon&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Supra-Supraphon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Supraphon&lt;/h2&gt;
Subgroup: 2.3.7.11.13&lt;br /&gt;
Subgroup: 2.3.7.11.13&lt;br /&gt;
Commas: 64/63, 78/77, 99/98&lt;br /&gt;
Commas: 64/63, 78/77, 99/98&lt;br /&gt;
Line 836: Line 896:
Error: 10.534 cents&lt;br /&gt;
Error: 10.534 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Supra-Machine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Machine&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Supra-Machine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Machine&lt;/h2&gt;
Subgroup: 2.9.7.11&lt;br /&gt;
Subgroup: 2.9.7.11&lt;br /&gt;
Commas: 64/63, 99/98&lt;br /&gt;
Commas: 64/63, 99/98&lt;br /&gt;
Line 850: Line 910:
&lt;a class="wiki_link" href="/machine11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/machine11"&gt;Eleven note chromatic scale&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc28"&gt;&lt;a name="Augment"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Augment&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Augment"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Augment&lt;/h1&gt;
Subgroup: 2.5.7.11&lt;br /&gt;
Subgroup: 2.5.7.11&lt;br /&gt;
Commas: 56/55, 128/125&lt;br /&gt;
Commas: 56/55, 128/125&lt;br /&gt;