Meantone family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>

: This revision was by author [[User:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-03-~~09 16~~:40:29 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 15:36:12 UTC</tt>.<br>

: The original revision id was <tt>~~208972928~~</tt>.<br>

: The original revision id was <tt>209716986</tt>.<br>

: The revision comment was: <tt>~~some links added~~</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>

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The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1>, |-13 10 0 -1>], flattone, with normal list [|-4 4 -1>, |-17 9 0 1>], dominant, with normal list [|-4 4 -1>, |6 -2 0 -1>], sharptone, with normal list [|-4 4 -1>, |2 -3 0 1>], injera, with normal list [|-4 4 -1>, |-7 8 0 -2>], mohajira, with normal list [|-4 4 -1>, |-23 11 0 2>], godzilla, with normal list [|-4 4 -1>, |-4 -1 0 2>], mothra, with normal list [|-4 4 -1>, |-10 1 0 3>], squares, with normal list [|-4 4 -1>, |-3 9 0 -4>], and liese, with normal list [|-4 4 -1>, |-9 11 0 -3>].

==Septimal meantone==

=Septimal meantone=

The comma |-13 10 0 -1> for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The [[Wedgies and Multivals|wedgie]] for septimal meantone is <<1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and [[31edo]] is a good tuning for it.

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[[Badness]]: 0.0212

==Flattone==

=Flattone=

[[Comma]]s: 81/80, 525/512

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[[Badness]]: 0.0386

==Dominant==

=Dominant=

[[Comma]]s: 36/35, 64/63

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[[Badness]]: 0.0207

==Sharptone==

=Sharptone=

[[Comma]]s: 21/20, 28/27

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[[Badness]]: 0.0248

==Injera==

=Injera=

[[Comma]]s: 50/49, 81/80

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[[Badness]]: 0.0311

==Godzilla==

=Godzilla=

[[Comma]]s: 49/48, 81/80

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Music: Igliashon Jones, [[http://tinyurl.com/4uyumk9|"Change is on the Wind"]], in Godzilla[9]

==Mohajira==

=Mohajira=

[[Comma]]s: 81/80, 6144/6125

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[[Badness]]: 0.0557

===11-limit===

==11-limit==

[[Comma]]s: 81/80, 121/120, 176/175

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[[Badness]]: 0.0261

==Mothra==

=Mothra=

Commas: 81/80, 1029/1024

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[[Badness]]: 0.0371

===11-limit===

==11-limit==

[[Comma]]s: 81/80, 99/98, 385/384

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[[Badness[[: 0.0256

==Squares==

=Squares=

[[Comma]]s: 81/80, 2401/2400

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http://tinyurl.com/24cbxse

===11-limit===

==11-limit==

[[Comma]]s: 81/80, 385/384, 1375/1372

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[[Badness]]: 0.0568

==Liese==

=Liese=

[[Comma]]s: 81/80, 686/675

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The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&gt;, |-13 10 0 -1&gt;], flattone, with normal list [|-4 4 -1&gt;, |-17 9 0 1&gt;], dominant, with normal list [|-4 4 -1&gt;, |6 -2 0 -1&gt;], sharptone, with normal list [|-4 4 -1&gt;, |2 -3 0 1&gt;], injera, with normal list [|-4 4 -1&gt;, |-7 8 0 -2&gt;], mohajira, with normal list [|-4 4 -1&gt;, |-23 11 0 2&gt;], godzilla, with normal list [|-4 4 -1&gt;, |-4 -1 0 2&gt;], mothra, with normal list [|-4 4 -1&gt;, |-10 1 0 3&gt;], squares, with normal list [|-4 4 -1&gt;, |-3 9 0 -4&gt;], and liese, with normal list [|-4 4 -1&gt;, |-9 11 0 -3&gt;].<br />

<br />

<h2 id="toc1"><a name="x-Septimal meantone"></a>Septimal meantone</h2>

<h1 id="toc1"><a name="Septimal meantone"></a>Septimal meantone</h1>

The comma |-13 10 0 -1&gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The <a class="wiki_link" href="/Wedgies%20and%20Multivals">wedgie</a> for septimal meantone is &lt;&lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and <a class="wiki_link" href="/31edo">31edo</a> is a good tuning for it.<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0137<br />

<br />

<h2 id="toc2"><a name="x-Unidecimal meantone aka Huygens"></a>Unidecimal meantone aka Huygens</h2>

<h2 id="toc2"><a name="Septimal meantone-Unidecimal meantone aka Huygens"></a>Unidecimal meantone aka Huygens</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125, 99/98<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0170<br />

<br />

<h3 id="toc3"><a name="x-Unidecimal meantone aka Huygens-Tridecimal meantone"></a>Tridecimal meantone</h3>

<h3 id="toc3"><a name="Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone"></a>Tridecimal meantone</h3>

<a class="wiki_link" href="/Comma">Comma</a>s: 66/65, 81/80, 99/98, 105/104<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0180<br />

<br />

<h2 id="toc4"><a name="x-Meanpop"></a>Meanpop</h2>

<h2 id="toc4"><a name="Septimal meantone-Meanpop"></a>Meanpop</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 126/125, 385/384<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0215<br />

<br />

<h3 id="toc5"><a name="x-Meanpop-13-limit Meanpop"></a>13-limit Meanpop</h3>

<h3 id="toc5"><a name="Septimal meantone-Meanpop-13-limit Meanpop"></a>13-limit Meanpop</h3>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 105/104, 144/143, 196/195<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0209<br />

<br />

<h2 id="toc6"><a name="x-Meanenneadecal"></a>Meanenneadecal</h2>

<h2 id="toc6"><a name="Septimal meantone-Meanenneadecal"></a>Meanenneadecal</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 81/80<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0214<br />

<br />

<h3 id="toc7"><a name="x-Meanenneadecal-13-limit"></a>13-limit</h3>

<h3 id="toc7"><a name="Septimal meantone-Meanenneadecal-13-limit"></a>13-limit</h3>

<a class="wiki_link" href="/Comma">Comma</a>s: 45/44, 56/55, 78/77, 81/80<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0212<br />

<br />

<h2 id="toc8"><a name="x-Flattone"></a>Flattone</h2>

<h1 id="toc8"><a name="Flattone"></a>Flattone</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 525/512<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0386<br />

<br />

<h2 id="toc9"><a name="x-Dominant"></a>Dominant</h2>

<h1 id="toc9"><a name="Dominant"></a>Dominant</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 64/63<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0207<br />

<br />

<h2 id="toc10"><a name="x-Sharptone"></a>Sharptone</h2>

<h1 id="toc10"><a name="Sharptone"></a>Sharptone</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 21/20, 28/27<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0248<br />

<br />

<h2 id="toc11"><a name="x-Injera"></a>Injera</h2>

<h1 id="toc11"><a name="Injera"></a>Injera</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 50/49, 81/80<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0311<br />

<br />

<h2 id="toc12"><a name="x-Godzilla"></a>Godzilla</h2>

<h1 id="toc12"><a name="Godzilla"></a>Godzilla</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 49/48, 81/80<br />

<br />

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<br />

Music: Igliashon Jones, <a class="wiki_link_ext" href="http://tinyurl.com/4uyumk9" rel="nofollow">&quot;Change is on the Wind&quot;</a>, in Godzilla[9]<br />

<h2 id="toc13"><a name="x-Mohajira"></a>Mohajira</h2>

<br />

<h1 id="toc13"><a name="Mohajira"></a>Mohajira</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 6144/6125<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0557<br />

<br />

<h3 id="toc14"><a name="x-Mohajira-11-limit"></a>11-limit</h3>

<h2 id="toc14"><a name="Mohajira-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 121/120, 176/175<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0261<br />

<br />

<h2 id="toc15"><a name="x-Mothra"></a>Mothra</h2>

<h1 id="toc15"><a name="Mothra"></a>Mothra</h1>

Commas: 81/80, 1029/1024<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0371<br />

<br />

<h3 id="toc16"><a name="x-Mothra-11-limit"></a>11-limit</h3>

<h2 id="toc16"><a name="Mothra-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 99/98, 385/384<br />

<br />

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Map: [&lt;1 1 0 3 5|, &lt;0 3 12 -1 -8|]<br />

EDOs: 5, <a class="wiki_link" href="/26edo">26</a>, 31, <a class="wiki_link" href="/88edo">88</a>, <a class="wiki_link" href="/150edo">150</a>, <a class="wiki_link" href="/181edo">181</a><br />

[[Badness[[: 0.0256==Squares==<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br />

[[Badness[[: 0.0256=Squares=<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 2401/2400<br />

<br />

Squares, with wedgie &lt;&lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (9/7) intervals, and uses it for a generator. <a class="wiki_link" href="/31edo">31edo</a>, with a generator of 11/31, makes for a good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out 2401/2400, the breedsma, as well as 2430/2401.<br />

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Music:<br />

By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />

<a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow">http://tinyurl.com/25kv7cq</a><br />

<a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow">http://tinyurl.com/25kv7cq</a><br />

<a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow">http://tinyurl.com/24cbxse</a><br />

<a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow">http://tinyurl.com/24cbxse</a><br />

<br />

<h3 id="toc17"><a name="x-Mothra-11-limit"></a>11-limit</h3>

<h2 id="toc17"><a name="Mothra-11-limit"></a>11-limit</h2>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 385/384, 1375/1372<br />

<br />

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<a class="wiki_link" href="/Badness">Badness</a>: 0.0568<br />

<br />

<h2 id="toc18"><a name="x-Liese"></a>Liese</h2>

<h1 id="toc18"><a name="Liese"></a>Liese</h1>

<a class="wiki_link" href="/Comma">Comma</a>s: 81/80, 686/675<br />

<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2011-03-09 16:40:29 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-11 15:36:12 UTC</tt>.<br>
-: The original revision id was <tt>208972928</tt>.<br>
+: The original revision id was <tt>209716986</tt>.<br>
-: The revision comment was: <tt>some links added</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>
@@ Line 17: / Line 17: @@
 The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&gt;, |-13 10 0 -1&gt;], flattone, with normal list [|-4 4 -1&gt;, |-17 9 0 1&gt;], dominant, with normal list [|-4 4 -1&gt;, |6 -2 0 -1&gt;], sharptone, with normal list [|-4 4 -1&gt;, |2 -3 0 1&gt;], injera, with normal list [|-4 4 -1&gt;, |-7 8 0 -2&gt;], mohajira, with normal list [|-4 4 -1&gt;, |-23 11 0 2&gt;], godzilla, with normal list [|-4 4 -1&gt;, |-4 -1 0 2&gt;], mothra, with normal list [|-4 4 -1&gt;, |-10 1 0 3&gt;], squares, with normal list [|-4 4 -1&gt;, |-3 9 0 -4&gt;], and liese, with normal list [|-4 4 -1&gt;, |-9 11 0 -3&gt;].
-==Septimal meantone==
+=Septimal meantone=
 The comma |-13 10 0 -1&gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The [[Wedgies and Multivals|wedgie]] for septimal meantone is &lt;&lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and [[31edo]] is a good tuning for it.
@@ Line 106: / Line 106: @@
 [[Badness]]: 0.0212
-==Flattone==
+=Flattone=
 [[Comma]]s: 81/80, 525/512
@@ Line 131: / Line 131: @@
 [[Badness]]: 0.0386
-==Dominant==
+=Dominant=
 [[Comma]]s: 36/35, 64/63
@@ Line 143: / Line 143: @@
 [[Badness]]: 0.0207
-==Sharptone==
+=Sharptone=
 [[Comma]]s: 21/20, 28/27
@@ Line 155: / Line 155: @@
 [[Badness]]: 0.0248
-==Injera==
+=Injera=
 [[Comma]]s: 50/49, 81/80
@@ Line 167: / Line 167: @@
 [[Badness]]: 0.0311
-==Godzilla==
+=Godzilla=
 [[Comma]]s: 49/48, 81/80
@@ Line 180: / Line 180: @@
 Music: Igliashon Jones, [[http://tinyurl.com/4uyumk9|"Change is on the Wind"]], in Godzilla[9]
-==Mohajira==
+=Mohajira=
 [[Comma]]s: 81/80, 6144/6125
@@ Line 199: / Line 200: @@
 [[Badness]]: 0.0557
-===11-limit===
+==11-limit==
 [[Comma]]s: 81/80, 121/120, 176/175
@@ Line 214: / Line 215: @@
 [[Badness]]: 0.0261
-==Mothra==
+=Mothra=
 Commas: 81/80, 1029/1024
@@ Line 233: / Line 234: @@
 [[Badness]]: 0.0371
-===11-limit===
+==11-limit==
 [[Comma]]s: 81/80, 99/98, 385/384
@@ Line 242: / Line 243: @@
 [[Badness[[: 0.0256
-==Squares==
+=Squares=
 [[Comma]]s: 81/80, 2401/2400
@@ Line 265: / Line 266: @@
 http://tinyurl.com/24cbxse
-===11-limit===
+==11-limit==
 [[Comma]]s: 81/80, 385/384, 1375/1372
@@ Line 274: / Line 275: @@
 [[Badness]]: 0.0568
-==Liese==
+=Liese=
 [[Comma]]s: 81/80, 686/675
@@ Line 303: / Line 304: @@
 The 7-limit children of 81/80 are septimal meantone, with normal comma list [|-4 4 -1&amp;gt;, |-13 10 0 -1&amp;gt;], flattone, with normal list [|-4 4 -1&amp;gt;, |-17 9 0 1&amp;gt;], dominant, with normal list [|-4 4 -1&amp;gt;, |6 -2 0 -1&amp;gt;], sharptone, with normal list [|-4 4 -1&amp;gt;, |2 -3 0 1&amp;gt;], injera, with normal list [|-4 4 -1&amp;gt;, |-7 8 0 -2&amp;gt;], mohajira, with normal list [|-4 4 -1&amp;gt;, |-23 11 0 2&amp;gt;], godzilla, with normal list [|-4 4 -1&amp;gt;, |-4 -1 0 2&amp;gt;], mothra, with normal list [|-4 4 -1&amp;gt;, |-10 1 0 3&amp;gt;], squares, with normal list [|-4 4 -1&amp;gt;, |-3 9 0 -4&amp;gt;], and liese, with normal list [|-4 4 -1&amp;gt;, |-9 11 0 -3&amp;gt;].&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Septimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal meantone&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Septimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Septimal meantone&lt;/h1&gt;
 The comma |-13 10 0 -1&amp;gt; for septimal meantone tells us that the interval class for 7 is 10 generator steps up. Hence, the 7/4 of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are 7/6, C-D#, the augmented second, and 7/5, C-F#, the tritone. The &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt; for septimal meantone is &amp;lt;&amp;lt;1 4 10 4 13 12||, again telling us how to get to 5 and 7 in terms of generator steps. The temperament, aside from what is on the normal list, tempers out 126/125 and 225/224, and &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; is a good tuning for it.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 322: / Line 323: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0137&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-Unidecimal meantone aka Huygens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal meantone aka Huygens&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Unidecimal meantone aka Huygens&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 126/125, 99/98&lt;br /&gt;
 &lt;br /&gt;
@@ Line 339: / Line 340: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0170&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x-Unidecimal meantone aka Huygens-Tridecimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tridecimal meantone&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Septimal meantone-Unidecimal meantone aka Huygens-Tridecimal meantone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tridecimal meantone&lt;/h3&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 66/65, 81/80, 99/98, 105/104&lt;br /&gt;
 &lt;br /&gt;
@@ Line 348: / Line 349: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0180&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Meanpop&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Septimal meantone-Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Meanpop&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 126/125, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 365: / Line 366: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0215&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x-Meanpop-13-limit Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit Meanpop&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Septimal meantone-Meanpop-13-limit Meanpop"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit Meanpop&lt;/h3&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 105/104, 144/143, 196/195&lt;br /&gt;
 &lt;br /&gt;
@@ Line 374: / Line 375: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0209&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Meanenneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Meanenneadecal&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Septimal meantone-Meanenneadecal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Meanenneadecal&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 45/44, 56/55, 81/80&lt;br /&gt;
 &lt;br /&gt;
@@ Line 383: / Line 384: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0214&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Meanenneadecal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Septimal meantone-Meanenneadecal-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 45/44, 56/55, 78/77, 81/80&lt;br /&gt;
 &lt;br /&gt;
@@ Line 392: / Line 393: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0212&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Flattone&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Flattone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Flattone&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 525/512&lt;br /&gt;
 &lt;br /&gt;
@@ Line 417: / Line 418: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0386&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="x-Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Dominant&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Dominant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Dominant&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 36/35, 64/63&lt;br /&gt;
 &lt;br /&gt;
@@ Line 429: / Line 430: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0207&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="x-Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Sharptone&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Sharptone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Sharptone&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 21/20, 28/27&lt;br /&gt;
 &lt;br /&gt;
@@ Line 441: / Line 442: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0248&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="x-Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Injera&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Injera"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Injera&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 50/49, 81/80&lt;br /&gt;
 &lt;br /&gt;
@@ Line 453: / Line 454: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0311&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="x-Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Godzilla&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Godzilla"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Godzilla&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 81/80&lt;br /&gt;
 &lt;br /&gt;
@@ Line 466: / Line 467: @@
 &lt;br /&gt;
 Music: Igliashon Jones, &lt;a class="wiki_link_ext" href="http://tinyurl.com/4uyumk9" rel="nofollow"&gt;&amp;quot;Change is on the Wind&amp;quot;&lt;/a&gt;, in Godzilla[9]&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="x-Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Mohajira&lt;/h2&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc13"&gt;&lt;a name="Mohajira"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Mohajira&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 6144/6125&lt;br /&gt;
 &lt;br /&gt;
@@ Line 485: / Line 487: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0557&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="x-Mohajira-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Mohajira-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 121/120, 176/175&lt;br /&gt;
 &lt;br /&gt;
@@ Line 500: / Line 502: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0261&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="x-Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Mothra&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Mothra"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Mothra&lt;/h1&gt;
 Commas: 81/80, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 519: / Line 521: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0371&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x-Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 99/98, 385/384&lt;br /&gt;
 &lt;br /&gt;
@@ Line 526: / Line 528: @@
 Map: [&amp;lt;1 1 0 3 5|, &amp;lt;0 3 12 -1 -8|]&lt;br /&gt;
 EDOs: 5, &lt;a class="wiki_link" href="/26edo"&gt;26&lt;/a&gt;, 31, &lt;a class="wiki_link" href="/88edo"&gt;88&lt;/a&gt;, &lt;a class="wiki_link" href="/150edo"&gt;150&lt;/a&gt;, &lt;a class="wiki_link" href="/181edo"&gt;181&lt;/a&gt;&lt;br /&gt;
-[[Badness[[: 0.0256==Squares==&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 2401/2400&lt;br /&gt;
+[[Badness[[: 0.0256=Squares=&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 2401/2400&lt;br /&gt;
 &lt;br /&gt;
 Squares, with wedgie &amp;lt;&amp;lt;4 16 9 16 3 -24||, splits the interval of an eleventh, or 8/3, into four supermajor third (9/7) intervals, and uses it for a generator. &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, with a generator of 11/31, makes for a  good squares tuning, with 8, 11, and 14 note MOS available. Squares tempers out 2401/2400, the breedsma, as well as 2430/2401.&lt;br /&gt;
@@ Line 545: / Line 547: @@
 Music:&lt;br /&gt;
 By &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextUrlRule:462:http://tinyurl.com/25kv7cq --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow"&gt;http://tinyurl.com/25kv7cq&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:462 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:463:http://tinyurl.com/25kv7cq --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/25kv7cq" rel="nofollow"&gt;http://tinyurl.com/25kv7cq&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:463 --&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextUrlRule:463:http://tinyurl.com/24cbxse --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow"&gt;http://tinyurl.com/24cbxse&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:463 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:464:http://tinyurl.com/24cbxse --&gt;&lt;a class="wiki_link_ext" href="http://tinyurl.com/24cbxse" rel="nofollow"&gt;http://tinyurl.com/24cbxse&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:464 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x-Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Mothra-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 385/384, 1375/1372&lt;br /&gt;
 &lt;br /&gt;
@@ Line 557: / Line 559: @@
 &lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0568&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="x-Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Liese&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc18"&gt;&lt;a name="Liese"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Liese&lt;/h1&gt;
 &lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 686/675&lt;br /&gt;
 &lt;br /&gt;