Diaschismic 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:~~Kosmorsky~~|~~Kosmorsky~~]] and made on <tt>2012-04-~~01 08~~:05:26 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-12 13:33:32 UTC</tt>.<br>

: The original revision id was <tt>~~316579400~~</tt>.<br>

: The original revision id was <tt>319896024</tt>.<br>

: The revision comment was: <tt></tt><br>

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EDOs: 10, 12e, 22, 120bce, 142bce

Badness: 0.0283

==13-limit==

Commas: 50/49, 55/54, 64/63, 65/63

POTE generator: ~3/2 = 710.240

Map: [<2 0 11 12 -9 1|, <0 1 -2 -2 5 2|]

EDOs: 10, 22, 54f, 76bdf

Badness: 0.0252

==Pajaro==

Commas: 40/39, 50/49, 55/54, 64/63

POTE generator ~3/2 = 710.818

Map: [<2 0 11 12 -9 17|, <0 1 -2 -2 5 -3|]

EDOs: 10, 22f, 32f, 54f

Badness: 0.0274

=Diaschismic=

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Badness: 0.0238</pre></div>

<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>Diaschismic family</title></head><body> | <a href="#Pajara">Pajara</a> | <a href="#Diaschismic">Diaschismic</a> | <a href="#Keen">Keen</a> | <a href="#Bidia">Bidia</a> | <a href="#Echidna">Echidna</a> | <a href="#Echidnic">Echidnic</a> | <a href="#Shrutar">Shrutar</a> | <a href="#Sruti">Sruti</a>

<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>Diaschismic family</title></head><body> | <a href="#Pajara">Pajara</a> | <a href="#Diaschismic">Diaschismic</a> | <a href="#Keen">Keen</a> | <a href="#Bidia">Bidia</a> | <a href="#Echidna">Echidna</a> | <a href="#Echidnic">Echidnic</a> | <a href="#Shrutar">Shrutar</a> | <a href="#Sruti">Sruti</a>

The 5-limit parent comma for the <strong>diaschismic family</strong> is 2048/2025, the <a class="wiki_link" href="/diaschisma">diaschisma</a>. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or <strong>srutal</strong>, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br />

The 5-limit parent comma for the <strong>diaschismic family</strong> is 2048/2025, the <a class="wiki_link" href="/diaschisma">diaschisma</a>. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or <strong>srutal</strong>, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. <a class="wiki_link" href="/34edo">34edo</a> is a good tuning choice, with <a class="wiki_link" href="/46edo">46edo</a>, <a class="wiki_link" href="/56edo">56edo</a>, <a class="wiki_link" href="/58edo">58edo</a> or <a class="wiki_link" href="/80edo">80edo</a> being other possibilities. Both <a class="wiki_link" href="/12edo">12edo</a> and <a class="wiki_link" href="/22edo">22edo</a> support it, and retuning them to a MOS of diaschismic gives two scale possibilities.<br />

<br />

<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 704.898<br />

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Badness: 0.0283<br />

<br />

<h1 id="~~toc4~~"><a name="Diaschismic"></a>Diaschismic</h1>

<h2 id="toc4"><a name="Pajara-13-limit"></a>13-limit</h2>

Commas: 50/49, 55/54, 64/63, 65/63<br />

<br />

POTE generator: ~3/2 = 710.240<br />

<br />

Map: [&lt;2 0 11 12 -9 1|, &lt;0 1 -2 -2 5 2|]<br />

EDOs: 10, 22, 54f, 76bdf<br />

Badness: 0.0252<br />

<br />

<h2 id="toc5"><a name="Pajara-Pajaro"></a>Pajaro</h2>

Commas: 40/39, 50/49, 55/54, 64/63<br />

<br />

POTE generator ~3/2 = 710.818<br />

<br />

Map: [&lt;2 0 11 12 -9 17|, &lt;0 1 -2 -2 5 -3|]<br />

EDOs: 10, 22f, 32f, 54f<br />

Badness: 0.0274<br />

<br />

<h1 id="toc6"><a name="Diaschismic"></a>Diaschismic</h1>

A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&amp;58. However described, diaschismic has wedgie &lt;&lt;2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. <a class="wiki_link" href="/58edo">58et</a> provides an excellent tuning, but an alternative is to make <a class="wiki_link" href="/7_4">7/4</a> just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et.<br />

<br />

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EDOs: 46, 58, 104c, 162c<br />

<br />

<h2 id="~~toc5~~"><a name="Diaschismic-11-limit"></a>11-limit</h2>

<h2 id="toc7"><a name="Diaschismic-11-limit"></a>11-limit</h2>

Commas: 126/125, 176/175, 896/891<br />

<br />

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EDOs: 46, 58, 104c, 162ce<br />

<br />

<h2 id="~~toc6~~"><a name="Diaschismic-13-limit"></a>13-limit</h2>

<h2 id="toc8"><a name="Diaschismic-13-limit"></a>13-limit</h2>

Commas: 126/125, 196/195, 364/363, 2048/2025<br />

<br />

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EDOs: <a class="wiki_link" href="/46edo">46</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/104edo">104c</a>, <a class="wiki_link" href="/162edo">162cef</a><br />

<br />

<h2 id="~~toc7~~"><a name="Diaschismic-17-limit"></a>17-limit</h2>

<h2 id="toc9"><a name="Diaschismic-17-limit"></a>17-limit</h2>

Commas: 126/125, 136/135, 176/175, 196/195, 256/255<br />

<br />

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EDOs: 46, 58, 104c<br />

<br />

<h1 id="~~toc8~~"><a name="Keen"></a>Keen</h1>

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

Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie &lt;&lt;2 -4 18 -11 23 53||. It may also be described as the 22&amp;56 temperament. <a class="wiki_link" href="/78edo">78et</a> is a good tuning choice, and remains a good one in the 11-limit, where keen, &lt;&lt;2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas.<br />

<br />

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EDOs: 22, 56, 78, 134b, 212b, 290b<br />

<br />

<h2 id="~~toc9~~"><a name="Keen-11-limit"></a>11-limit</h2>

<h2 id="toc11"><a name="Keen-11-limit"></a>11-limit</h2>

Commas: 100/99, 385/384, 1232/1215<br />

<br />

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EDOs: 22, 56, 78, 212bf, 290bf<br />

<br />

<h1 id="~~toc10~~"><a name="Bidia"></a>Bidia</h1>

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

Bidia adds 3136/3125 to the commas, splitting the period into 1/4 octave. It may be called the 12&amp;56 temperament.<br />

<br />

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Badness: 0.0565<br />

<br />

<h2 id="~~toc11~~"><a name="Bidia-11-limit"></a>11-limit</h2>

<h2 id="toc13"><a name="Bidia-11-limit"></a>11-limit</h2>

Commas: 176/175, 896/891, 1375/1372<br />

<br />

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Badness: 0.0402<br />

<br />

<h2 id="~~toc12~~"><a name="Bidia-13-limit"></a>13-limit</h2>

<h2 id="toc14"><a name="Bidia-13-limit"></a>13-limit</h2>

Commas: 176/175, 325/324, 640/637, 896/891<br />

<br />

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Badness: 0.0411<br />

<br />

<h1 id="~~toc13~~"><a name="Echidna"></a>Echidna</h1>

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

Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie &lt;&lt;6 -12 10 -33 -1 57|| and may be called the 22&amp;58 temperament. <a class="wiki_link" href="/58edo">58et</a> or <a class="wiki_link" href="/80edo">80et</a> make for good tunings, or their vals can be add to &lt;138 219 321 388|.<br />

<br />

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Badness: 0.0580<br />

<br />

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

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

Commas: 176/175, 896/891, 540/539<br />

<br />

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Badness: 0.0260<br />

<br />

<h2 id="~~toc15~~"><a name="Echidna-13-limit"></a>13-limit</h2>

<h2 id="toc17"><a name="Echidna-13-limit"></a>13-limit</h2>

Commas: 176/175, 351/350, 364/363, 540/539<br />

<br />

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Badness: 0.0237<br />

<br />

<h2 id="~~toc16~~"><a name="Echidna-17-limit"></a>17-limit</h2>

<h2 id="toc18"><a name="Echidna-17-limit"></a>17-limit</h2>

Commas: 136/135, 176/175, 221/220, 256/255, 540/539<br />

<br />

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Badness: 0.0203<br />

<br />

<h1 id="~~toc17~~"><a name="Echidnic"></a>Echidnic</h1>

<h1 id="toc19"><a name="Echidnic"></a>Echidnic</h1>

Commas: 686/675, 1029/1024<br />

<br />

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Badness: 0.0722<br />

<br />

<h2 id="~~toc18~~"><a name="Echidnic-11-limit"></a>11-limit</h2>

<h2 id="toc20"><a name="Echidnic-11-limit"></a>11-limit</h2>

Commas: 385/384, 441/440, 686/675<br />

<br />

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Badness: 0.0451<br />

<br />

<h2 id="~~toc19~~"><a name="Echidnic-13-limit"></a>13-limit</h2>

<h2 id="toc21"><a name="Echidnic-13-limit"></a>13-limit</h2>

Commas: 91/90, 169/168, 385/384, 441/440<br />

<br />

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Compositions:<br />

<br />

<a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow">http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3</a><br />

<a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow">http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3</a><br />

(the description says &quot;lemba&quot; which has a similar sale structure but different mapping for 5)<br />

<br />

<h1 id="~~toc20~~"><a name="Shrutar"></a>Shrutar</h1>

<h1 id="toc22"><a name="Shrutar"></a>Shrutar</h1>

Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &lt;&lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. <a class="wiki_link" href="/68edo">68edo</a> makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.<br />

<br />

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EDOs: 22, 46, 68, 182b, 250bc<br />

<br />

<h2 id="~~toc21~~"><a name="Shrutar-11-limit"></a>11-limit</h2>

<h2 id="toc23"><a name="Shrutar-11-limit"></a>11-limit</h2>

Commas: 2048/2025, 245/243, 121/120<br />

<br />

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EDOs: 22, 46, 68, 114, 296bce, 410bce<br />

<br />

<h2 id="~~toc22~~"><a name="Shrutar-13-limit"></a>13-limit</h2>

<h2 id="toc24"><a name="Shrutar-13-limit"></a>13-limit</h2>

Commas: 121/120, 176/175, 196/195, 245/243<br />

<br />

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Badness: 0.0281<br />

<br />

<h2 id="~~toc23~~"><a name="Shrutar-17-limit"></a>17-limit</h2>

<h2 id="toc25"><a name="Shrutar-17-limit"></a>17-limit</h2>

Commas: 121/120, 136/135, 154/153, 176/175, 196/195<br />

<br />

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Badness: 0.0187<br />

<br />

<h2 id="~~toc24~~"><a name="Shrutar-19-limit"></a>19-limit</h2>

<h2 id="toc26"><a name="Shrutar-19-limit"></a>19-limit</h2>

Commas: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342<br />

<br />

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Badness: 0.0175<br />

<br />

<h1 id="~~toc25~~"><a name="Sruti"></a>Sruti</h1>

<h1 id="toc27"><a name="Sruti"></a>Sruti</h1>

Commas: 2048/2025, 19683/19600<br />

<br />

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Badness: 0.1174<br />

<br />

<h2 id="~~toc26~~"><a name="Sruti-11-limit"></a>11-limit</h2>

<h2 id="toc28"><a name="Sruti-11-limit"></a>11-limit</h2>

Commas: 176/175, 243/242, 896/891<br />

<br />

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Badness: 0.0415<br />

<br />

<h2 id="~~toc27~~"><a name="Sruti-13-limit"></a>13-limit</h2>

<h2 id="toc29"><a name="Sruti-13-limit"></a>13-limit</h2>

Commas: 144/143, 176/175, 351/350, 676/675<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:Kosmorsky|Kosmorsky]] and made on <tt>2012-04-01 08:05:26 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-04-12 13:33:32 UTC</tt>.<br>
-: The original revision id was <tt>316579400</tt>.<br>
+: The original revision id was <tt>319896024</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>
@@ Line 48: / Line 48: @@
 EDOs: 10, 12e, 22, 120bce, 142bce
 Badness: 0.0283
+==13-limit==
+Commas: 50/49, 55/54, 64/63, 65/63
+POTE generator: ~3/2 = 710.240
+Map: [&lt;2 0 11 12 -9 1|, &lt;0 1 -2 -2 5 2|]
+EDOs: 10, 22, 54f, 76bdf
+Badness: 0.0252
+==Pajaro==
+Commas: 40/39, 50/49, 55/54, 64/63
+POTE generator ~3/2 = 710.818
+Map: [&lt;2 0 11 12 -9 17|, &lt;0 1 -2 -2 5 -3|]
+EDOs: 10, 22f, 32f, 54f
+Badness: 0.0274
 =Diaschismic=
@@ Line 286: / Line 304: @@
 Badness: 0.0238</pre></div>
 <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;Diaschismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:56:&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:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt; | &lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Keen"&gt;Keen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Bidia"&gt;Bidia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&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="#Echidna"&gt;Echidna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt; | &lt;a href="#Echidnic"&gt;Echidnic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt; | &lt;a href="#Shrutar"&gt;Shrutar&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&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;!-- ws:end:WikiTextTocRule:81 --&gt;&lt;!-- ws:start:WikiTextTocRule:82: --&gt; | &lt;a href="#Sruti"&gt;Sruti&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:82 --&gt;&lt;!-- ws:start:WikiTextTocRule:83: --&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&gt;&lt;!-- ws:end:WikiTextTocRule:84 --&gt;&lt;!-- ws:start:WikiTextTocRule:85: --&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;Diaschismic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:60:&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:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&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;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&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;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Keen"&gt;Keen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Bidia"&gt;Bidia&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Echidna"&gt;Echidna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;!-- ws:start:WikiTextTocRule:80: --&gt; | &lt;a href="#Echidnic"&gt;Echidnic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:80 --&gt;&lt;!-- ws:start:WikiTextTocRule:81: --&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="#Shrutar"&gt;Shrutar&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:83 --&gt;&lt;!-- ws:start:WikiTextTocRule:84: --&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;!-- ws:end:WikiTextTocRule:87 --&gt;&lt;!-- ws:start:WikiTextTocRule:88: --&gt; | &lt;a href="#Sruti"&gt;Sruti&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:88 --&gt;&lt;!-- ws:start:WikiTextTocRule:89: --&gt;&lt;!-- ws:end:WikiTextTocRule:89 --&gt;&lt;!-- ws:start:WikiTextTocRule:90: --&gt;&lt;!-- ws:end:WikiTextTocRule:90 --&gt;&lt;!-- ws:start:WikiTextTocRule:91: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:85 --&gt;The 5-limit parent comma for the &lt;strong&gt;diaschismic family&lt;/strong&gt; is 2048/2025, the &lt;a class="wiki_link" href="/diaschisma"&gt;diaschisma&lt;/a&gt;. Its monzo is |11 -4 -2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or &lt;strong&gt;srutal&lt;/strong&gt;, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; is a good tuning choice, with &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; or &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; being other possibilities. Both &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; support it, and retuning them to a MOS of diaschismic gives two scale possibilities.&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:91 --&gt;The 5-limit parent comma for the &lt;strong&gt;diaschismic family&lt;/strong&gt; is 2048/2025, the &lt;a class="wiki_link" href="/diaschisma"&gt;diaschisma&lt;/a&gt;. Its monzo is |11 -4 -2&amp;gt;, and flipping that yields &amp;lt;&amp;lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or &lt;strong&gt;srutal&lt;/strong&gt;, temperament. This tells us the period is half an octave, the GCD of 2 and -4, and that the generator is a fifth. Three periods gives 1800 cents, and decreasing this by two fifths gives the major third. &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt; is a good tuning choice, with &lt;a class="wiki_link" href="/46edo"&gt;46edo&lt;/a&gt;, &lt;a class="wiki_link" href="/56edo"&gt;56edo&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58edo&lt;/a&gt; or &lt;a class="wiki_link" href="/80edo"&gt;80edo&lt;/a&gt; being other possibilities. Both &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt; support it, and retuning them to a MOS of diaschismic gives two scale possibilities.&lt;br /&gt;
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 704.898&lt;br /&gt;
@@ Line 329: / Line 347: @@
 Badness: 0.0283&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Diaschismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Diaschismic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Pajara-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
+Commas: 50/49, 55/54, 64/63, 65/63&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~3/2 = 710.240&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 0 11 12 -9 1|, &amp;lt;0 1 -2 -2 5 2|]&lt;br /&gt;
+EDOs: 10, 22, 54f, 76bdf&lt;br /&gt;
+Badness: 0.0252&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Pajara-Pajaro"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Pajaro&lt;/h2&gt;
+Commas: 40/39, 50/49, 55/54, 64/63&lt;br /&gt;
+&lt;br /&gt;
+POTE generator ~3/2 = 710.818&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;2 0 11 12 -9 17|, &amp;lt;0 1 -2 -2 5 -3|]&lt;br /&gt;
+EDOs: 10, 22f, 32f, 54f&lt;br /&gt;
+Badness: 0.0274&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Diaschismic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Diaschismic&lt;/h1&gt;
   A simpler characterization than the one given by the normal comma list is that diaschismic adds 126/125 or 5120/5103 to the set of commas, and it can also be called 46&amp;amp;58. However described, diaschismic has wedgie &amp;lt;&amp;lt;2 -4 -16 -11 -31 -26||, with a 1/2 period and a sharp fifth generator like pajara, but not so sharp, giving a more accurate but more complex temperament. &lt;a class="wiki_link" href="/58edo"&gt;58et&lt;/a&gt; provides an excellent tuning, but an alternative is to make &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; just by making the fifth 703.897 cents, as opposed to 703.448 cents for 58et.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 341: / Line 377: @@
 EDOs: 46, 58, 104c, 162c&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Diaschismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Diaschismic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;11-limit&lt;/h2&gt;
   Commas: 126/125, 176/175, 896/891&lt;br /&gt;
 &lt;br /&gt;
@@ Line 349: / Line 385: @@
 EDOs: 46, 58, 104c, 162ce&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="Diaschismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Diaschismic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
   Commas: 126/125, 196/195, 364/363, 2048/2025&lt;br /&gt;
 &lt;br /&gt;
@@ Line 357: / Line 393: @@
 EDOs: &lt;a class="wiki_link" href="/46edo"&gt;46&lt;/a&gt;, &lt;a class="wiki_link" href="/58edo"&gt;58&lt;/a&gt;, &lt;a class="wiki_link" href="/104edo"&gt;104c&lt;/a&gt;, &lt;a class="wiki_link" href="/162edo"&gt;162cef&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Diaschismic-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Diaschismic-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;17-limit&lt;/h2&gt;
   Commas: 126/125, 136/135, 176/175, 196/195, 256/255&lt;br /&gt;
 &lt;br /&gt;
@@ Line 365: / Line 401: @@
 EDOs: 46, 58, 104c&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="Keen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Keen&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc10"&gt;&lt;a name="Keen"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Keen&lt;/h1&gt;
   Keen adds 875/864 as well as 2240/2187 to the set of commas, and has wedgie &amp;lt;&amp;lt;2 -4 18 -11 23 53||. It may also be described as the 22&amp;amp;56 temperament. &lt;a class="wiki_link" href="/78edo"&gt;78et&lt;/a&gt; is a good tuning choice, and remains a good one in the 11-limit, where keen, &amp;lt;&amp;lt;2 -4 18 -12 ...||, is really more interesting, adding 100/99 and 385/384 to the commas.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 375: / Line 411: @@
 EDOs: 22, 56, 78, 134b, 212b, 290b&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="Keen-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Keen-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
   Commas: 100/99, 385/384, 1232/1215&lt;br /&gt;
 &lt;br /&gt;
@@ Line 383: / Line 419: @@
 EDOs: 22, 56, 78, 212bf, 290bf&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="Bidia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Bidia&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc12"&gt;&lt;a name="Bidia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Bidia&lt;/h1&gt;
   Bidia adds 3136/3125 to the commas, splitting the period into 1/4 octave. It may be called the 12&amp;amp;56 temperament.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 395: / Line 431: @@
 Badness: 0.0565&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="Bidia-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Bidia-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
   Commas: 176/175, 896/891, 1375/1372&lt;br /&gt;
 &lt;br /&gt;
@@ Line 404: / Line 440: @@
 Badness: 0.0402&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="Bidia-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Bidia-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
   Commas: 176/175, 325/324, 640/637, 896/891&lt;br /&gt;
 &lt;br /&gt;
@@ Line 413: / Line 449: @@
 Badness: 0.0411&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="Echidna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Echidna&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc15"&gt;&lt;a name="Echidna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Echidna&lt;/h1&gt;
   Echidna adds 1728/1715 to the commas and takes 9/7 as a generator. It has a wedgie &amp;lt;&amp;lt;6 -12 10 -33 -1 57|| and may be called the 22&amp;amp;58 temperament. &lt;a class="wiki_link" href="/58edo"&gt;58et&lt;/a&gt; or &lt;a class="wiki_link" href="/80edo"&gt;80et&lt;/a&gt; make for good tunings, or their vals can be add to &amp;lt;138 219 321 388|.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 426: / Line 462: @@
 Badness: 0.0580&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Echidna-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Echidna-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;11-limit&lt;/h2&gt;
   Commas: 176/175, 896/891, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 441: / Line 477: @@
 Badness: 0.0260&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="Echidna-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Echidna-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;13-limit&lt;/h2&gt;
   Commas: 176/175, 351/350, 364/363, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 450: / Line 486: @@
 Badness: 0.0237&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Echidna-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Echidna-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;17-limit&lt;/h2&gt;
   Commas: 136/135, 176/175, 221/220, 256/255, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 459: / Line 495: @@
 Badness: 0.0203&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="Echidnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Echidnic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Echidnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Echidnic&lt;/h1&gt;
   Commas: 686/675, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 468: / Line 504: @@
 Badness: 0.0722&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="Echidnic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Echidnic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
   Commas: 385/384, 441/440, 686/675&lt;br /&gt;
 &lt;br /&gt;
@@ Line 477: / Line 513: @@
 Badness: 0.0451&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Echidnic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Echidnic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
   Commas: 91/90, 169/168, 385/384, 441/440&lt;br /&gt;
 &lt;br /&gt;
@@ Line 488: / Line 524: @@
 Compositions:&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextUrlRule:377:http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 --&gt;&lt;a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow"&gt;http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:377 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextUrlRule:399:http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3 --&gt;&lt;a class="wiki_link_ext" href="http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3" rel="nofollow"&gt;http://untwelve.org/2011competition_audio/Kosmorsky-A_Stiff_Shot_of_Turpentine.mp3&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:399 --&gt;&lt;br /&gt;
 (the description says &amp;quot;lemba&amp;quot; which has a similar sale structure but different mapping for 5)&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="Shrutar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Shrutar&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc22"&gt;&lt;a name="Shrutar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Shrutar&lt;/h1&gt;
   Shrutar adds 245/243 to the commas, and also tempers out 6144/6125. With wedgie &amp;lt;&amp;lt;4 -8 14 -22 11 55||, it can also be described as 22&amp;amp;46. Its generator can be taken as either 36/35 or 35/24; the latter is interesting since along with 15/14 and 21/20, it connects opposite sides of a hexany. &lt;a class="wiki_link" href="/68edo"&gt;68edo&lt;/a&gt; makes for a good tuning, but another and excellent choice is a generator of 14^(1/7), making 7s just.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 503: / Line 539: @@
 EDOs: 22, 46, 68, 182b, 250bc&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="Shrutar-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Shrutar-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
   Commas: 2048/2025, 245/243, 121/120&lt;br /&gt;
 &lt;br /&gt;
@@ Line 511: / Line 547: @@
 EDOs: 22, 46, 68, 114, 296bce, 410bce&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Shrutar-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Shrutar-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;13-limit&lt;/h2&gt;
   Commas: 121/120, 176/175, 196/195, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 520: / Line 556: @@
 Badness: 0.0281&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="Shrutar-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Shrutar-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;17-limit&lt;/h2&gt;
   Commas: 121/120, 136/135, 154/153, 176/175, 196/195&lt;br /&gt;
 &lt;br /&gt;
@@ Line 529: / Line 565: @@
 Badness: 0.0187&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Shrutar-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;19-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Shrutar-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;19-limit&lt;/h2&gt;
   Commas: 121/120, 136/135, 154/153, 176/175, 196/195, 343/342&lt;br /&gt;
 &lt;br /&gt;
@@ Line 538: / Line 574: @@
 Badness: 0.0175&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="Sruti"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Sruti&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc27"&gt;&lt;a name="Sruti"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Sruti&lt;/h1&gt;
   Commas: 2048/2025, 19683/19600&lt;br /&gt;
 &lt;br /&gt;
@@ Line 548: / Line 584: @@
 Badness: 0.1174&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="Sruti-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Sruti-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
   Commas: 176/175, 243/242, 896/891&lt;br /&gt;
 &lt;br /&gt;
@@ Line 557: / Line 593: @@
 Badness: 0.0415&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="Sruti-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Sruti-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
   Commas: 144/143, 176/175, 351/350, 676/675&lt;br /&gt;
 &lt;br /&gt;