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:genewardsmith|genewardsmith]] and made on <tt>2011-03-~~24 00~~:15:43 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-26 07:55:52 UTC</tt>.<br>

: The original revision id was <tt>~~213465386~~</tt>.<br>

: The original revision id was <tt>214170830</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>

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Map: [<2 0 11 -23 26|, <0 1 -2 9 -6|]

EDOs: 22, 56, 78

=Bidia=

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

Commas: 2048/2025, 3136/3125

POTE generator: ~3/2 = 705.364

Map: [<4 0 22 43|,<0 1 -2 -5|]

Wedgie: <<4 -8 -20 -22 -43 -24||

EDOs: 12, 56, 68, 80, 148

Badness: 0.0565

==11-limit==

Commas: 176/175, 896/891, 1375/1372

POTE generator: ~3/2 = 705.087

Map: [<4 0 22 43 71|,<0 1 -2 -5 -9|]

EDOs: 12, 68, 80

Badness: 0.0402

==13-limit==

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

POTE generator: ~3/2 = 705.301

Map: [<4 0 22 43 71|,<0 1 -2 -5 -9|]

EDOs: 12, 68, 80, 148, 228

Badness: 0.0411

=Echidna=

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Badness: 0.0175</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="#Echidna">Echidna</a> | <a href="#Echidnic">Echidnic</a> | <a href="#Shrutar">Shrutar</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>

<br />

<br />

The 5-limit parent comma for the diaschismic family is 2048/2025, the diaschisma. Its monzo is |11 -4 -2&gt;, and flipping that yields &lt;&lt;2 -4 -11|| for the wedgie for 5-limit diaschismic, or srutal, 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 />

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EDOs: 22, 56, 78<br />

<br />

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

<h1 id="toc9"><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 />

Commas: 2048/2025, 3136/3125<br />

<br />

POTE generator: ~3/2 = 705.364<br />

<br />

Map: [&lt;4 0 22 43|,&lt;0 1 -2 -5|]<br />

Wedgie: &lt;&lt;4 -8 -20 -22 -43 -24||<br />

EDOs: 12, 56, 68, 80, 148<br />

Badness: 0.0565<br />

<br />

<h2 id="toc10"><a name="Bidia-11-limit"></a>11-limit</h2>

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

<br />

POTE generator: ~3/2 = 705.087<br />

<br />

Map: [&lt;4 0 22 43 71|,&lt;0 1 -2 -5 -9|]<br />

EDOs: 12, 68, 80<br />

Badness: 0.0402<br />

<br />

<h2 id="toc11"><a name="Bidia-13-limit"></a>13-limit</h2>

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

<br />

POTE generator: ~3/2 = 705.301<br />

<br />

Map: [&lt;4 0 22 43 71|,&lt;0 1 -2 -5 -9|]<br />

EDOs: 12, 68, 80, 148, 228<br />

Badness: 0.0411<br />

<br />

<h1 id="toc12"><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="~~toc10~~"><a name="Echidna-11-limit"></a>11-limit</h2>

<h2 id="toc13"><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="~~toc11~~"><a name="Echidna-13-limit"></a>13-limit</h2>

<h2 id="toc14"><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="~~toc12~~"><a name="Echidna-17-limit"></a>17-limit</h2>

<h2 id="toc15"><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="~~toc13~~"><a name="Echidnic"></a>Echidnic</h1>

<h1 id="toc16"><a name="Echidnic"></a>Echidnic</h1>

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

<br />

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Badness: 0.0722<br />

<br />

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

<h2 id="toc17"><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="~~toc15~~"><a name="Echidnic-13-limit"></a>13-limit</h2>

<h2 id="toc18"><a name="Echidnic-13-limit"></a>13-limit</h2>

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

<br />

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Badness: 0.0289<br />

<br />

<h1 id="~~toc16~~"><a name="Shrutar"></a>Shrutar</h1>

<h1 id="toc19"><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, 250<br />

<br />

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

<h2 id="toc20"><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, 410<br />

<br />

<h2 id="~~toc18~~"><a name="Shrutar-13-limit"></a>13-limit</h2>

<h2 id="toc21"><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="~~toc19~~"><a name="Shrutar-17-limit"></a>17-limit</h2>

<h2 id="toc22"><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="~~toc20~~"><a name="Shrutar-19-limit"></a>19-limit</h2>

<h2 id="toc23"><a name="Shrutar-19-limit"></a>19-limit</h2>

Commas: 121/120, 136/135, 154/154, 176/175, 196/195, 343/342<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:genewardsmith|genewardsmith]] and made on <tt>2011-03-24 00:15:43 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-26 07:55:52 UTC</tt>.<br>
-: The original revision id was <tt>213465386</tt>.<br>
+: The original revision id was <tt>214170830</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 91: / Line 91: @@
 Map: [&lt;2 0 11 -23 26|, &lt;0 1 -2 9 -6|]
 EDOs: 22, 56, 78
+=Bidia=
+Bidia adds 3136/3125 to the commas, splitting the period into 1/4 octave. It may be called the 12&amp;56 temperament.
+Commas: 2048/2025, 3136/3125
+POTE generator: ~3/2 = 705.364
+Map: [&lt;4 0 22 43|,&lt;0 1 -2 -5|]
+Wedgie: &lt;&lt;4 -8 -20 -22 -43 -24||
+EDOs: 12, 56, 68, 80, 148
+Badness: 0.0565
+==11-limit==
+Commas: 176/175, 896/891, 1375/1372
+POTE generator: ~3/2 = 705.087
+Map: [&lt;4 0 22 43 71|,&lt;0 1 -2 -5 -9|]
+EDOs: 12, 68, 80
+Badness: 0.0402
+==13-limit==
+Commas: 176/175, 325/324, 640/637, 896/891
+POTE generator: ~3/2 = 705.301
+Map: [&lt;4 0 22 43 71|,&lt;0 1 -2 -5 -9|]
+EDOs: 12, 68, 80, 148, 228
+Badness: 0.0411
 =Echidna=
@@ Line 212: / Line 242: @@
 Badness: 0.0175</pre></div>
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-<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:42:&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:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt; | &lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Keen"&gt;Keen&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Echidna"&gt;Echidna&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Echidnic"&gt;Echidnic&lt;/a&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;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Shrutar"&gt;Shrutar&lt;/a&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;!-- 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;
+<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:48:&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:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Pajara"&gt;Pajara&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt; | &lt;a href="#Diaschismic"&gt;Diaschismic&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Keen"&gt;Keen&lt;/a&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="#Bidia"&gt;Bidia&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="#Echidna"&gt;Echidna&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="#Echidnic"&gt;Echidnic&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;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Shrutar"&gt;Shrutar&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;!-- 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:64 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;br /&gt;
 The 5-limit parent comma for the diaschismic family is 2048/2025, the diaschisma. 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 srutal, 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;
@@ Line 298: / Line 328: @@
 EDOs: 22, 56, 78&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="Echidna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Echidna&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Bidia"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&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;
+Commas: 2048/2025, 3136/3125&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~3/2 = 705.364&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;4 0 22 43|,&amp;lt;0 1 -2 -5|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;4 -8 -20 -22 -43 -24||&lt;br /&gt;
+EDOs: 12, 56, 68, 80, 148&lt;br /&gt;
+Badness: 0.0565&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="Bidia-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;11-limit&lt;/h2&gt;
+Commas: 176/175, 896/891, 1375/1372&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~3/2 = 705.087&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;4 0 22 43 71|,&amp;lt;0 1 -2 -5 -9|]&lt;br /&gt;
+EDOs: 12, 68, 80&lt;br /&gt;
+Badness: 0.0402&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-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;13-limit&lt;/h2&gt;
+Commas: 176/175, 325/324, 640/637, 896/891&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~3/2 = 705.301&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;4 0 22 43 71|,&amp;lt;0 1 -2 -5 -9|]&lt;br /&gt;
+EDOs: 12, 68, 80, 148, 228&lt;br /&gt;
+Badness: 0.0411&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="Echidna"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&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 311: / Line 371: @@
 Badness: 0.0580&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="Echidna-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&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="Echidna-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;11-limit&lt;/h2&gt;
   Commas: 176/175, 896/891, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 326: / Line 386: @@
 Badness: 0.0260&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="Echidna-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&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="Echidna-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;13-limit&lt;/h2&gt;
 Commas: 176/175, 351/350, 364/363, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 335: / Line 395: @@
 Badness: 0.0237&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="Echidna-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Echidna-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;17-limit&lt;/h2&gt;
 Commas: 136/135, 176/175, 221/220, 256/255, 540/539&lt;br /&gt;
 &lt;br /&gt;
@@ Line 344: / Line 404: @@
 Badness: 0.0203&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="Echidnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Echidnic&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc16"&gt;&lt;a name="Echidnic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Echidnic&lt;/h1&gt;
   Commas: 686/675, 1029/1024&lt;br /&gt;
 &lt;br /&gt;
@@ Line 353: / Line 413: @@
 Badness: 0.0722&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="Echidnic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;11-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Echidnic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;11-limit&lt;/h2&gt;
   Commas: 385/384, 441/440, 686/675&lt;br /&gt;
 &lt;br /&gt;
@@ Line 362: / Line 422: @@
 Badness: 0.0451&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="Echidnic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;13-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Echidnic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;13-limit&lt;/h2&gt;
   Commas: 91/90, 169/168, 385/384, 441/440&lt;br /&gt;
 &lt;br /&gt;
@@ Line 371: / Line 431: @@
 Badness: 0.0289&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="Shrutar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Shrutar&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Shrutar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&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 383: / Line 443: @@
 EDOs: 22, 46, 68, 250&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Shrutar-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&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="Shrutar-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
 Commas: 2048/2025, 245/243, 121/120&lt;br /&gt;
 &lt;br /&gt;
@@ Line 391: / Line 451: @@
 EDOs: 22, 46, 68, 114, 410&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="Shrutar-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&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="Shrutar-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;13-limit&lt;/h2&gt;
 Commas: 121/120, 176/175, 196/195, 245/243&lt;br /&gt;
 &lt;br /&gt;
@@ Line 400: / Line 460: @@
 Badness: 0.0281&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="Shrutar-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;17-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Shrutar-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;17-limit&lt;/h2&gt;
 Commas: 121/120, 136/135, 154/153, 176/175, 196/195&lt;br /&gt;
 &lt;br /&gt;
@@ Line 409: / Line 469: @@
 Badness: 0.0187&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Shrutar-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;19-limit&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Shrutar-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;19-limit&lt;/h2&gt;
 Commas:  121/120, 136/135, 154/154, 176/175, 196/195, 343/342&lt;br /&gt;
 &lt;br /&gt;