Archytas clan: Difference between revisions

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**Imported revision 189491203 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 191834716 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-21 00:22:20 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-08 12:24:46 UTC</tt>.<br>
: The original revision id was <tt>189491203</tt>.<br>
: The original revision id was <tt>191834716</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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<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;white-space: pre-wrap ! important" class="old-revision-html">The //archytas clan// tempers out the Archytas comma, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under [[diaschismic family]], dominant under [[meantone family]], augene under [[augmented family]] and porcupine under [[porcupine family]]. The rest are considered below.
<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;white-space: pre-wrap ! important" class="old-revision-html">The //archytas clan// tempers out the Archytas comma, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under [[diaschismic family]], dominant under [[meantone family]], augene under [[augmented family]] and porcupine under [[porcupine family]]. The rest are considered below.


===Mother===
==Mother==
Commas: 16/15, 21/20
Commas: 16/15, 21/20


Line 16: Line 16:
Wedgie: &lt;&lt;1 -1 -2 -4 -6 -2||
Wedgie: &lt;&lt;1 -1 -2 -4 -6 -2||
EDOs: 5, 148, 153
EDOs: 5, 148, 153
Badness: 0.0242


===Blacksmith===
==Blacksmith==
Commas: 28/27, 49/48
Commas: 28/27, 49/48


Line 24: Line 25:
Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]
Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]
Wedgie: &lt;&lt;0 5 0 8 0 -14||
Wedgie: &lt;&lt;0 5 0 8 0 -14||
EDOs: 5, 10, 15, 55
EDOs: 5, 10, 15, 25, 55
Badness: 0.0256


===Superpyth===
===Blackwood (5-limit)===
Comma: 256/243
 
[[POTE tuning|POTE generator]]: 399.594
 
Map: [&lt;5 8 0|, &lt;0 0 1|]
EDOs: 5, 10, 15
Badness: 0.0638
 
==Superpyth==
Commas: 64/63, 245/243
Commas: 64/63, 245/243


Line 34: Line 45:
Wedgie: &lt;&lt;1 9 -2 12 -6 -30||
Wedgie: &lt;&lt;1 9 -2 12 -6 -30||
EDOs: 5, 17, 22, 27, 49
EDOs: 5, 17, 22, 27, 49
Badness: 0.0323


===Beatles===
==Beatles==
Commas: 64/63, 686/675
Commas: 64/63, 686/675


Line 43: Line 55:
Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||
Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||
EDOs: 10, 27, 118
EDOs: 10, 27, 118
Badness: 0.0459


Music: http://sites.google.com/site/teamouse/
Music: http://sites.google.com/site/teamouse/


===Schism===
==Schism==
Commas: 64/63, 360/343
Commas: 64/63, 360/343


Line 54: Line 67:
Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||
Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||
EDOs: 12, 53, 65
EDOs: 12, 53, 65
Badness: 0.0566


===Passion===
==Passion==
Commas: 64/63, 3125/3087
Commas: 64/63, 3125/3087


Line 64: Line 78:
Generators: 2, 16/15
Generators: 2, 16/15
EDOs: 12, 37, 49, 110, 379
EDOs: 12, 37, 49, 110, 379
Badness: 0.0623


===Quasisuper===
==Quasisuper==
Commas: 64/63, 2430/2401
Commas: 64/63, 2430/2401


Line 72: Line 87:
Map: [&lt;1 0 23 6|, &lt;0 1 -13 -2|]
Map: [&lt;1 0 23 6|, &lt;0 1 -13 -2|]
Wedgie: &lt;&lt;1 -13 -2 -23 -2 -6 32||
Wedgie: &lt;&lt;1 -13 -2 -23 -2 -6 32||
EDOs: 22, 61</pre></div>
EDOs: 22, 61
Badness: 0.0638</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Archytas clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the Archytas comma, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under &lt;a class="wiki_link" href="/diaschismic%20family"&gt;diaschismic family&lt;/a&gt;, dominant under &lt;a class="wiki_link" href="/meantone%20family"&gt;meantone family&lt;/a&gt;, augene under &lt;a class="wiki_link" href="/augmented%20family"&gt;augmented family&lt;/a&gt; and porcupine under &lt;a class="wiki_link" href="/porcupine%20family"&gt;porcupine family&lt;/a&gt;. The rest are considered below.&lt;br /&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;Archytas clan&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the Archytas comma, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under &lt;a class="wiki_link" href="/diaschismic%20family"&gt;diaschismic family&lt;/a&gt;, dominant under &lt;a class="wiki_link" href="/meantone%20family"&gt;meantone family&lt;/a&gt;, augene under &lt;a class="wiki_link" href="/augmented%20family"&gt;augmented family&lt;/a&gt; and porcupine under &lt;a class="wiki_link" href="/porcupine%20family"&gt;porcupine family&lt;/a&gt;. The rest are considered below.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Mother"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mother&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Mother"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mother&lt;/h2&gt;
Commas: 16/15, 21/20&lt;br /&gt;
Commas: 16/15, 21/20&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 84: Line 100:
Wedgie: &amp;lt;&amp;lt;1 -1 -2 -4 -6 -2||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -1 -2 -4 -6 -2||&lt;br /&gt;
EDOs: 5, 148, 153&lt;br /&gt;
EDOs: 5, 148, 153&lt;br /&gt;
Badness: 0.0242&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Blacksmith"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Blacksmith&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Blacksmith"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Blacksmith&lt;/h2&gt;
Commas: 28/27, 49/48&lt;br /&gt;
Commas: 28/27, 49/48&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 92: Line 109:
Map: [&amp;lt;5 8 0 14|, &amp;lt;0 0 1 0|]&lt;br /&gt;
Map: [&amp;lt;5 8 0 14|, &amp;lt;0 0 1 0|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;0 5 0 8 0 -14||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;0 5 0 8 0 -14||&lt;br /&gt;
EDOs: 5, 10, 15, 55&lt;br /&gt;
EDOs: 5, 10, 15, 25, 55&lt;br /&gt;
Badness: 0.0256&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Blacksmith-Blackwood (5-limit)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Blackwood (5-limit)&lt;/h3&gt;
Comma: 256/243&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 399.594&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;5 8 0|, &amp;lt;0 0 1|]&lt;br /&gt;
EDOs: 5, 10, 15&lt;br /&gt;
Badness: 0.0638&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--Superpyth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Superpyth&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Superpyth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Superpyth&lt;/h2&gt;
Commas: 64/63, 245/243&lt;br /&gt;
Commas: 64/63, 245/243&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 102: Line 129:
Wedgie: &amp;lt;&amp;lt;1 9 -2 12 -6 -30||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 9 -2 12 -6 -30||&lt;br /&gt;
EDOs: 5, 17, 22, 27, 49&lt;br /&gt;
EDOs: 5, 17, 22, 27, 49&lt;br /&gt;
Badness: 0.0323&lt;br /&gt;
&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--Beatles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Beatles&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Beatles"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Beatles&lt;/h2&gt;
Commas: 64/63, 686/675&lt;br /&gt;
Commas: 64/63, 686/675&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 111: Line 139:
Wedgie: &amp;lt;&amp;lt;2 -9 -4 -19 -12 16||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;2 -9 -4 -19 -12 16||&lt;br /&gt;
EDOs: 10, 27, 118&lt;br /&gt;
EDOs: 10, 27, 118&lt;br /&gt;
Badness: 0.0459&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Music: &lt;!-- ws:start:WikiTextUrlRule:85:http://sites.google.com/site/teamouse/ --&gt;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/" rel="nofollow"&gt;http://sites.google.com/site/teamouse/&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:85 --&gt;&lt;br /&gt;
Music: &lt;!-- ws:start:WikiTextUrlRule:103:http://sites.google.com/site/teamouse/ --&gt;&lt;a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/" rel="nofollow"&gt;http://sites.google.com/site/teamouse/&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:103 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x--Schism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Schism&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Schism"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Schism&lt;/h2&gt;
Commas: 64/63, 360/343&lt;br /&gt;
Commas: 64/63, 360/343&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 122: Line 151:
Wedgie: &amp;lt;&amp;lt;1 -8 -2 -15 -6 18||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -8 -2 -15 -6 18||&lt;br /&gt;
EDOs: 12, 53, 65&lt;br /&gt;
EDOs: 12, 53, 65&lt;br /&gt;
Badness: 0.0566&lt;br /&gt;
&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--Passion"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Passion&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="x-Passion"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Passion&lt;/h2&gt;
Commas: 64/63, 3125/3087&lt;br /&gt;
Commas: 64/63, 3125/3087&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 132: Line 162:
Generators: 2, 16/15&lt;br /&gt;
Generators: 2, 16/15&lt;br /&gt;
EDOs: 12, 37, 49, 110, 379&lt;br /&gt;
EDOs: 12, 37, 49, 110, 379&lt;br /&gt;
Badness: 0.0623&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x--Quasisuper"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Quasisuper&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-Quasisuper"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Quasisuper&lt;/h2&gt;
Commas: 64/63, 2430/2401&lt;br /&gt;
Commas: 64/63, 2430/2401&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 140: Line 171:
Map: [&amp;lt;1 0 23 6|, &amp;lt;0 1 -13 -2|]&lt;br /&gt;
Map: [&amp;lt;1 0 23 6|, &amp;lt;0 1 -13 -2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -13 -2 -23 -2 -6 32||&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;1 -13 -2 -23 -2 -6 32||&lt;br /&gt;
EDOs: 22, 61&lt;/body&gt;&lt;/html&gt;</pre></div>
EDOs: 22, 61&lt;br /&gt;
Badness: 0.0638&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 12:24, 8 January 2011

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author genewardsmith and made on 2011-01-08 12:24:46 UTC.
The original revision id was 191834716.
The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The //archytas clan// tempers out the Archytas comma, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of [[22edo]]. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under [[diaschismic family]], dominant under [[meantone family]], augene under [[augmented family]] and porcupine under [[porcupine family]]. The rest are considered below.

==Mother==
Commas: 16/15, 21/20

[[POTE tuning|POTE generator]]: 721.569

Map: [<1 0 4 6|, <0 1 -1 -2|]
Wedgie: <<1 -1 -2 -4 -6 -2||
EDOs: 5, 148, 153
Badness: 0.0242

==Blacksmith==
Commas: 28/27, 49/48

[[POTE tuning|POTE generator]]: 392.767

Map: [<5 8 0 14|, <0 0 1 0|]
Wedgie: <<0 5 0 8 0 -14||
EDOs: 5, 10, 15, 25, 55
Badness: 0.0256

===Blackwood (5-limit)===
Comma: 256/243

[[POTE tuning|POTE generator]]: 399.594

Map: [<5 8 0|, <0 0 1|]
EDOs: 5, 10, 15
Badness: 0.0638

==Superpyth==
Commas: 64/63, 245/243

[[POTE tuning|POTE generator]]: 710.291

Map: [<1 0 -12 6|, <0 1 9 -2|]
Wedgie: <<1 9 -2 12 -6 -30||
EDOs: 5, 17, 22, 27, 49
Badness: 0.0323

==Beatles==
Commas: 64/63, 686/675

[[POTE tuning|POTE generator]]: 355.904

Map: [<1 1 5 4|,<0 2 -9 -4|]
Wedgie: <<2 -9 -4 -19 -12 16||
EDOs: 10, 27, 118
Badness: 0.0459

Music: http://sites.google.com/site/teamouse/

==Schism==
Commas: 64/63, 360/343

[[POTE tuning|POTE generator]]: 701.556

Map: [<1 0 15 6|, <0 1 -8 -2|]
Wedgie: <<1 -8 -2 -15 -6 18||
EDOs: 12, 53, 65
Badness: 0.0566

==Passion==
Commas: 64/63, 3125/3087

[[POTE tuning|POTE generator]]: 98.153

Map: [<1 2 2 2|, <0 -5 4 10|]
Wedgie: <<5 -4 -10 -18 -30 -12||
Generators: 2, 16/15
EDOs: 12, 37, 49, 110, 379
Badness: 0.0623

==Quasisuper==
Commas: 64/63, 2430/2401

[[POTE tuning|POTE generator]]: 708.328

Map: [<1 0 23 6|, <0 1 -13 -2|]
Wedgie: <<1 -13 -2 -23 -2 -6 32||
EDOs: 22, 61
Badness: 0.0638

Original HTML content:

<html><head><title>Archytas clan</title></head><body>The <em>archytas clan</em> tempers out the Archytas comma, 64/63. This leads to tunings with 3s and 7s quite sharp, such as those of <a class="wiki_link" href="/22edo">22edo</a>. Adding 50/49 to the list of commas gives pajara, 36/35 gives dominant, 16/15 gives mother, 126/125 gives augene, 28/27 gives blacksmith, 245/243 gives superpyth, 250/243 gives porcupine, 686/675 gives beatles, 360/343 gives schism, 3125/3087 gives passion, and 2430/2401 gives quasisuper. Pajara is discussed under <a class="wiki_link" href="/diaschismic%20family">diaschismic family</a>, dominant under <a class="wiki_link" href="/meantone%20family">meantone family</a>, augene under <a class="wiki_link" href="/augmented%20family">augmented family</a> and porcupine under <a class="wiki_link" href="/porcupine%20family">porcupine family</a>. The rest are considered below.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Mother"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mother</h2>
Commas: 16/15, 21/20<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 721.569<br />
<br />
Map: [&lt;1 0 4 6|, &lt;0 1 -1 -2|]<br />
Wedgie: &lt;&lt;1 -1 -2 -4 -6 -2||<br />
EDOs: 5, 148, 153<br />
Badness: 0.0242<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Blacksmith"></a><!-- ws:end:WikiTextHeadingRule:2 -->Blacksmith</h2>
Commas: 28/27, 49/48<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 392.767<br />
<br />
Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]<br />
Wedgie: &lt;&lt;0 5 0 8 0 -14||<br />
EDOs: 5, 10, 15, 25, 55<br />
Badness: 0.0256<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Blacksmith-Blackwood (5-limit)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Blackwood (5-limit)</h3>
Comma: 256/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 399.594<br />
<br />
Map: [&lt;5 8 0|, &lt;0 0 1|]<br />
EDOs: 5, 10, 15<br />
Badness: 0.0638<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Superpyth"></a><!-- ws:end:WikiTextHeadingRule:6 -->Superpyth</h2>
Commas: 64/63, 245/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.291<br />
<br />
Map: [&lt;1 0 -12 6|, &lt;0 1 9 -2|]<br />
Wedgie: &lt;&lt;1 9 -2 12 -6 -30||<br />
EDOs: 5, 17, 22, 27, 49<br />
Badness: 0.0323<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Beatles"></a><!-- ws:end:WikiTextHeadingRule:8 -->Beatles</h2>
Commas: 64/63, 686/675<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 355.904<br />
<br />
Map: [&lt;1 1 5 4|,&lt;0 2 -9 -4|]<br />
Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||<br />
EDOs: 10, 27, 118<br />
Badness: 0.0459<br />
<br />
Music: <!-- ws:start:WikiTextUrlRule:103:http://sites.google.com/site/teamouse/ --><a class="wiki_link_ext" href="http://sites.google.com/site/teamouse/" rel="nofollow">http://sites.google.com/site/teamouse/</a><!-- ws:end:WikiTextUrlRule:103 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-Schism"></a><!-- ws:end:WikiTextHeadingRule:10 -->Schism</h2>
Commas: 64/63, 360/343<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.556<br />
<br />
Map: [&lt;1 0 15 6|, &lt;0 1 -8 -2|]<br />
Wedgie: &lt;&lt;1 -8 -2 -15 -6 18||<br />
EDOs: 12, 53, 65<br />
Badness: 0.0566<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Passion"></a><!-- ws:end:WikiTextHeadingRule:12 -->Passion</h2>
Commas: 64/63, 3125/3087<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 98.153<br />
<br />
Map: [&lt;1 2 2 2|, &lt;0 -5 4 10|]<br />
Wedgie: &lt;&lt;5 -4 -10 -18 -30 -12||<br />
Generators: 2, 16/15<br />
EDOs: 12, 37, 49, 110, 379<br />
Badness: 0.0623<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:14 -->Quasisuper</h2>
Commas: 64/63, 2430/2401<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 708.328<br />
<br />
Map: [&lt;1 0 23 6|, &lt;0 1 -13 -2|]<br />
Wedgie: &lt;&lt;1 -13 -2 -23 -2 -6 32||<br />
EDOs: 22, 61<br />
Badness: 0.0638</body></html>