Archytas clan: Difference between revisions

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**Imported revision 288828285 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 288876029 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-30 10:46:39 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-30 21:49:46 UTC</tt>.<br>
: The original revision id was <tt>288828285</tt>.<br>
: The original revision id was <tt>288876029</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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Map: [&lt;1 2 -3 2 1|, &lt;0 -1 13 2 6|]
Map: [&lt;1 2 -3 2 1|, &lt;0 -1 13 2 6|]
EDOs: 17c, 22, 27c, 39d, 61d
EDOs: 17c, 22, 27c, 39d, 61d
Badness: 0.0322</pre></div>
Badness: 0.0322
 
=Progress=
Commas: 64/63, 392/375
 
POTE generator: ~7/5 = 562.122
 
Map: [&lt;1 0 5 6|, &lt;0 3 -5 -6|]
Wedgie: &lt;&lt;3 -5 -6 -15 -18 0||
EDOs: 13, 15, 32c, 79bcc, 111bcc
Badness: 0.0664
 
==11-limit==
Commas: 56/55, 64/63, 77/75
 
POTE generator: ~7/5 = 562.085
 
Map: [&lt;1 0 5 6 4|, &lt;0 3 -5 -6 -1|]
EDOs: 13, 15, 32c, 47bc, 79bcce
Badness: 0.0310</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;&lt;!-- ws:start:WikiTextTocRule:22:&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:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;a href="#Mother"&gt;Mother&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt; | &lt;a href="#Blacksmith"&gt;Blacksmith&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt; | &lt;a href="#Superpyth"&gt;Superpyth&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt; | &lt;a href="#Beatles"&gt;Beatles&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Schism"&gt;Schism&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Passion"&gt;Passion&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt; | &lt;a href="#Quasisuper"&gt;Quasisuper&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&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;&lt;!-- ws:start:WikiTextTocRule:26:&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:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;a href="#Mother"&gt;Mother&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt; | &lt;a href="#Blacksmith"&gt;Blacksmith&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt; | &lt;a href="#Superpyth"&gt;Superpyth&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt; | &lt;a href="#Beatles"&gt;Beatles&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt; | &lt;a href="#Schism"&gt;Schism&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt; | &lt;a href="#Passion"&gt;Passion&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt; | &lt;a href="#Quasisuper"&gt;Quasisuper&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt; | &lt;a href="#Progress"&gt;Progress&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;
&lt;!-- ws:end:WikiTextTocRule:34 --&gt;The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;Archytas comma&lt;/a&gt;, 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;!-- ws:end:WikiTextTocRule:40 --&gt;The &lt;em&gt;archytas clan&lt;/em&gt; tempers out the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow"&gt;Archytas comma&lt;/a&gt;, 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;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Mother"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mother&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Mother"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Mother&lt;/h1&gt;
Line 148: Line 167:
Badness: 0.0256&lt;br /&gt;
Badness: 0.0256&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:35:&amp;lt;img src=&amp;quot;/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg" alt="blacksmith10.jpg" title="blacksmith10.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:35 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:41:&amp;lt;img src=&amp;quot;/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg" alt="blacksmith10.jpg" title="blacksmith10.jpg" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:41 --&gt;&lt;br /&gt;
&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="Blacksmith-Blackwood"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Blackwood&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Blacksmith-Blackwood"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Blackwood&lt;/h2&gt;
Line 242: Line 261:
Map: [&amp;lt;1 2 -3 2 1|, &amp;lt;0 -1 13 2 6|]&lt;br /&gt;
Map: [&amp;lt;1 2 -3 2 1|, &amp;lt;0 -1 13 2 6|]&lt;br /&gt;
EDOs: 17c, 22, 27c, 39d, 61d&lt;br /&gt;
EDOs: 17c, 22, 27c, 39d, 61d&lt;br /&gt;
Badness: 0.0322&lt;/body&gt;&lt;/html&gt;</pre></div>
Badness: 0.0322&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Progress"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Progress&lt;/h1&gt;
Commas: 64/63, 392/375&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 562.122&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 6|, &amp;lt;0 3 -5 -6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 -5 -6 -15 -18 0||&lt;br /&gt;
EDOs: 13, 15, 32c, 79bcc, 111bcc&lt;br /&gt;
Badness: 0.0664&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="Progress-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;11-limit&lt;/h2&gt;
Commas: 56/55, 64/63, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 562.085&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 5 6 4|, &amp;lt;0 3 -5 -6 -1|]&lt;br /&gt;
EDOs: 13, 15, 32c, 47bc, 79bcce&lt;br /&gt;
Badness: 0.0310&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 21:49, 30 December 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 2011-12-30 21:49:46 UTC.
The original revision id was 288876029.
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:

[[toc|flat]]
The //archytas clan// tempers out the [[http://en.wikipedia.org/wiki/Septimal_comma|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

[[image:blacksmith10.jpg]]

==Blackwood== 
//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= 
[[Superpyth|Main article]]
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

==11-limit== 
Commas: 64/63, 100/99, 245/243

[[POTE tuning|POTE generator]]: 710.175

Map: [<1 0 -12 6 -22|, <0 1 9 -2 16|]
EDOs: 22, 49
Badness: 0.0250

==Suprapyth== 
Commas: 55/54, 64/63, 99/98

POTE generator: ~3/2 = 709.495

Map: [<1 0 -12 6 13|, <0 1 9 -2 -6|]
EDOs: 5, 7, 12, 17, 22
Badness: 0.0328

=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://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3|Beatles Improv]] by Herman Miller

=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

==Quasisupra== 
Commas: 64/63, 99/98, 121/120

Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament [[supra]], with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).

POTE generator: 708.205

Map: [<1 2 -3 2 1|, <0 -1 13 2 6|]
EDOs: 17c, 22, 27c, 39d, 61d
Badness: 0.0322

=Progress=
Commas: 64/63, 392/375

POTE generator: ~7/5 = 562.122

Map: [<1 0 5 6|, <0 3 -5 -6|]
Wedgie: <<3 -5 -6 -15 -18 0||
EDOs: 13, 15, 32c, 79bcc, 111bcc
Badness: 0.0664

==11-limit==
Commas: 56/55, 64/63, 77/75

POTE generator: ~7/5 = 562.085

Map: [<1 0 5 6 4|, <0 3 -5 -6 -1|]
EDOs: 13, 15, 32c, 47bc, 79bcce
Badness: 0.0310

Original HTML content:

<html><head><title>Archytas clan</title></head><body><!-- ws:start:WikiTextTocRule:26:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Quasisuper">Quasisuper</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Progress">Progress</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: -->
<!-- ws:end:WikiTextTocRule:40 -->The <em>archytas clan</em> tempers out the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_comma" rel="nofollow">Archytas comma</a>, 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;h1&gt; --><h1 id="toc0"><a name="Mother"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mother</h1>
 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;h1&gt; --><h1 id="toc1"><a name="Blacksmith"></a><!-- ws:end:WikiTextHeadingRule:2 -->Blacksmith</h1>
 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:WikiTextLocalImageRule:41:&lt;img src=&quot;/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/blacksmith10.jpg/271383136/blacksmith10.jpg" alt="blacksmith10.jpg" title="blacksmith10.jpg" /><!-- ws:end:WikiTextLocalImageRule:41 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Blacksmith-Blackwood"></a><!-- ws:end:WikiTextHeadingRule:4 -->Blackwood</h2>
 <em>Blackwood (5-limit)</em><br />
<br />
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;h1&gt; --><h1 id="toc3"><a name="Superpyth"></a><!-- ws:end:WikiTextHeadingRule:6 -->Superpyth</h1>
 <a class="wiki_link" href="/Superpyth">Main article</a><br />
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="Superpyth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h2>
 Commas: 64/63, 100/99, 245/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.175<br />
<br />
Map: [&lt;1 0 -12 6 -22|, &lt;0 1 9 -2 16|]<br />
EDOs: 22, 49<br />
Badness: 0.0250<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Superpyth-Suprapyth"></a><!-- ws:end:WikiTextHeadingRule:10 -->Suprapyth</h2>
 Commas: 55/54, 64/63, 99/98<br />
<br />
POTE generator: ~3/2 = 709.495<br />
<br />
Map: [&lt;1 0 -12 6 13|, &lt;0 1 9 -2 -6|]<br />
EDOs: 5, 7, 12, 17, 22<br />
Badness: 0.0328<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Beatles"></a><!-- ws:end:WikiTextHeadingRule:12 -->Beatles</h1>
 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: <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/beatles-improv.mp3" rel="nofollow">Beatles Improv</a> by Herman Miller<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:14 -->Schism</h1>
 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:16:&lt;h1&gt; --><h1 id="toc8"><a name="Passion"></a><!-- ws:end:WikiTextHeadingRule:16 -->Passion</h1>
 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:18:&lt;h1&gt; --><h1 id="toc9"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:18 -->Quasisuper</h1>
 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<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Quasisuper-Quasisupra"></a><!-- ws:end:WikiTextHeadingRule:20 -->Quasisupra</h2>
 Commas: 64/63, 99/98, 121/120<br />
<br />
Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament <a class="wiki_link" href="/supra">supra</a>, with the quasisuper mapping of 5 thrown in (rather than the superpyth mapping of 5, which results in suprapyth).<br />
<br />
POTE generator: 708.205<br />
<br />
Map: [&lt;1 2 -3 2 1|, &lt;0 -1 13 2 6|]<br />
EDOs: 17c, 22, 27c, 39d, 61d<br />
Badness: 0.0322<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Progress"></a><!-- ws:end:WikiTextHeadingRule:22 -->Progress</h1>
Commas: 64/63, 392/375<br />
<br />
POTE generator: ~7/5 = 562.122<br />
<br />
Map: [&lt;1 0 5 6|, &lt;0 3 -5 -6|]<br />
Wedgie: &lt;&lt;3 -5 -6 -15 -18 0||<br />
EDOs: 13, 15, 32c, 79bcc, 111bcc<br />
Badness: 0.0664<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Progress-11-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->11-limit</h2>
Commas: 56/55, 64/63, 77/75<br />
<br />
POTE generator: ~7/5 = 562.085<br />
<br />
Map: [&lt;1 0 5 6 4|, &lt;0 3 -5 -6 -1|]<br />
EDOs: 13, 15, 32c, 47bc, 79bcce<br />
Badness: 0.0310</body></html>