Archytas clan: Difference between revisions
Wikispaces>genewardsmith **Imported revision 212606300 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 246369499 - 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: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-08-16 20:38:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>246369499</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | <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">[[toc|flat]] | ||
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. | 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 20: | Line 19: | ||
Badness: 0.0242 | Badness: 0.0242 | ||
=Blacksmith= | =Blacksmith= | ||
Commas: 28/27, 49/48 | Commas: 28/27, 49/48 | ||
| Line 30: | Line 29: | ||
Badness: 0.0256 | Badness: 0.0256 | ||
==Blackwood (5-limit)== | ==Blackwood (5-limit)== | ||
Comma: 256/243 | Comma: 256/243 | ||
| Line 39: | Line 38: | ||
Badness: 0.0638 | Badness: 0.0638 | ||
=Superpyth= | =Superpyth= | ||
[[Superpyth|Main article]] | |||
Commas: 64/63, 245/243 | Commas: 64/63, 245/243 | ||
| Line 49: | Line 49: | ||
Badness: 0.0323 | Badness: 0.0323 | ||
==11-limit== | ==11-limit== | ||
Commas: 64/63, 100/99, 245/243 | Commas: 64/63, 100/99, 245/243 | ||
| Line 58: | Line 58: | ||
Badness: 0.0250 | Badness: 0.0250 | ||
==Suprapyth== | ==Suprapyth== | ||
Commas: 55/54, 64/63, 99/98 | Commas: 55/54, 64/63, 99/98 | ||
| Line 67: | Line 67: | ||
Badness: 0.0328 | Badness: 0.0328 | ||
=Beatles= | =Beatles= | ||
Commas: 64/63, 686/675 | Commas: 64/63, 686/675 | ||
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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 | ||
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Badness: 0.0566 | Badness: 0.0566 | ||
=Passion= | =Passion= | ||
Commas: 64/63, 3125/3087 | Commas: 64/63, 3125/3087 | ||
| Line 100: | Line 100: | ||
Badness: 0.0623 | Badness: 0.0623 | ||
=Quasisuper= | =Quasisuper= | ||
Commas: 64/63, 2430/2401 | Commas: 64/63, 2430/2401 | ||
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<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"><html><head><title>Archytas clan</title></head><body><!-- ws:start:WikiTextTocRule:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Quasisuper">Quasisuper</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <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>Archytas clan</title></head><body><!-- ws:start:WikiTextTocRule:20:&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:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Mother">Mother</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Blacksmith">Blacksmith</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | <a href="#Superpyth">Superpyth</a><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Beatles">Beatles</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Schism">Schism</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --> | <a href="#Passion">Passion</a><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Quasisuper">Quasisuper</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | ||
<!-- ws:end:WikiTextTocRule:31 --> | <!-- ws:end:WikiTextTocRule:31 -->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 /> | ||
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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Mother"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mother</h1> | <!-- 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 /> | Commas: 16/15, 21/20<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 721.569<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 721.569<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Blacksmith"></a><!-- ws:end:WikiTextHeadingRule:2 -->Blacksmith</h1> | <!-- 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 /> | Commas: 28/27, 49/48<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 392.767<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 392.767<br /> | ||
| Line 135: | Line 134: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Blacksmith-Blackwood (5-limit)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Blackwood (5-limit)</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Blacksmith-Blackwood (5-limit)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Blackwood (5-limit)</h2> | ||
Comma: 256/243<br /> | Comma: 256/243<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 399.594<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 399.594<br /> | ||
| Line 144: | Line 143: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Superpyth"></a><!-- ws:end:WikiTextHeadingRule:6 -->Superpyth</h1> | <!-- 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 /> | Commas: 64/63, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 154: | Line 154: | ||
<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> | <!-- 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 /> | Commas: 64/63, 100/99, 245/243<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.175<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.175<br /> | ||
| Line 163: | Line 163: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Superpyth-Suprapyth"></a><!-- ws:end:WikiTextHeadingRule:10 -->Suprapyth</h2> | <!-- 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 /> | Commas: 55/54, 64/63, 99/98<br /> | ||
<br /> | <br /> | ||
POTE generator: ~3/2 = 709.495<br /> | POTE generator: ~3/2 = 709.495<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Beatles"></a><!-- ws:end:WikiTextHeadingRule:12 -->Beatles</h1> | <!-- 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 /> | Commas: 64/63, 686/675<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 355.904<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 355.904<br /> | ||
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Badness: 0.0459<br /> | Badness: 0.0459<br /> | ||
<br /> | <br /> | ||
Music: <!-- ws:start:WikiTextUrlRule: | Music: <!-- ws:start:WikiTextUrlRule:138: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:138 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Schism"></a><!-- ws:end:WikiTextHeadingRule:14 -->Schism</h1> | <!-- 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 /> | Commas: 64/63, 360/343<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.556<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.556<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Passion"></a><!-- ws:end:WikiTextHeadingRule:16 -->Passion</h1> | <!-- 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 /> | Commas: 64/63, 3125/3087<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 98.153<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 98.153<br /> | ||
| Line 205: | Line 205: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:18 -->Quasisuper</h1> | <!-- 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 /> | Commas: 64/63, 2430/2401<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 708.328<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 708.328<br /> | ||