Archytas clan: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 191834716 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 192628922 - 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>2011-01- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-11 23:09:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>192628922</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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EDOs: 5, 17, 22, 27, 49 | EDOs: 5, 17, 22, 27, 49 | ||
Badness: 0.0323 | 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 | |||
==Beatles== | ==Beatles== | ||
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Badness: 0.0323<br /> | Badness: 0.0323<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Superpyth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h3> | ||
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="x-Beatles"></a><!-- ws:end:WikiTextHeadingRule:10 -->Beatles</h2> | |||
Commas: 64/63, 686/675<br /> | Commas: 64/63, 686/675<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0459<br /> | Badness: 0.0459<br /> | ||
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Music: <!-- ws:start:WikiTextUrlRule: | Music: <!-- ws:start:WikiTextUrlRule:114: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:114 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-Schism"></a><!-- ws:end:WikiTextHeadingRule:12 -->Schism</h2> | ||
Commas: 64/63, 360/343<br /> | Commas: 64/63, 360/343<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0566<br /> | Badness: 0.0566<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-Passion"></a><!-- ws:end:WikiTextHeadingRule:14 -->Passion</h2> | ||
Commas: 64/63, 3125/3087<br /> | Commas: 64/63, 3125/3087<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0623<br /> | Badness: 0.0623<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:16 -->Quasisuper</h2> | ||
Commas: 64/63, 2430/2401<br /> | Commas: 64/63, 2430/2401<br /> | ||
<br /> | <br /> | ||
Revision as of 23:09, 11 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 2011-01-11 23:09:09 UTC.
- The original revision id was 192628922.
- 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 ===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 ==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:<h2> --><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: [<1 0 4 6|, <0 1 -1 -2|]<br /> Wedgie: <<1 -1 -2 -4 -6 -2||<br /> EDOs: 5, 148, 153<br /> Badness: 0.0242<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><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: [<5 8 0 14|, <0 0 1 0|]<br /> Wedgie: <<0 5 0 8 0 -14||<br /> EDOs: 5, 10, 15, 25, 55<br /> Badness: 0.0256<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><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: [<5 8 0|, <0 0 1|]<br /> EDOs: 5, 10, 15<br /> Badness: 0.0638<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><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: [<1 0 -12 6|, <0 1 9 -2|]<br /> Wedgie: <<1 9 -2 12 -6 -30||<br /> EDOs: 5, 17, 22, 27, 49<br /> Badness: 0.0323<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Superpyth-11-limit"></a><!-- ws:end:WikiTextHeadingRule:8 -->11-limit</h3> Commas: 64/63, 100/99, 245/243<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.175<br /> <br /> Map: [<1 0 -12 6 -22|, <0 1 9 -2 16|]<br /> EDOs: 22, 49<br /> Badness: 0.0250<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-Beatles"></a><!-- ws:end:WikiTextHeadingRule:10 -->Beatles</h2> Commas: 64/63, 686/675<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 355.904<br /> <br /> Map: [<1 1 5 4|,<0 2 -9 -4|]<br /> Wedgie: <<2 -9 -4 -19 -12 16||<br /> EDOs: 10, 27, 118<br /> Badness: 0.0459<br /> <br /> Music: <!-- ws:start:WikiTextUrlRule:114: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:114 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-Schism"></a><!-- ws:end:WikiTextHeadingRule:12 -->Schism</h2> Commas: 64/63, 360/343<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 701.556<br /> <br /> Map: [<1 0 15 6|, <0 1 -8 -2|]<br /> Wedgie: <<1 -8 -2 -15 -6 18||<br /> EDOs: 12, 53, 65<br /> Badness: 0.0566<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x-Passion"></a><!-- ws:end:WikiTextHeadingRule:14 -->Passion</h2> Commas: 64/63, 3125/3087<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 98.153<br /> <br /> Map: [<1 2 2 2|, <0 -5 4 10|]<br /> Wedgie: <<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:16:<h2> --><h2 id="toc8"><a name="x-Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:16 -->Quasisuper</h2> Commas: 64/63, 2430/2401<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 708.328<br /> <br /> Map: [<1 0 23 6|, <0 1 -13 -2|]<br /> Wedgie: <<1 -13 -2 -23 -2 -6 32||<br /> EDOs: 22, 61<br /> Badness: 0.0638</body></html>