Archytas clan: Difference between revisions

Revision as of 01:03, 20 December 2010

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2010-12-20 01:03:23 UTC.

The original revision id was 189282803.

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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

===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, 55

===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

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

[[POTE tuning|POTE generator]]:

Map: [<1 1 5 4|,<0 2 -9 -4|]
Wedgie: <<2 -9 -4 -19 -12 16||

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

[[POTE tuning|POTE generator]]:

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

[[POTE tuning|POTE generator]]:

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

[[POTE tuning|POTE generator]]:

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;h3&gt; --><h3 id="toc0"><a name="x--Mother"></a><!-- ws:end:WikiTextHeadingRule:0 -->Mother</h3>
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 />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x--Blacksmith"></a><!-- ws:end:WikiTextHeadingRule:2 -->Blacksmith</h3>
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, 55<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x--Superpyth"></a><!-- ws:end:WikiTextHeadingRule:4 -->Superpyth</h3>
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 />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x--Beatles"></a><!-- ws:end:WikiTextHeadingRule:6 -->Beatles</h3>
Commas: 64/63, 686/675<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:<br />
<br />
Map: [&lt;1 1 5 4|,&lt;0 2 -9 -4|]<br />
Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x--Schism"></a><!-- ws:end:WikiTextHeadingRule:8 -->Schism</h3>
Commas: 64/63, 360/343<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="x--Passion"></a><!-- ws:end:WikiTextHeadingRule:10 -->Passion</h3>
Commas: 64/63, 3125/3087<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x--Quasisuper"></a><!-- ws:end:WikiTextHeadingRule:12 -->Quasisuper</h3>
Commas: 64/63, 2430/2401<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>:</body></html>

@@ 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>2010-12-19 19:06:26 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-12-20 01:03:23 UTC</tt>.<br>
-: The original revision id was <tt>189250641</tt>.<br>
+: The original revision id was <tt>189282803</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 14: / Line 14: @@
 Map: [&lt;1 0 4 6|, &lt;0 1 -1 -2|]
+Wedgie: &lt;&lt;1 -1 -2 -4 -6 -2||
 EDOs: 5, 148, 153
@@ Line 22: / Line 23: @@
 Map: [&lt;5 8 0 14|, &lt;0 0 1 0|]
+Wedgie: &lt;&lt;0 5 0 8 0 -14||
 EDOs: 5, 10, 15, 55
@@ Line 30: / Line 32: @@
 Map: [&lt;1 0 -12 6|, &lt;0 1 9 -2|]
+Wedgie: &lt;&lt;1 9 -2 12 -6 -30||
 EDOs: 5, 17, 22, 27, 49
@@ Line 36: / Line 39: @@
 [[POTE tuning|POTE generator]]:
+Map: [&lt;1 1 5 4|,&lt;0 2 -9 -4|]
+Wedgie: &lt;&lt;2 -9 -4 -19 -12 16||
 ===Schism===
@@ Line 60: / Line 66: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 4 6|, &amp;lt;0 1 -1 -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;
 &lt;br /&gt;
@@ Line 68: / Line 75: @@
 &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;
 EDOs: 5, 10, 15, 55&lt;br /&gt;
 &lt;br /&gt;
@@ Line 76: / Line 84: @@
 &lt;br /&gt;
 Map: [&amp;lt;1 0 -12 6|, &amp;lt;0 1 9 -2|]&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;
 &lt;br /&gt;
@@ Line 82: / Line 91: @@
 &lt;br /&gt;
 &lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;:&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 5 4|,&amp;lt;0 2 -9 -4|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;2 -9 -4 -19 -12 16||&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;

Archytas clan: Difference between revisions

Revision as of 01:03, 20 December 2010

IMPORTED REVISION FROM WIKISPACES

Original Wikitext content:

Original HTML content:

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