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Subgroup temperaments: Difference between revisions

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Wikispaces>genewardsmith
**Imported revision 346010014 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 351932256 - 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>2012-06-17 17:50:47 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-07-10 03:54:41 UTC</tt>.<br>
: The original revision id was <tt>346010014</tt>.<br>
: The original revision id was <tt>351932256</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>
Line 14: Line 14:
Comma: 49/48
Comma: 49/48


POTE generator: ~8/7~7/6 = 250.385
[[Lp tuning|POL2 generator]]: ~8/7~7/6 = 250.385


[[Gencom]]: [2 8/7; 49/48]
[[Gencom]]: [2 8/7; 49/48]
Line 20: Line 20:


Map: [&lt;1 2 3|, &lt;0 -2 -1|]
Map: [&lt;1 2 3|, &lt;0 -2 -1|]
EDOs: 5, 19, 24
EDOs: 5, 14, 19, 24, 67c, 91c
[[Lp tuning#L2 tuning|L2 error]]: 5.046 cents


==Archy==  
==Archy==  
Line 27: Line 28:
Comma: 64/63
Comma: 64/63


POTE generator: ~3/2 = 709.322
[[Lp tuning|POL2 generator]]: ~3/2 = 709.321


Gencom: [2 3/2; 64/63]
Gencom: [2 3/2; 64/63]
Line 34: Line 35:
Map: [&lt;1 2 2|, &lt;0 -1 2|]
Map: [&lt;1 2 2|, &lt;0 -1 2|]
EDOs: 5, 12, 17, 22, 27, 137bc
EDOs: 5, 12, 17, 22, 27, 137bc
[[Lp tuning#L2 tuning|L2 error]]: 3.713 cents


==[[Slendric]]==  
==[[Slendric]]==  
Comma: 1029/1024
Comma: 1029/1024


POTE generator: ~8/7 = 233.688
[[Lp tuning|POL2 generator]]: ~8/7 = 233.688


Gencom: [2 8/7; 1029/1024]
Gencom: [2 8/7; 1029/1024]
Line 45: Line 47:
Map: [&lt;1 1 3|, &lt;0 3 -1|]
Map: [&lt;1 1 3|, &lt;0 3 -1|]
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
EDOs: 5, 21, 26, 31, 36, 77, 113, 190
Badness: 0.00461
[[Lp tuning#L2 tuning|L2 error]]: 0.6403 cents


=2.3.11=  
=2.3.11=  
Line 54: Line 56:
Comma: 243/242
Comma: 243/242


POTE generator: ~11/9 = 350.525
[[Lp tuning|POL2 generator]]: ~11/9 = 350.525


Gencom: [2 11/9; 243/242]
Gencom: [2 11/9; 243/242]
Line 61: Line 63:
Map: [&lt;1 1 2|, &lt;0 2 5|]
Map: [&lt;1 1 2|, &lt;0 2 5|]
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
[[Lp tuning#L2 tuning|L2 error]]: 0.6756 cents


[[xenharmonic/neutraltet7|Seven note albitonic scale]]
[[xenharmonic/neutraltet7|Seven note albitonic scale]]
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Commas: 55/54, 100/99
Commas: 55/54, 100/99


POTE generator: 164.078
[[Lp tuning|POL2 generator]]: ~10/9 = 164.078


Gencom: [2 10/9; 55/54, 100/99]
Gencom: [2 10/9; 55/54, 100/99]
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Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -4|]
Map: [&lt;1 2 3 4|, &lt;0 -3 -5 -4|]
EDOs: 7, 15, 22, 37
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd
[[Lp tuning#L2 tuning|L2 error]]: 5.114 cents


==Mohaha==  
==Mohaha==  
Commas: 81/80, 121/120
Commas: 81/80, 121/120


POTE generator: ~11/9 = 348.094
[[Lp tuning|POL2 generator]]: ~11/9 = 348.094


Gencom: [2 11/9; 81/80 121/120]
Gencom: [2 11/9; 81/80 121/120]
Line 88: Line 92:


Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]
Map: [&lt;1 1 0 2|, &lt;0 2 8 5|]
EDOs: 7, 10, 17, 24, 31
EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd
[[Lp tuning#L2 tuning|L2 error]]: 3.113 cents


===Music===
===Music===
Line 255: Line 260:
  Comma: 49/48&lt;br /&gt;
  Comma: 49/48&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7~7/6 = 250.385&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~8/7~7/6 = 250.385&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 8/7; 49/48]&lt;br /&gt;
&lt;a class="wiki_link" href="/Gencom"&gt;Gencom&lt;/a&gt;: [2 8/7; 49/48]&lt;br /&gt;
Line 261: Line 266:
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3|, &amp;lt;0 -2 -1|]&lt;br /&gt;
Map: [&amp;lt;1 2 3|, &amp;lt;0 -2 -1|]&lt;br /&gt;
EDOs: 5, 19, 24&lt;br /&gt;
EDOs: 5, 14, 19, 24, 67c, 91c&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 5.046 cents&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="x2.3.7-Archy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Archy&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x2.3.7-Archy"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Archy&lt;/h2&gt;
Line 268: Line 274:
Comma: 64/63&lt;br /&gt;
Comma: 64/63&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~3/2 = 709.322&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~3/2 = 709.321&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 3/2; 64/63]&lt;br /&gt;
Gencom: [2 3/2; 64/63]&lt;br /&gt;
Line 275: Line 281:
Map: [&amp;lt;1 2 2|, &amp;lt;0 -1 2|]&lt;br /&gt;
Map: [&amp;lt;1 2 2|, &amp;lt;0 -1 2|]&lt;br /&gt;
EDOs: 5, 12, 17, 22, 27, 137bc&lt;br /&gt;
EDOs: 5, 12, 17, 22, 27, 137bc&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 3.713 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x2.3.7-Slendric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/Slendric"&gt;Slendric&lt;/a&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x2.3.7-Slendric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;a class="wiki_link" href="/Slendric"&gt;Slendric&lt;/a&gt;&lt;/h2&gt;
  Comma: 1029/1024&lt;br /&gt;
  Comma: 1029/1024&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 233.688&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~8/7 = 233.688&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 8/7; 1029/1024]&lt;br /&gt;
Gencom: [2 8/7; 1029/1024]&lt;br /&gt;
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Map: [&amp;lt;1 1 3|, &amp;lt;0 3 -1|]&lt;br /&gt;
Map: [&amp;lt;1 1 3|, &amp;lt;0 3 -1|]&lt;br /&gt;
EDOs: 5, 21, 26, 31, 36, 77, 113, 190&lt;br /&gt;
EDOs: 5, 21, 26, 31, 36, 77, 113, 190&lt;br /&gt;
Badness: 0.00461&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 0.6403 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="x2.3.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;2.3.11&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="x2.3.11"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;2.3.11&lt;/h1&gt;
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Comma: 243/242&lt;br /&gt;
Comma: 243/242&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 350.525&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~11/9 = 350.525&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 243/242]&lt;br /&gt;
Gencom: [2 11/9; 243/242]&lt;br /&gt;
Line 302: Line 309:
Map: [&amp;lt;1 1 2|, &amp;lt;0 2 5|]&lt;br /&gt;
Map: [&amp;lt;1 1 2|, &amp;lt;0 2 5|]&lt;br /&gt;
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380&lt;br /&gt;
EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 0.6756 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/neutraltet7"&gt;Seven note albitonic scale&lt;/a&gt;&lt;br /&gt;
Line 312: Line 320:
  Commas: 55/54, 100/99&lt;br /&gt;
  Commas: 55/54, 100/99&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: 164.078&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~10/9 = 164.078&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 10/9; 55/54, 100/99]&lt;br /&gt;
Gencom: [2 10/9; 55/54, 100/99]&lt;br /&gt;
Line 318: Line 326:
&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 3 4|, &amp;lt;0 -3 -5 -4|]&lt;br /&gt;
Map: [&amp;lt;1 2 3 4|, &amp;lt;0 -3 -5 -4|]&lt;br /&gt;
EDOs: 7, 15, 22, 37&lt;br /&gt;
EDOs: 7, 15, 22, 37, 73cd, 95cd, 117bcd&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 5.114 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x2.3.5.11-Mohaha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Mohaha&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x2.3.5.11-Mohaha"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Mohaha&lt;/h2&gt;
  Commas: 81/80, 121/120&lt;br /&gt;
  Commas: 81/80, 121/120&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/9 = 348.094&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning"&gt;POL2 generator&lt;/a&gt;: ~11/9 = 348.094&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Gencom: [2 11/9; 81/80 121/120]&lt;br /&gt;
Gencom: [2 11/9; 81/80 121/120]&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 0 2|, &amp;lt;0 2 8 5|]&lt;br /&gt;
Map: [&amp;lt;1 1 0 2|, &amp;lt;0 2 8 5|]&lt;br /&gt;
EDOs: 7, 10, 17, 24, 31&lt;br /&gt;
EDOs: 7, 10, 17, 24, 31, 69d, 100d, 131bd&lt;br /&gt;
&lt;a class="wiki_link" href="/Lp%20tuning#L2 tuning"&gt;L2 error&lt;/a&gt;: 3.113 cents&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x2.3.5.11-Mohaha-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Music&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x2.3.5.11-Mohaha-Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Music&lt;/h3&gt;
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