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**Imported revision 199713370 - Original comment: **
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**Imported revision 201077202 - 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>2011-02-08 10:24:33 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-11 21:19:10 UTC</tt>.<br>
: The original revision id was <tt>199713370</tt>.<br>
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===Barbados===  
===Barbados===  
Subgroup: 2.3.13/5
Commas: 676/675
Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[Just intonation subgroups|just intontation subgroup]]. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[135edo]], with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 [[Just intonation subgroups|just intontation subgroup]]. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are [[24edo]], [[29edo]], [[53edo]] and [[135edo]], with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.
[[POTE tuning|POTE generator]]: ~15/13 = 248.621
[[Smonzos and Svals|Sval map]]: [&lt;1 0 -1|, &lt;0 2 3|]
EDOs: 5, 14, 19, 24, 29, 82, 111, 251, 362
Badness: 0.002335


===Trinidad===  
===Trinidad===  
Subgroup: 2.3.5.13
Commas: 325/324, 625/624
Trinidad may be viewed as the reduction of [[Kleismic family|catakleismic temperament]] to the 2.3.5.13 subgroup. Another way to put it is that it is the rank two 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675.
Trinidad may be viewed as the reduction of [[Kleismic family|catakleismic temperament]] to the 2.3.5.13 subgroup. Another way to put it is that it is the rank two 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675.
Commas: 325/324, 625/624 in 2.3.5.13


[[POTE tuning|POTE generator]]: 317.076
[[POTE tuning|POTE generator]]: 317.076


[[Smonzos and Svals|Sval map]]:
Map: [&lt;1 0 1 0 0 0|, &lt;0 6 5 0 0 14|]
Map: [&lt;1 0 1 0 0 0|, &lt;0 6 5 0 0 14|]
EDOs: 15, 19, 34, 53, 87, 193, 246
EDOs: 15, 19, 34, 53, 87, 193, 246
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  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x-Subgroup temperaments-Barbados"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Barbados&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="x-Subgroup temperaments-Barbados"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Barbados&lt;/h3&gt;
  Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intontation subgroup&lt;/a&gt;. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; and &lt;a class="wiki_link" href="/135edo"&gt;135edo&lt;/a&gt;, with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.&lt;br /&gt;
  Subgroup: 2.3.13/5&lt;br /&gt;
Commas: 676/675&lt;br /&gt;
&lt;br /&gt;
Perhaps the simplest method of making use of the barbados triad and other characteristic island harmonies is to strip things down to essentials by tempering the 2.3.13/5 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intontation subgroup&lt;/a&gt;. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; and &lt;a class="wiki_link" href="/135edo"&gt;135edo&lt;/a&gt;, with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~15/13 = 248.621&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;: [&amp;lt;1 0 -1|, &amp;lt;0 2 3|]&lt;br /&gt;
EDOs: 5, 14, 19, 24, 29, 82, 111, 251, 362&lt;br /&gt;
Badness: 0.002335&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x-Subgroup temperaments-Trinidad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Trinidad&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="x-Subgroup temperaments-Trinidad"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Trinidad&lt;/h3&gt;
  Trinidad may be viewed as the reduction of &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt; to the 2.3.5.13 subgroup. Another way to put it is that it is the rank two 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675.&lt;br /&gt;
  Subgroup: 2.3.5.13&lt;br /&gt;
Commas: 325/324, 625/624&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Commas: 325/324, 625/624 in 2.3.5.13&lt;br /&gt;
Trinidad may be viewed as the reduction of &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic temperament&lt;/a&gt; to the 2.3.5.13 subgroup. Another way to put it is that it is the rank two 2.3.5.13 subgroup temperament tempering out 325/324, 625/624 and hence also 676/675.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.076&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 317.076&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Smonzos%20and%20Svals"&gt;Sval map&lt;/a&gt;:&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 0 0|, &amp;lt;0 6 5 0 0 14|]&lt;br /&gt;
Map: [&amp;lt;1 0 1 0 0 0|, &amp;lt;0 6 5 0 0 14|]&lt;br /&gt;
EDOs: 15, 19, 34, 53, 87, 193, 246&lt;br /&gt;
EDOs: 15, 19, 34, 53, 87, 193, 246&lt;br /&gt;
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