The Archipelago: Difference between revisions
Wikispaces>genewardsmith **Imported revision 199623892 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 199627174 - 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 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-08 03:19:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>199627174</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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===Barbados=== | ===Barbados=== | ||
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. | ||
===Trinidad=== | |||
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 | |||
Map: [<1 0 1 0 0 0|, <0 6 5 0 0 14|] | |||
EDOs: 15, 19, 34, 53, 87, 193, 246 | |||
===Parizekmic=== | ===Parizekmic=== | ||
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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 <a class="wiki_link" href="/Just%20intonation%20subgroups">just intontation subgroup</a>. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/53edo">53edo</a> and <a class="wiki_link" href="/135edo">135edo</a>, with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.<br /> | 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 <a class="wiki_link" href="/Just%20intonation%20subgroups">just intontation subgroup</a>. The minimax tuning for this makes the generator 2/sqrt(3), or 249.0225 cents. EDOs which may be used for it are <a class="wiki_link" href="/24edo">24edo</a>, <a class="wiki_link" href="/29edo">29edo</a>, <a class="wiki_link" href="/53edo">53edo</a> and <a class="wiki_link" href="/135edo">135edo</a>, with MOS of size 5, 9, 14, 19, 24 and 29 making for a good variety of scales.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="x-Subgroup temperaments-Parizekmic"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="x-Subgroup temperaments-Trinidad"></a><!-- ws:end:WikiTextHeadingRule:34 -->Trinidad</h3> | ||
Trinidad may be viewed as the reduction of <a class="wiki_link" href="/Kleismic%20family">catakleismic temperament</a> 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.<br /> | |||
<br /> | |||
Commas: 325/324, 625/624 in 2.3.5.13<br /> | |||
<br /> | |||
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.076<br /> | |||
<br /> | |||
Map: [&lt;1 0 1 0 0 0|, &lt;0 6 5 0 0 14|]<br /> | |||
EDOs: 15, 19, 34, 53, 87, 193, 246<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="x-Subgroup temperaments-Parizekmic"></a><!-- ws:end:WikiTextHeadingRule:36 -->Parizekmic</h3> | |||
Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. <br /> | Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. <br /> | ||
<br /> | <br /> | ||