The Archipelago: Difference between revisions
Wikispaces>genewardsmith **Imported revision 201077202 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 201079046 - 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>2011-02-11 21: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-11 21:31:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>201079046</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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[[POTE tuning|POTE generator]]: 317.076 | [[POTE tuning|POTE generator]]: 317.076 | ||
[[Smonzos and Svals|Sval map]] | [[Smonzos and Svals|Sval map]]: [<1 0 1 0 |, <0 6 5 14|] | ||
EDOs: 15, 19, 34, 53, 87, 140, 193, 246 | |||
EDOs: 15, 19, 34, 53, 87, 193, 246 | |||
===Parizekmic=== | ===Parizekmic=== | ||
Subgroup: 2.3.5.13 | |||
Commas: 676/675 | |||
Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat. | Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat. | ||
[[Smonzos and Svals|Sval map]] | |||
<1 | <1 0 0 -1| | ||
<0 2 | <0 2 0 3| | ||
<0 0 1 | <0 0 1 1| | ||
EDOs: | EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>The Archipelago</title></head><body>The archipelago is a rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments, associated with island temperament: the rank five thirteen limit temperament tempering out the island comma, 676/675. Common to all of them is the observation that two intervals of 15/13 are equated with a fourth. Hence a 1-15/13-4/3 chord is a characteristic island chord, and 15/13 tends to be of low complexity. Also characteristic is the barbados triad, the 1-13/10-3/2 triad, as well as its inversion 1-15/13-3/2, and the barbados tetrad, 1-13/10-3/2-26/15. This is because the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> generated by 2, 4/3 and 15/13 is 2.3.13/5, and the triad is found in that.<br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>The Archipelago</title></head><body>The archipelago is a rag-tag collection of various regular temperaments of different ranks, including subgroup temperaments, associated with island temperament: the rank five thirteen limit temperament tempering out the island comma, 676/675. Common to all of them is the observation that two intervals of 15/13 are equated with a fourth. Hence a 1-15/13-4/3 chord is a characteristic island chord, and 15/13 tends to be of low complexity. Also characteristic is the barbados triad, the 1-13/10-3/2 triad, as well as its inversion 1-15/13-3/2, and the barbados tetrad, 1-13/10-3/2-26/15. This is because the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> generated by 2, 4/3 and 15/13 is 2.3.13/5, and the triad is found in that.<br /> | ||
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<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.076<br /> | <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 317.076<br /> | ||
<br /> | <br /> | ||
<a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a> | <a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a>: [&lt;1 0 1 0 |, &lt;0 6 5 14|]<br /> | ||
EDOs: 15, 19, 34, 53, 87, 140, 193, 246<br /> | |||
EDOs: 15, 19, 34, 53, 87, 193, 246<br /> | |||
<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> | <!-- 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. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat.<br /> | Subgroup: 2.3.5.13<br /> | ||
Commas: 676/675<br /> | |||
<br /> | |||
Closely related to barbados temperament is parizekmic, the rank three 2.3.5.13 subgroup temperament tempering out 676/675. This is generated by 2, 5, and 15/13, where the minimax tuning makes 2 and 5 pure, and 15/13 sharp by sqrt(676/675), or 1.28145 cents. This is, in other words, the same sqrt(4/3) generator as the minimax tuning for barbados, and it gives parizekmic a just 5-limit, with barbados triads where the 13/10 is a cent flat.<br /> | |||
<br /> | <br /> | ||
<a class="wiki_link" href="/Smonzos%20and%20Svals">Sval map</a><br /> | |||
&lt;1 | &lt;1 0 0 -1|<br /> | ||
&lt;0 2 | &lt;0 2 0 3|<br /> | ||
&lt;0 0 1 | &lt;0 0 1 1|<br /> | ||
EDOs: | EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270</body></html></pre></div> | ||