The Archipelago: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 231249770 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 238036431 - 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: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-21 16:41:55 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>238036431</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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Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7 | Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7 | ||
==Borneo== | ==Borneo== | ||
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Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7 | Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7 | ||
==Sumatra== | |||
Commas: 325/324, 385/384, 625/624 | |||
EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299 | |||
Optimal patent val: [[299edo]] | |||
Badness: 0.000680 | |||
==[[Cataharry family|Madagascar]]== | ==[[Cataharry family|Madagascar]]== | ||
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EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270</pre></div> | 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><!-- ws:start:WikiTextTocRule: | <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><!-- ws:start:WikiTextTocRule:50:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><a href="#Parent Temperaments">Parent Temperaments</a><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Island">Island</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --> | <a href="#toc2"> </a><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | <a href="#Rank four temperaments">Rank four temperaments</a><!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --> | <a href="#Rank three temperaments">Rank three temperaments</a><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --> | <a href="#Subgroup temperaments">Subgroup temperaments</a><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:76 -->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, the barbados tetrad, 1-13/10-3/2-26/15, plus the tetrads 1-13/10-3/2-8/5 and 1-13/10-3/2-9/5. 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 barbados triad and tetrad are found in that, while the other two tetrads are found in the larger 2.3.5.13 subgroup.<br /> | ||
<br /> | <br /> | ||
The barbados triad is of particular theoretical interest because, when reduced to lowest terms, it is the 10:13:15 triad. Thus, this triad is only slightly higher in complexity than the 5-limit 10:12:15 minor triad, which means it may be of distinct value as a relatively unexplored musical consonance. It is one of only a few low-complexity triads with a 3/2 on the outer dyad, some others being 4:5:6, 6:7:9, and 10:12:15. It works out to 0-454-702 cents, which means that it is an <em>ultramajor</em> triad, with a third sharper even than the 9/7 supermajor third.<br /> | The barbados triad is of particular theoretical interest because, when reduced to lowest terms, it is the 10:13:15 triad. Thus, this triad is only slightly higher in complexity than the 5-limit 10:12:15 minor triad, which means it may be of distinct value as a relatively unexplored musical consonance. It is one of only a few low-complexity triads with a 3/2 on the outer dyad, some others being 4:5:6, 6:7:9, and 10:12:15. It works out to 0-454-702 cents, which means that it is an <em>ultramajor</em> triad, with a third sharper even than the 9/7 supermajor third.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --> </h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><!-- ws:end:WikiTextHeadingRule:4 --> </h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Island-Barbados"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Island-Barbados"></a><!-- ws:end:WikiTextHeadingRule:6 --><!-- ws:start:WikiTextAnchorRule:77:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Subgroup temperaments-Barbados&quot; title=&quot;Anchor: Subgroup temperaments-Barbados&quot;/&gt; --><a name="Subgroup temperaments-Barbados"></a><!-- ws:end:WikiTextAnchorRule:77 -->Barbados</h2> | ||
Subgroup: 2.3.13/5<br /> | Subgroup: 2.3.13/5<br /> | ||
Commas: 676/675<br /> | Commas: 676/675<br /> | ||
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<br /> | <br /> | ||
Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7<br /> | Spectrum: 11/10, 15/13, 14/11, 4/3, 7/5, 5/4, 11/8, 18/13, 15/11, 13/12, 13/10, 6/5, 8/7, 16/15, 12/11, 13/11, 9/8, 16/13, 15/14, 10/9, 7/6, 11/9, 14/13, 9/7<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Rank three temperaments-Borneo"></a><!-- ws:end:WikiTextHeadingRule:26 -->Borneo</h2> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Rank three temperaments-Borneo"></a><!-- ws:end:WikiTextHeadingRule:26 -->Borneo</h2> | ||
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Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7<br /> | Spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Rank three temperaments-Madagascar"></a><!-- ws:end:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Rank three temperaments-Sumatra"></a><!-- ws:end:WikiTextHeadingRule:28 -->Sumatra</h2> | ||
Commas: 325/324, 385/384, 625/624<br /> | |||
<br /> | |||
EDOs: 15, 19, 34, 53, 72, 87, 140, 159, 212, 299<br /> | |||
Optimal patent val: <a class="wiki_link" href="/299edo">299edo</a><br /> | |||
Badness: 0.000680<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h2&gt; --><h2 id="toc15"><a name="Rank three temperaments-Madagascar"></a><!-- ws:end:WikiTextHeadingRule:30 --><a class="wiki_link" href="/Cataharry%20family">Madagascar</a></h2> | |||
Commas: 351/350, 540/539, 676/675<br /> | Commas: 351/350, 540/539, 676/675<br /> | ||
<br /> | <br /> | ||
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<a class="wiki_link" href="/madagascar19">madagascar19</a><br /> | <a class="wiki_link" href="/madagascar19">madagascar19</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Rank three temperaments-Baffin"></a><!-- ws:end:WikiTextHeadingRule:32 -->Baffin</h2> | ||
Commas: 676/675, 1001/1000, 4225/4224<br /> | Commas: 676/675, 1001/1000, 4225/4224<br /> | ||
<br /> | <br /> | ||
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Spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11<br /> | Spectrum: 15/13, 16/15, 13/12, 4/3, 16/13, 5/4, 18/13, 13/10, 6/5, 9/8, 11/10, 8/7, 7/5, 15/11, 10/9, 13/11, 15/14, 11/8, 7/6, 14/13, 12/11, 9/7, 11/9, 14/11<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:34 -->Rank two temperaments</h1> | ||
Rank two temperaments tempering out 676/675 include the 13-limit versions of <a class="wiki_link" href="/Ragismic%20microtemperaments">hemiennealimmal</a>, <a class="wiki_link" href="/Breedsmic%20temperaments">harry</a>, <a class="wiki_link" href="/Kleismic%20family">tritikleismic</a>, <a class="wiki_link" href="/Kleismic%20family">catakleimsic</a>, <a class="wiki_link" href="/Marvel%20temperaments">negri</a>, <a class="wiki_link" href="/Hemifamity%20temperaments">mystery</a>, <a class="wiki_link" href="/Hemifamity%20temperaments">buzzard</a>, <a class="wiki_link" href="/Kleismic%20family">quadritikleismic</a>.<br /> | Rank two temperaments tempering out 676/675 include the 13-limit versions of <a class="wiki_link" href="/Ragismic%20microtemperaments">hemiennealimmal</a>, <a class="wiki_link" href="/Breedsmic%20temperaments">harry</a>, <a class="wiki_link" href="/Kleismic%20family">tritikleismic</a>, <a class="wiki_link" href="/Kleismic%20family">catakleimsic</a>, <a class="wiki_link" href="/Marvel%20temperaments">negri</a>, <a class="wiki_link" href="/Hemifamity%20temperaments">mystery</a>, <a class="wiki_link" href="/Hemifamity%20temperaments">buzzard</a>, <a class="wiki_link" href="/Kleismic%20family">quadritikleismic</a>.<br /> | ||
<br /> | <br /> | ||
It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to <a class="wiki_link" href="/29edo">29edo</a> alone.<br /> | It is interesting to note the Graham complexity of 15/13 in these temperaments. This is 18 in hemiennealimmal, 6 in harry, 9 in tritikleismic, 3 in catakleismic, 2 in negri, 2 in buzzard, 12 in quadritikleismic. Catakleismic and buzzard are particularly interesting from an archipelago point of view. Mystery is special case, since the 15/13 part of it belongs to <a class="wiki_link" href="/29edo">29edo</a> alone.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Rank two temperaments-Decitonic"></a><!-- ws:end:WikiTextHeadingRule:36 -->Decitonic</h2> | ||
Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | ||
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Badness: 0.0135<br /> | Badness: 0.0135<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Rank two temperaments-Avicenna"></a><!-- ws:end:WikiTextHeadingRule:38 -->Avicenna</h2> | ||
Commas: 676/675, 1001/1000, 3025/3024, 4096/4095<br /> | Commas: 676/675, 1001/1000, 3025/3024, 4096/4095<br /> | ||
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Badness: 0.0156<br /> | Badness: 0.0156<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="Subgroup temperaments"></a><!-- ws:end:WikiTextHeadingRule:40 -->Subgroup temperaments</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h2&gt; --><h2 id="toc21"><a name="Subgroup temperaments-Barbados"></a><!-- ws:end:WikiTextHeadingRule:42 -->Barbados</h2> | ||
Subgroup: 2.3.13/5<br /> | Subgroup: 2.3.13/5<br /> | ||
Commas: 676/675<br /> | Commas: 676/675<br /> | ||
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Badness: 0.002335<br /> | Badness: 0.002335<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:44:&lt;h2&gt; --><h2 id="toc22"><a name="Subgroup temperaments-Trinidad"></a><!-- ws:end:WikiTextHeadingRule:44 -->Trinidad</h2> | ||
Subgroup: 2.3.5.13<br /> | Subgroup: 2.3.5.13<br /> | ||
Commas: 325/324, 625/624<br /> | Commas: 325/324, 625/624<br /> | ||
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EDOs: 15, 19, 34, 53, 87, 140, 193, 246<br /> | EDOs: 15, 19, 34, 53, 87, 140, 193, 246<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:46:&lt;h2&gt; --><h2 id="toc23"><a name="Subgroup temperaments-Parizekmic"></a><!-- ws:end:WikiTextHeadingRule:46 -->Parizekmic</h2> | ||
Subgroup: 2.3.5.13<br /> | Subgroup: 2.3.5.13<br /> | ||
Commas: 676/675<br /> | Commas: 676/675<br /> | ||
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&lt;0 0 1 1|<br /> | &lt;0 0 1 1|<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:48:&lt;h3&gt; --><h3 id="toc24"><a name="Subgroup temperaments-Parizekmic-Music"></a><!-- ws:end:WikiTextHeadingRule:48 -->Music</h3> | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/petr_parizek/pp_pump_675.mp3" rel="nofollow">Petr's Pump</a>, a comma pump based ditty in Parizekmic temperament.<br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/petr_parizek/pp_pump_675.mp3" rel="nofollow">Petr's Pump</a>, a comma pump based ditty in Parizekmic temperament.<br /> | ||
EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270</body></html></pre></div> | EDOs: 5, 9, 10, 15, 19, 34, 53, 130, 140, 164, 183, 217, 270</body></html></pre></div> | ||