The Archipelago: Difference between revisions

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-07 02:32:57 UTC</tt>.<br>

: The original revision id was <tt>199240444</tt>.<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;white-space: pre-wrap ! important" class="old-revision-html">The archepelago 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 characteritic 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 [[Just intonation subgroups|just intonation subgroup]] generated by 2, 4/3 and 15/13 is 2.3.13/5 and the triad is found in that.

EDOs: 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940

==Rank four temperaments==

===1001/1000===

===49/48===

===1716/1715===

===364/363===

===351/350===

==Rank three temperaments==

===Kalaallisut===

===Papua===

===Borneo===

===Madagascar===

===Baffin===

==Rank two temperaments==

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 [[29edo]] alone.

===Decitonic===

===Avicenna===

Badness: 0.0156

</pre></div>

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;The Archipelago&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The archepelago 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 characteritic 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 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;just intonation subgroup&lt;/a&gt; generated by 2, 4/3 and 15/13 is 2.3.13/5 and the triad is found in that.&lt;br /&gt;

EDOs: 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940&lt;br /&gt;

&lt;br /&gt;

Commas: 676/675, 1001/1000&lt;br /&gt;

Commas: 49/48, 91/90&lt;br /&gt;

Commas: 676/675, 1716/1715&lt;br /&gt;

Commas: 364/363, 676/675&lt;br /&gt;

Commas: 351/350, 676/675&lt;br /&gt;

&lt;br /&gt;

Commas: 676/675, 1001/1000, 1716/1715&lt;br /&gt;

Commas: 364/363, 441/440, 1001/1000&lt;br /&gt;

Commas: 676/675, 1001/1000, 3025/3024&lt;br /&gt;

Commas: 351/350, 540/539, 676/675&lt;br /&gt;

Commas: 676/675, 1001/1000, 4225/4224&lt;br /&gt;

Rank two temperaments tempering out 676/675 include the 13-limit versions of &lt;a class="wiki_link" href="/Ragismic%20microtemperaments"&gt;hemiennealimmal&lt;/a&gt;, &lt;a class="wiki_link" href="/Breedsmic%20temperaments"&gt;harry&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;tritikleismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleimsic&lt;/a&gt;, &lt;a class="wiki_link" href="/Marvel%20temperaments"&gt;negri&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments"&gt;mystery&lt;/a&gt;, &lt;a class="wiki_link" href="/Hemifamity%20temperaments"&gt;buzzard&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;quadritikleismic&lt;/a&gt;. &lt;br /&gt;

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 &lt;a class="wiki_link" href="/29edo"&gt;29edo&lt;/a&gt; alone.&lt;br /&gt;

Commas: 676/675, 1001/1000, 1716/1715, 4225/4224&lt;br /&gt;

Commas: 676/675, 1001/1000, 3025/3024, 4096/4095&lt;br /&gt;