The Archipelago
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-02-06 01:44:17 UTC.
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Original Wikitext content:
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; this is because the [[just intonation subgroup]] generated by 2, 4/3 and 15/13 is 2.3.13/5 and the triad is found in that. Comma: 676/675 Map <1 0 0 0 0 -1| <0 2 0 0 0 3| <0 0 1 0 0 1| <0 0 0 1 0 0| <0 0 0 0 1 0| EDOs: 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940 ==Rank four temperaments== ===1001/1000=== Commas: 676/675, 1001/1000 ===49/48=== Commas: 49/48, 91/90 ===1716/1715=== Commas: 676/675, 1716/1715 ===364/363=== Commas: 364/363, 676/675 ===351/350=== Commas: 351/350, 676/675 ==Rank three temperaments== ===Kalaallisut=== Commas: 676/675, 1001/1000, 1716/1715 ===Papua=== Commas: 364/363, 441/440, 1001/1000 ===Borneo=== Commas: 676/675, 1001/1000, 3025/3024 ===Madagascar=== Commas: 351/350, 540/539, 676/675 ===Baffin=== Commas: 676/675, 1001/1000, 4225/4224 ==Rank two temperaments== Rank two temperaments tempering out 676/675 include the 13-limit versions of hemiennealimmal, harry, tritikleismic, catakleimsic, negri, mystery and buzzard.
Original HTML content:
<html><head><title>The Archipelago</title></head><body>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; this is because the <a class="wiki_link" href="/just%20intonation%20subgroup">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 /> <br /> Comma: 676/675<br /> <br /> Map<br /> <1 0 0 0 0 -1| <br /> <0 2 0 0 0 3| <br /> <0 0 1 0 0 1| <br /> <0 0 0 1 0 0| <br /> <0 0 0 0 1 0|<br /> EDOs: 5, 9, 10, 15, 19, 24, 29, 43, 53, 58, 72, 87, 111, 121, 130, 183, 940<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Rank four temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Rank four temperaments</h2> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Rank four temperaments-1001/1000"></a><!-- ws:end:WikiTextHeadingRule:2 -->1001/1000</h3> Commas: 676/675, 1001/1000<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-Rank four temperaments-49/48"></a><!-- ws:end:WikiTextHeadingRule:4 -->49/48</h3> Commas: 49/48, 91/90<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="x-Rank four temperaments-1716/1715"></a><!-- ws:end:WikiTextHeadingRule:6 -->1716/1715</h3> Commas: 676/675, 1716/1715<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="x-Rank four temperaments-364/363"></a><!-- ws:end:WikiTextHeadingRule:8 -->364/363</h3> Commas: 364/363, 676/675<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="x-Rank four temperaments-351/350"></a><!-- ws:end:WikiTextHeadingRule:10 -->351/350</h3> Commas: 351/350, 676/675<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-Rank three temperaments"></a><!-- ws:end:WikiTextHeadingRule:12 -->Rank three temperaments</h2> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h3> --><h3 id="toc7"><a name="x-Rank three temperaments-Kalaallisut"></a><!-- ws:end:WikiTextHeadingRule:14 -->Kalaallisut</h3> Commas: 676/675, 1001/1000, 1716/1715<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h3> --><h3 id="toc8"><a name="x-Rank three temperaments-Papua"></a><!-- ws:end:WikiTextHeadingRule:16 -->Papua</h3> Commas: 364/363, 441/440, 1001/1000<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h3> --><h3 id="toc9"><a name="x-Rank three temperaments-Borneo"></a><!-- ws:end:WikiTextHeadingRule:18 -->Borneo</h3> Commas: 676/675, 1001/1000, 3025/3024<br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h3> --><h3 id="toc10"><a name="x-Rank three temperaments-Madagascar"></a><!-- ws:end:WikiTextHeadingRule:20 -->Madagascar</h3> Commas: 351/350, 540/539, 676/675<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h3> --><h3 id="toc11"><a name="x-Rank three temperaments-Baffin"></a><!-- ws:end:WikiTextHeadingRule:22 -->Baffin</h3> Commas: 676/675, 1001/1000, 4225/4224<br /> <br /> <!-- ws:start:WikiTextHeadingRule:24:<h2> --><h2 id="toc12"><a name="x-Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:24 -->Rank two temperaments</h2> Rank two temperaments tempering out 676/675 include the 13-limit versions of hemiennealimmal, harry, tritikleismic, catakleimsic, negri, mystery and buzzard.</body></html>