31st-octave temperaments
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-12-01 15:14:49 UTC.
- The original revision id was 281230670.
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Original Wikitext content:
By the //31-3-comma// is meant 617673396283947/562949953421312 = <-49 31|, the amount (160.605 cents) by which 31 just (3/2) fifths exceed 18 octaves. This may not seem like much of a comma, but since 31et is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense. =Prajapati= Commas: 81/80, 126/125, 1029/1024 POTE generator: ~176/175 = 6.519 Map: [[<31 49 72 87 107|, <0 0 0 0 1|] EDOs: 31, 93, 124b, 155b, 186b Badness: 0.0430 ==13-limit== Commas: 81/80, 126/125, 105/104, 512/507 POTE generator: ~66/65 = 9.171 Map: [[<31 49 72 87 107 115|, <0 0 0 0 1 0|] EDOs: 31, 93f, 124bf Badness: 0.0379 ==Kumhar== Commas: 81/80, 126/125, 1029/1024, 144/143 POTE generator: ~196/195 = 10.120 Map: [[<31 49 72 87 107 115|, <0 0 0 0 1 -1|] EDOs: 31, 62e, 93, 124b, 341b Badness: 0.0486 =Gallium= Commas: 81/80, 126/125, 99/98, 121/120 POTE generator: ~16807/16640 = 15.541 Map: [<31 49 72 87 107 0|, <0 0 0 0 0 1|] EDOs: 31, 62, 93e, 155bef Badness: 0.0255 =Birds= The birds temperament tempers out the //31-5 comma//, |72 0 -31>, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 "As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it." Commas: 3136/3125, 823543/819200 POTE generator:
Original HTML content:
<html><head><title>31 comma temperaments</title></head><body>By the <em>31-3-comma</em> is meant 617673396283947/562949953421312 = <-49 31|, the amount (160.605 cents) by which 31 just (3/2) fifths exceed 18 octaves. This may not seem like much of a comma, but since 31et is such a strong 7-limit system, 11- and 13-limit temperaments based on the cycle of 31 fifths actually make sense.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Prajapati"></a><!-- ws:end:WikiTextHeadingRule:0 -->Prajapati</h1> Commas: 81/80, 126/125, 1029/1024<br /> <br /> POTE generator: ~176/175 = 6.519<br /> <br /> Map: [[<31 49 72 87 107|, <0 0 0 0 1|]<br /> EDOs: 31, 93, 124b, 155b, 186b<br /> Badness: 0.0430<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Prajapati-13-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->13-limit</h2> Commas: 81/80, 126/125, 105/104, 512/507<br /> <br /> POTE generator: ~66/65 = 9.171<br /> <br /> Map: [[<31 49 72 87 107 115|, <0 0 0 0 1 0|]<br /> EDOs: 31, 93f, 124bf<br /> Badness: 0.0379<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Prajapati-Kumhar"></a><!-- ws:end:WikiTextHeadingRule:4 -->Kumhar</h2> Commas: 81/80, 126/125, 1029/1024, 144/143<br /> <br /> POTE generator: ~196/195 = 10.120<br /> <br /> Map: [[<31 49 72 87 107 115|, <0 0 0 0 1 -1|]<br /> EDOs: 31, 62e, 93, 124b, 341b<br /> Badness: 0.0486<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Gallium"></a><!-- ws:end:WikiTextHeadingRule:6 -->Gallium</h1> Commas: 81/80, 126/125, 99/98, 121/120<br /> <br /> POTE generator: ~16807/16640 = 15.541<br /> <br /> Map: [<31 49 72 87 107 0|, <0 0 0 0 0 1|]<br /> EDOs: 31, 62, 93e, 155bef<br /> Badness: 0.0255<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Birds"></a><!-- ws:end:WikiTextHeadingRule:8 -->Birds</h1> The birds temperament tempers out the <em>31-5 comma</em>, |72 0 -31>, which is the amount (24.275 cents) by which 31 just (5/4) major thirds fall short of ten octaves. The name comes from Isaiah 31:5 "As birds flying, so wil the Lord of hostes defend Ierusalem, defending also hee will deliuer it, and passing ouer, he will preserue it."<br /> <br /> Commas: 3136/3125, 823543/819200<br /> <br /> POTE generator:</body></html>