Orgonia
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2011-12-09 02:16:35 UTC.
- The original revision id was 284059972.
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Original Wikitext content:
[[toc]] Welcome to Orgonia, the commatic realm of the orgonisma, the [[11-limit]] [[comma]] 65536/65219! =Orgonismic temperament= Comma: 65536/65219 [[Eigenmonzo subgroup|Minimax tuning subgroup]]: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)^(1/5), which is 1.679 cents, and the [[5-limit]] just. Map: <<1 0 0 2 4] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 3 -2]|| EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282 [[Spectrum of a temperament|Spectrum]]: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11 =Subgroup temperaments= ==Orgone== Commas:65536/65219 Subgroup: 2.7.11 POTE generator: ~77/64 = 323.372 Sval map: [<1 2 4|, <0 3 -2|] EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc [[image:orgone_heptatonic.jpg]] ==Oregon== Commas: 55/54, 64/63, 100/99 Subgroup: 2.9.15.7.11 POTE generator: ~6/5 = 326.139 Sval map: [<1 1 1 5 2|, <0 3 4 -3 2|] EDOs: 7, 11, 59b, 70bc, 81bcd, 92bcd The subgroup 2.9.15.7.11 is the [[11-limit]] [[k*N subgroups|2*11 subgroup]], the largest subgroup of the 11-limit on which [[11edo]] acts like [[22edo]], in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit [[Porcupine family|porcupine temperament]] restricted to this subgroup. ===Orca=== Commas: 55/54, 64/63, 100/99, 85/84 Subgroup: 2.9.15.7.11.17 POTE generator: ~6/5 = 326.644 Sval map: [<1 1 1 5 2 7|, <0 3 4 -3 2 -4|] EDOs: 7, 11, 92bcd, 103bcd
Original HTML content:
<html><head><title>Orgonia</title></head><body><!-- ws:start:WikiTextTocRule:10:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><div style="margin-left: 1em;"><a href="#Orgonismic temperament">Orgonismic temperament</a></div> <!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><div style="margin-left: 1em;"><a href="#Subgroup temperaments">Subgroup temperaments</a></div> <!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><div style="margin-left: 2em;"><a href="#Subgroup temperaments-Orgone">Orgone</a></div> <!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><div style="margin-left: 2em;"><a href="#Subgroup temperaments-Oregon">Oregon</a></div> <!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 3em;"><a href="#Subgroup temperaments-Oregon-Orca">Orca</a></div> <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --></div> <!-- ws:end:WikiTextTocRule:16 --><br /> Welcome to Orgonia, the commatic realm of the orgonisma, the <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/comma">comma</a> 65536/65219!<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Orgonismic temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->Orgonismic temperament</h1> Comma: 65536/65219<br /> <br /> <a class="wiki_link" href="/Eigenmonzo%20subgroup">Minimax tuning subgroup</a>: 2.3.5.11/7. The minimax tuning makes 7 and 11 both sharp by (65536/65219)^(1/5), which is 1.679 cents, and the <a class="wiki_link" href="/5-limit">5-limit</a> just.<br /> <br /> Map: <<1 0 0 2 4]<br /> [0 1 0 0 0]<br /> [0 0 1 0 0]<br /> [0 0 0 3 -2]||<br /> <br /> EDOs: 15, 19, 22, 37, 41, 89, 111, 130, 152, 282<br /> <a class="wiki_link" href="/Spectrum%20of%20a%20temperament">Spectrum</a>: 4/3, 11/8, 12/11, 5/4, 8/7, 6/5, 11/10, 7/6, 9/8, 7/5, 11/9, 10/9, 9/7, 14/11<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Subgroup temperaments"></a><!-- ws:end:WikiTextHeadingRule:2 -->Subgroup temperaments</h1> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Subgroup temperaments-Orgone"></a><!-- ws:end:WikiTextHeadingRule:4 -->Orgone</h2> Commas:65536/65219<br /> Subgroup: 2.7.11<br /> <br /> POTE generator: ~77/64 = 323.372<br /> <br /> Sval map: [<1 2 4|, <0 3 -2|]<br /> EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:17:<img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="" title="" /> --><img src="/file/view/orgone_heptatonic.jpg/155606933/orgone_heptatonic.jpg" alt="orgone_heptatonic.jpg" title="orgone_heptatonic.jpg" /><!-- ws:end:WikiTextLocalImageRule:17 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Subgroup temperaments-Oregon"></a><!-- ws:end:WikiTextHeadingRule:6 -->Oregon</h2> Commas: 55/54, 64/63, 100/99<br /> Subgroup: 2.9.15.7.11<br /> <br /> POTE generator: ~6/5 = 326.139<br /> <br /> Sval map: [<1 1 1 5 2|, <0 3 4 -3 2|]<br /> EDOs: 7, 11, 59b, 70bc, 81bcd, 92bcd<br /> <br /> The subgroup 2.9.15.7.11 is the <a class="wiki_link" href="/11-limit">11-limit</a> <a class="wiki_link" href="/k%2AN%20subgroups">2*11 subgroup</a>, the largest subgroup of the 11-limit on which <a class="wiki_link" href="/11edo">11edo</a> acts like <a class="wiki_link" href="/22edo">22edo</a>, in the sense that it gives the same tuning to intervals and has the same commas. Oregon temperament is just 11-limit <a class="wiki_link" href="/Porcupine%20family">porcupine temperament</a> restricted to this subgroup.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="Subgroup temperaments-Oregon-Orca"></a><!-- ws:end:WikiTextHeadingRule:8 -->Orca</h3> Commas: 55/54, 64/63, 100/99, 85/84<br /> Subgroup: 2.9.15.7.11.17<br /> <br /> POTE generator: ~6/5 = 326.644<br /> <br /> Sval map: [<1 1 1 5 2 7|, <0 3 4 -3 2 -4|]<br /> EDOs: 7, 11, 92bcd, 103bcd</body></html>