Diminished family
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2012-05-08 01:52:37 UTC.
- The original revision id was 331608928.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
[[toc|flat]] The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo. =Dimipent= Comma: 648/625 POTE generator: ~3/2 = 699.507 Map: [<4 0 3|, <0 1 1|] EDOs: 8, 12 Badness: 0.0472 =Hemidim= Commas: 49/48, 648/625 POTE generator: ~8/7 = 252.555 Map: [<4 0 3 8|, <0 2 2 1|] Wedgie: <<8 8 4 -6 -16 -13|| EDOs: 24, 52d, 76cd Badness: 0.0864 ==11-limit== Commas: 49/48, 77/75, 243/242 POTE generator: ~8/7 = 251.658 Map: [<4 0 3 8 -2|, <0 2 2 1 5|] EDOs: 24, 76cde Badness: 0.0566 ==13-limit== Commas: 49/48, 66/65, 77/75, 648/625 POTE generator: ~8/7 = 252.225 Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|] EDOs: 24, 52de, 76cde Badness: 0.039
Original HTML content:
<html><head><title>Dimipent family</title></head><body><!-- ws:start:WikiTextTocRule:8:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Dimipent">Dimipent</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <a href="#Hemidim">Hemidim</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --> <!-- ws:end:WikiTextTocRule:13 --><br /> The dimipent family tempers out the major diesis aka diminished comma, 648/625, the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as 12edo. <br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Dimipent"></a><!-- ws:end:WikiTextHeadingRule:0 -->Dimipent</h1> Comma: 648/625<br /> <br /> POTE generator: ~3/2 = 699.507<br /> <br /> Map: [<4 0 3|, <0 1 1|]<br /> EDOs: 8, 12<br /> Badness: 0.0472<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Hemidim"></a><!-- ws:end:WikiTextHeadingRule:2 -->Hemidim</h1> Commas: 49/48, 648/625<br /> <br /> POTE generator: ~8/7 = 252.555<br /> <br /> Map: [<4 0 3 8|, <0 2 2 1|]<br /> Wedgie: <<8 8 4 -6 -16 -13||<br /> EDOs: 24, 52d, 76cd<br /> Badness: 0.0864<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Hemidim-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> Commas: 49/48, 77/75, 243/242<br /> <br /> POTE generator: ~8/7 = 251.658<br /> <br /> Map: [<4 0 3 8 -2|, <0 2 2 1 5|]<br /> EDOs: 24, 76cde<br /> Badness: 0.0566<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Hemidim-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 49/48, 66/65, 77/75, 648/625<br /> <br /> POTE generator: ~8/7 = 252.225<br /> <br /> Map: [<4 0 3 8 -2 -1|, <0 2 2 1 5 5|]<br /> EDOs: 24, 52de, 76cde<br /> Badness: 0.039</body></html>