Father family
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2012-02-05 14:12:09 UTC.
- The original revision id was 298610088.
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Original Wikitext content:
[[toc|flat]] This tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments. =Father= Comma: 16/15 POTE generator: ~3/2 = 743.986 Map: [<1 0 4|, <0 1 -1|] EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc Badness: 0.0149 ==7-limit== Commas: 16/15, 28/27 7-limit minimax [<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|] [[Eigenmonzo subgroup]]: 2.7/5 9-limit eigenmonzo subgroup: 2.9/5 [[POTE tuning|POTE generator]]: 742.002 Map: [<1 0 4 -2|, <0 1 -1 3|] Wedgie: <<1 -1 3 -4 2 10|| EDOs: 5, 8d, 13cd, 21bcd Badness: 0.0213 =Pater= Commas: 16/15, 126/125 POTE generator: ~3/2 = 753.113 Map: [<1 0 4 11|, <0 1 -1 -5|] Wedgie: <<1 -1 -5 -4 -11 -9|| EDOs: 3, 11b, 16bcd, 27bcd Badness: 0.0530 =Walid= Commas: 16/15, 50/49 POTE generator: ~3/2 = 749.415 Map: [<2 0 8 9|, <0 1 -1 -1|] Wedgie: <<2 -2 -2 -8 -9 1|| EDOs: 2, 6, 10cd, 14bd, 16bcd Badness: 0.0490 =Baba= Commas: 16/15, 49/45 POTE generator: ~8/7 = 226.704 Map: [<1 0 4 2|, <0 2 -2 1|] Wedgie: <<2 -2 1 -8 -4 8|| EDOs: 1, 5, 11b, 16bc Badness: 0.0443 =Quint= Commas: 16/15, 27/25 POTE generator: ~8/7 = 182.097 Map: [<5 8 12 0|, <0 0 0 1|] Wedgie: <<0 0 5 0 8 12|| EDOs: 5, 15cd Badness: 0.0483
Original HTML content:
<html><head><title>Father family</title></head><body><!-- ws:start:WikiTextTocRule:12:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Father">Father</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --> | <a href="#Pater">Pater</a><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Walid">Walid</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Baba">Baba</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Quint">Quint</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> <!-- ws:end:WikiTextTocRule:19 --><br /> This tempers out 16/15, the just diatonic semitone. This equates 4/3 with 5/4, so these are "fourth-thirds", or father, temperaments.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Father"></a><!-- ws:end:WikiTextHeadingRule:0 -->Father</h1> Comma: 16/15<br /> <br /> POTE generator: ~3/2 = 743.986<br /> <br /> Map: [<1 0 4|, <0 1 -1|]<br /> EDOs: 1, 2, 3, 5, 8, 10c, 11b, 13c, 21bc<br /> Badness: 0.0149<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Father-7-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit</h2> Commas: 16/15, 28/27<br /> <br /> 7-limit minimax<br /> [<1 0 0 0|, <3/2 0 -1/4 1/4|, <5/2 0 1/4 -1/4|, <5/2 0 -3/4 3/4|]<br /> <a class="wiki_link" href="/Eigenmonzo%20subgroup">Eigenmonzo subgroup</a>: 2.7/5<br /> <br /> 9-limit eigenmonzo subgroup: 2.9/5<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 742.002<br /> <br /> Map: [<1 0 4 -2|, <0 1 -1 3|]<br /> Wedgie: <<1 -1 3 -4 2 10||<br /> EDOs: 5, 8d, 13cd, 21bcd<br /> Badness: 0.0213<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Pater"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pater</h1> Commas: 16/15, 126/125<br /> <br /> POTE generator: ~3/2 = 753.113<br /> <br /> Map: [<1 0 4 11|, <0 1 -1 -5|]<br /> Wedgie: <<1 -1 -5 -4 -11 -9||<br /> EDOs: 3, 11b, 16bcd, 27bcd<br /> Badness: 0.0530<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Walid"></a><!-- ws:end:WikiTextHeadingRule:6 -->Walid</h1> Commas: 16/15, 50/49<br /> <br /> POTE generator: ~3/2 = 749.415<br /> <br /> Map: [<2 0 8 9|, <0 1 -1 -1|]<br /> Wedgie: <<2 -2 -2 -8 -9 1||<br /> EDOs: 2, 6, 10cd, 14bd, 16bcd<br /> Badness: 0.0490<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Baba"></a><!-- ws:end:WikiTextHeadingRule:8 -->Baba</h1> Commas: 16/15, 49/45<br /> <br /> POTE generator: ~8/7 = 226.704<br /> <br /> Map: [<1 0 4 2|, <0 2 -2 1|]<br /> Wedgie: <<2 -2 1 -8 -4 8||<br /> EDOs: 1, 5, 11b, 16bc<br /> Badness: 0.0443<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Quint"></a><!-- ws:end:WikiTextHeadingRule:10 -->Quint</h1> Commas: 16/15, 27/25<br /> <br /> POTE generator: ~8/7 = 182.097<br /> <br /> Map: [<5 8 12 0|, <0 0 0 1|]<br /> Wedgie: <<0 0 5 0 8 12||<br /> EDOs: 5, 15cd<br /> Badness: 0.0483</body></html>