Bug family
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Original Wikitext content:
[[toc|flat]] The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of [[9edo]]. The monzo for 27/25 is |0 3 -2>, the dual of which is <<2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&5 temperament, and [[14edo]] is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it. Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the [[Ragismic microtemperaments|ennealimmal]] tempering is, we can reconstruct 7-limit JI. =Bug= Comma: 27/25 [[POTE tuning|POTE temperament]]: 260.388 Map: [<1 0 0|, <0 2 3|] EDOs: 4, 5, 9, 14, 23, 106 Badness: 0.0328 =Beep= Commas: 21/20, 27/25 [[POTE tuning|POTE temperament]]: ~6/5 = 263.395 Map: [<1 0 0 2|, <0 2 3 1|] Wedgie: <<2 3 1 0 -4 -6|| EDOs: 4, 5, 9, 32, 41 Badness: 0.0186 ==Pentoid== Commas: 21/20, 27/25, 99/98 [[POTE tuning|POTE temperament]]: ~6/5 = 264.312 Map: [<1 0 0 2 5|, <0 2 3 1 -2|] EDOs: 4, 5, 9, 50, 59 Badness: 0.0226 ==13-limit== Commas: 21/20, 26/25, 27/25, 33/32 POTE generator: ~6/5 = 263.935 Map: [<1 0 0 2 5 -1|, <0 2 3 1 -2 6|] EDOs: 5,9, 32bcde, 41bcdef, 50bcdef Badness: 0.0212 ==Pento== Commas: 21/20, 27/25, 45/44 POTE generator: ~6/5 = 265.847 Map: [<1 0 0 2 -2|, <0 2 3 1 7|] EDOs: 9 Badness: 0.0228 =Mite= Commas: 27/25, 28/25 POTE generator: ~6/5 = 240.712 Map: [<1 0 0 -2|, <0 2 3 6|] Wedgie: <<2 3 6 0 4 6|| EDOs: 1cdd, 5 Badness: 0.0548
Original HTML content:
<html><head><title>Bug 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="#Bug">Bug</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Beep">Beep</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Mite">Mite</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> <!-- ws:end:WikiTextTocRule:19 --><br /> The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or approximately one step of <a class="wiki_link" href="/9edo">9edo</a>. The monzo for 27/25 is |0 3 -2>, the dual of which is <<2 3 0||. The generator for bug is 5/3, two of which give the 3, and three of which give the 5. Bug may be described as the 4&5 temperament, and <a class="wiki_link" href="/14edo">14edo</a> is a good bug tuning, though wide latitude in these matters is possible. 4, 5, or 9 note MOS are a place to start with it.<br /> <br /> Bug has a 7-limit extension, beep, via the normal comma list [27/25, 36/35] which can also be obtained by adding 21/20. Beep has the curious property that if we know what the beep tempering is, and we know what the <a class="wiki_link" href="/Ragismic%20microtemperaments">ennealimmal</a> tempering is, we can reconstruct 7-limit JI.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Bug"></a><!-- ws:end:WikiTextHeadingRule:0 -->Bug</h1> Comma: 27/25<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 260.388<br /> <br /> Map: [<1 0 0|, <0 2 3|]<br /> EDOs: 4, 5, 9, 14, 23, 106<br /> Badness: 0.0328<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Beep"></a><!-- ws:end:WikiTextHeadingRule:2 -->Beep</h1> Commas: 21/20, 27/25<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~6/5 = 263.395<br /> <br /> Map: [<1 0 0 2|, <0 2 3 1|]<br /> Wedgie: <<2 3 1 0 -4 -6||<br /> EDOs: 4, 5, 9, 32, 41<br /> Badness: 0.0186<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Beep-Pentoid"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentoid</h2> Commas: 21/20, 27/25, 99/98<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: ~6/5 = 264.312<br /> <br /> Map: [<1 0 0 2 5|, <0 2 3 1 -2|]<br /> EDOs: 4, 5, 9, 50, 59<br /> Badness: 0.0226<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Beep-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 21/20, 26/25, 27/25, 33/32<br /> <br /> POTE generator: ~6/5 = 263.935<br /> <br /> Map: [<1 0 0 2 5 -1|, <0 2 3 1 -2 6|]<br /> EDOs: 5,9, 32bcde, 41bcdef, 50bcdef<br /> Badness: 0.0212<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Beep-Pento"></a><!-- ws:end:WikiTextHeadingRule:8 -->Pento</h2> Commas: 21/20, 27/25, 45/44<br /> <br /> POTE generator: ~6/5 = 265.847<br /> <br /> Map: [<1 0 0 2 -2|, <0 2 3 1 7|]<br /> EDOs: 9<br /> Badness: 0.0228<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Mite"></a><!-- ws:end:WikiTextHeadingRule:10 -->Mite</h1> Commas: 27/25, 28/25<br /> <br /> POTE generator: ~6/5 = 240.712<br /> <br /> Map: [<1 0 0 -2|, <0 2 3 6|]<br /> Wedgie: <<2 3 6 0 4 6||<br /> EDOs: 1cdd, 5<br /> Badness: 0.0548</body></html>