Bug 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 2011-01-06 00:04:11 UTC.
- The original revision id was 191305922.
- 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:
The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or 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]]: 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]]: 264.312 Map: [<1 0 0 2 5|, <0 2 3 1 -2|] EDOs: 4, 5, 9, 50, 59 Badness: 0.0226
Original HTML content:
<html><head><title>Bug family</title></head><body>The 5-limit parent of the bug family is bug, a temperament of sorts which tempers out 27/25, the large limma, or 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:<h2> --><h2 id="toc0"><a name="x-Bug"></a><!-- ws:end:WikiTextHeadingRule:0 -->Bug</h2> 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:<h2> --><h2 id="toc1"><a name="x-Beep"></a><!-- ws:end:WikiTextHeadingRule:2 -->Beep</h2> Commas: 21/20, 27/25<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 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:<h3> --><h3 id="toc2"><a name="x-Beep-Pentoid"></a><!-- ws:end:WikiTextHeadingRule:4 -->Pentoid</h3> Commas: 21/20, 27/25, 99/98<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE temperament</a>: 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</body></html>