Gravity 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 phylingual and made on 2012-06-14 20:44:00 UTC.
- The original revision id was 345484602.
- 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]] =Gravity= The gravity family tempers out [[graviton]], the 5-limit comma 129140163/128000000 = |-13 17 -6>. The graviton equals (81/80)^4/(25/24), so that four 81/80 commas come to a chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -> Mavila -> Dicot -> Porcupine -> Tetracot -> Amity -> ..... (Meantone) continuum, whereby (81/80)^n = 25/24. Comma: 129140163/128000000 POTE generator: ~40/27 = 683.156 Map: [<1 5 12|, <0 -6 -17|] EDOs: [[7edo|7]], [[58edo|58]], [[65edo|65]], [[137edo|137]], [[202edo|202]], [[267edo|267]], [[469edo|469]] Badness: 0.0932 =Harry= Commas: 2401/2400, 19683/19600 POTE generator: ~21/20 = 83.156 Map: [<2 4 7 7|, <0 -6 -17 -10|] Wedgie: <<12 34 20 26 -2 -49|| EDOs: 58, 72, 130, 202, 534 Badness: 0.0341 ==11-limit== Commas: 243/242, 441/440, 4000/3993 POTE generator: ~21/20 = 83.167 Map: [<2 4 7 7 9|, <0 -6 -17 -10 -15|] EDOs: 58, 72, 130, 202 Badness: 0.0159 ==13-limit== Commas: 243/242, 351/350, 441/440, 676/675 POTE generator: ~21/20 = 83.116 Map: [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|] EDOs: 58, 72, 130 Badness: 0.0130 =Gravid= Commas: 126/125, 1605632/1594323 POTE generator: ~27/20 = 517.140 Map: [<1 5 12 25|, <0 -6 -17 -39|] Wedgie: <<6 17 39 13 45 43|| EDOs: 58, 123, 181c Badness: 0.1312 ==11-limit== Commas: 126/125, 243/242, 896/891 POTE generator: ~27/20 = 517.155 Map: [<1 5 12 25 12|, <0 -6 -17 -39 -15|] EDOs: 58, 123, 181ce, 239ce Badness: 0.0473
Original HTML content:
<html><head><title>Gravity 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="#Gravity">Gravity</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Harry">Harry</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: --> | <a href="#Gravid">Gravid</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Gravity"></a><!-- ws:end:WikiTextHeadingRule:0 -->Gravity</h1> The gravity family tempers out <a class="wiki_link" href="/graviton">graviton</a>, the 5-limit comma 129140163/128000000 = |-13 17 -6>. The graviton equals (81/80)^4/(25/24), so that four 81/80 commas come to a chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the Whitewood -> Mavila -> Dicot -> Porcupine -> Tetracot -> Amity -> ..... (Meantone) continuum, whereby (81/80)^n = 25/24.<br /> <br /> Comma: 129140163/128000000<br /> <br /> POTE generator: ~40/27 = 683.156<br /> <br /> Map: [<1 5 12|, <0 -6 -17|]<br /> EDOs: <a class="wiki_link" href="/7edo">7</a>, <a class="wiki_link" href="/58edo">58</a>, <a class="wiki_link" href="/65edo">65</a>, <a class="wiki_link" href="/137edo">137</a>, <a class="wiki_link" href="/202edo">202</a>, <a class="wiki_link" href="/267edo">267</a>, <a class="wiki_link" href="/469edo">469</a><br /> Badness: 0.0932<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Harry"></a><!-- ws:end:WikiTextHeadingRule:2 -->Harry</h1> Commas: 2401/2400, 19683/19600<br /> <br /> POTE generator: ~21/20 = 83.156<br /> <br /> Map: [<2 4 7 7|, <0 -6 -17 -10|]<br /> Wedgie: <<12 34 20 26 -2 -49||<br /> EDOs: 58, 72, 130, 202, 534<br /> Badness: 0.0341<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Harry-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> Commas: 243/242, 441/440, 4000/3993<br /> <br /> POTE generator: ~21/20 = 83.167<br /> <br /> Map: [<2 4 7 7 9|, <0 -6 -17 -10 -15|]<br /> EDOs: 58, 72, 130, 202<br /> Badness: 0.0159<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Harry-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> Commas: 243/242, 351/350, 441/440, 676/675<br /> <br /> POTE generator: ~21/20 = 83.116<br /> <br /> Map: [<2 4 7 7 9 11|, <0 -6 -17 -10 -15 -26|]<br /> EDOs: 58, 72, 130<br /> Badness: 0.0130<br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Gravid"></a><!-- ws:end:WikiTextHeadingRule:8 -->Gravid</h1> Commas: 126/125, 1605632/1594323<br /> <br /> POTE generator: ~27/20 = 517.140<br /> <br /> Map: [<1 5 12 25|, <0 -6 -17 -39|]<br /> Wedgie: <<6 17 39 13 45 43||<br /> EDOs: 58, 123, 181c<br /> Badness: 0.1312<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Gravid-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> Commas: 126/125, 243/242, 896/891<br /> <br /> POTE generator: ~27/20 = 517.155<br /> <br /> Map: [<1 5 12 25 12|, <0 -6 -17 -39 -15|]<br /> EDOs: 58, 123, 181ce, 239ce<br /> Badness: 0.0473</body></html>