Sensamagic clan: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 300720162 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 300725550 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-11 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-11 03:58:08 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>300725550</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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=Pycnic= | =Pycnic= | ||
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. | |||
Commas: 245/243, 525/512 | Commas: 245/243, 525/512 | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Bohpier-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Bohpier-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> | ||
By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:141:http://micro.soonlabel.com/bophier/bophier-1.mp3 --><a class="wiki_link_ext" href="http://micro.soonlabel.com/bophier/bophier-1.mp3" rel="nofollow">http://micro.soonlabel.com/bophier/bophier-1.mp3</a><!-- ws:end:WikiTextUrlRule:141 --><br /> | ||
<!-- ws:start:WikiTextUrlRule: | <!-- ws:start:WikiTextUrlRule:142:http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 --><a class="wiki_link_ext" href="http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3" rel="nofollow">http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3</a><!-- ws:end:WikiTextUrlRule:142 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Sensa"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensa</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Sensa"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensa</h1> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Pycnic"></a><!-- ws:end:WikiTextHeadingRule:18 -->Pycnic</h1> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Pycnic"></a><!-- ws:end:WikiTextHeadingRule:18 -->Pycnic</h1> | ||
The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.<br /> | |||
<br /> | |||
Commas: 245/243, 525/512<br /> | Commas: 245/243, 525/512<br /> | ||
<br /> | <br /> | ||
Revision as of 03:58, 11 February 2012
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 2012-02-11 03:58:08 UTC.
- The original revision id was 300725550.
- 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 //sensamagic clan// tempers out the [[sensamagic comma]], [[245_243|245/243]], a [[triprime comma]] with no factors of 2. |0 -5 1 2> to be exact. There are a number of [[linear temperament]]s in the [[clan]] (magic, father, sensi, godzilla, superpyth, octacot, rodan, hedgehog, clyde, shrutar, sidi) but they've mostly been discussed elsewhere. Tempering out 245/243 alone leads to a [[rank three temperament]] for which [[283edo]] is the [[optimal patent val]]. =Bohpier= [[Comma]]s: 245/243, 3125/3087 [[POTE tuning|POTE generator]]: ~27/25 = 146.474 Map: [<1 0 0 0|, <0 13 19 23|] [[Wedgie]]: <<13 19 23 0 0 0|| EDOs: [[41edo|41]], [[49edo|49]], [[90edo|90]], [[139edo|139]] EDTs: [[13edt|13]] [[Badness]]: 0.0682 ==11-limit== Commas: 100/99, 245/243, 1344/1331 POTE generator: ~12/11 = 146.545 Map: [<1 0 0 0 0|, <0 13 19 23 12|] EDOs: 41, 90e, 131e Badness: 0.0339 ==13-limit== Commas: 100/99, 144/143, 245/243, 275/273 POTE generator: ~12/11 = 146.603 Map: [<1 0 0 0 0 0|, <0 13 19 23 12 14|] EDOs: 41, 90ef, 131ef, 221bdeff Badness: 0.0249 ==Music== By [[Chris Vaisvil]] http://micro.soonlabel.com/bophier/bophier-1.mp3 http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 =Sensa= Commas: 245/243, 65625/65536 POTE generator: ~28/27 = 55.122 Map: [<1 2 2 4|, <0 -9 7 -26|] Wedgie: <<9 -7 26 -32 16 80|| EDOs: [[22edo|22]], [[43edo|43]], [[65edo|65]], [[87edo|87]], [[109edo|109]], [[196edo|196]], [[283edo|283]] Badness: 0.0887 ==11-limit== Commas: 245/243, 385/384, 4000/3993 POTE generator: ~28/27 = 55.126 Map: [<1 2 2 4 3|, <0 -9 7 -26 10|] EDOs: 22, 43, 65, 87, 109, 196, 283 Badness: 0.0358 ==13-limit== Commas: 245/243, 352/351, 385/384, 625/624 POTE generator: ~28/27 = 55.138 Map: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|] EDOs: 22, 43, 65, 87, 109, 196, 283 Badness: 0.0317 =Salsa= Commas: 245/243, 32805/32768 POTE generator: ~128/105 = 351.049 Map: [<1 1 7 -1|, <0 2 -16 13|] Wedgie: <<2 -16 13 -30 15 75|| EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd Badness: 0.08015 ==11-limit== Commas: 243/242, 245/242, 385/384 POTE generator: ~11/9 = 351.014 Map: [<1 1 7 -1 2|, <0 2 -16 13 5|] EDOs: 17, 24, 41, 106d, 147d Badness: 0.0394 =Pycnic= The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune. Commas: 245/243, 525/512 POTE generator: ~45/32 = 567.720 Map: [<1 3 -1 8|, <0 -3 7 -11|] Wedgie: <<3 -7 11 -18 9 45|| EDOs: 17, 19, 55c, 74cd, 93cd Badness: 0.0737
Original HTML content:
<html><head><title>Sensamagic clan</title></head><body><!-- ws:start:WikiTextTocRule:20:<img id="wikitext@@toc@@flat" class="WikiMedia WikiMediaTocFlat" title="Table of Contents" src="/site/embedthumbnail/toc/flat?w=100&h=16"/> --><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><a href="#Bohpier">Bohpier</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Sensa">Sensa</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#Salsa">Salsa</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --> | <a href="#Pycnic">Pycnic</a><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> <!-- ws:end:WikiTextTocRule:31 --><br /> The <em>sensamagic clan</em> tempers out the <a class="wiki_link" href="/sensamagic%20comma">sensamagic comma</a>, <a class="wiki_link" href="/245_243">245/243</a>, a <a class="wiki_link" href="/triprime%20comma">triprime comma</a> with no factors of 2. |0 -5 1 2> to be exact. There are a number of <a class="wiki_link" href="/linear%20temperament">linear temperament</a>s in the <a class="wiki_link" href="/clan">clan</a> (magic, father, sensi, godzilla, superpyth, octacot, rodan, hedgehog, clyde, shrutar, sidi) but they've mostly been discussed elsewhere. Tempering out 245/243 alone leads to a <a class="wiki_link" href="/rank%20three%20temperament">rank three temperament</a> for which <a class="wiki_link" href="/283edo">283edo</a> is the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Bohpier"></a><!-- ws:end:WikiTextHeadingRule:0 -->Bohpier</h1> <a class="wiki_link" href="/Comma">Comma</a>s: 245/243, 3125/3087<br /> <br /> <a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: ~27/25 = 146.474<br /> <br /> Map: [<1 0 0 0|, <0 13 19 23|]<br /> <a class="wiki_link" href="/Wedgie">Wedgie</a>: <<13 19 23 0 0 0||<br /> EDOs: <a class="wiki_link" href="/41edo">41</a>, <a class="wiki_link" href="/49edo">49</a>, <a class="wiki_link" href="/90edo">90</a>, <a class="wiki_link" href="/139edo">139</a><br /> EDTs: <a class="wiki_link" href="/13edt">13</a><br /> <a class="wiki_link" href="/Badness">Badness</a>: 0.0682<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="Bohpier-11-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->11-limit</h2> Commas: 100/99, 245/243, 1344/1331<br /> <br /> POTE generator: ~12/11 = 146.545<br /> <br /> Map: [<1 0 0 0 0|, <0 13 19 23 12|]<br /> EDOs: 41, 90e, 131e<br /> Badness: 0.0339<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Bohpier-13-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->13-limit</h2> Commas: 100/99, 144/143, 245/243, 275/273<br /> <br /> POTE generator: ~12/11 = 146.603<br /> <br /> Map: [<1 0 0 0 0 0|, <0 13 19 23 12 14|]<br /> EDOs: 41, 90ef, 131ef, 221bdeff<br /> Badness: 0.0249<br /> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="Bohpier-Music"></a><!-- ws:end:WikiTextHeadingRule:6 -->Music</h2> By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br /> <!-- ws:start:WikiTextUrlRule:141:http://micro.soonlabel.com/bophier/bophier-1.mp3 --><a class="wiki_link_ext" href="http://micro.soonlabel.com/bophier/bophier-1.mp3" rel="nofollow">http://micro.soonlabel.com/bophier/bophier-1.mp3</a><!-- ws:end:WikiTextUrlRule:141 --><br /> <!-- ws:start:WikiTextUrlRule:142:http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3 --><a class="wiki_link_ext" href="http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3" rel="nofollow">http://micro.soonlabel.com/bophier/bophier-12equal-six-octaves.mp3</a><!-- ws:end:WikiTextUrlRule:142 --><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="Sensa"></a><!-- ws:end:WikiTextHeadingRule:8 -->Sensa</h1> Commas: 245/243, 65625/65536<br /> <br /> POTE generator: ~28/27 = 55.122<br /> <br /> Map: [<1 2 2 4|, <0 -9 7 -26|]<br /> Wedgie: <<9 -7 26 -32 16 80||<br /> EDOs: <a class="wiki_link" href="/22edo">22</a>, <a class="wiki_link" href="/43edo">43</a>, <a class="wiki_link" href="/65edo">65</a>, <a class="wiki_link" href="/87edo">87</a>, <a class="wiki_link" href="/109edo">109</a>, <a class="wiki_link" href="/196edo">196</a>, <a class="wiki_link" href="/283edo">283</a><br /> Badness: 0.0887<br /> <br /> <!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="Sensa-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> Commas: 245/243, 385/384, 4000/3993<br /> <br /> POTE generator: ~28/27 = 55.126<br /> <br /> Map: [<1 2 2 4 3|, <0 -9 7 -26 10|]<br /> EDOs: 22, 43, 65, 87, 109, 196, 283<br /> Badness: 0.0358<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Sensa-13-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->13-limit</h2> Commas: 245/243, 352/351, 385/384, 625/624<br /> <br /> POTE generator: ~28/27 = 55.138<br /> <br /> Map: [<1 2 2 4 3 2|, <0 -9 7 -26 10 37|]<br /> EDOs: 22, 43, 65, 87, 109, 196, 283<br /> Badness: 0.0317<br /> <br /> <!-- ws:start:WikiTextHeadingRule:14:<h1> --><h1 id="toc7"><a name="Salsa"></a><!-- ws:end:WikiTextHeadingRule:14 -->Salsa</h1> Commas: 245/243, 32805/32768<br /> <br /> POTE generator: ~128/105 = 351.049<br /> <br /> Map: [<1 1 7 -1|, <0 2 -16 13|]<br /> Wedgie: <<2 -16 13 -30 15 75||<br /> EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd<br /> Badness: 0.08015<br /> <br /> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Salsa-11-limit"></a><!-- ws:end:WikiTextHeadingRule:16 -->11-limit</h2> Commas: 243/242, 245/242, 385/384<br /> <br /> POTE generator: ~11/9 = 351.014<br /> <br /> Map: [<1 1 7 -1 2|, <0 2 -16 13 5|]<br /> EDOs: 17, 24, 41, 106d, 147d<br /> Badness: 0.0394<br /> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Pycnic"></a><!-- ws:end:WikiTextHeadingRule:18 -->Pycnic</h1> The fifth of pycnic in size is a meantone fifth, but four of them are not used to reach 5. This has the effect of making the Pythagorean major third, nominally 81/64, very close to 5/4 in tuning, being a cent sharp of it in the POTE tuning for instance. Pycnic has MOS of size 9, 11, 13, 15, 17... which contain these alternative thirds, leading to two kinds of major triads, an official one and a nominally Pythagorean one which is actually in better tune.<br /> <br /> Commas: 245/243, 525/512<br /> <br /> POTE generator: ~45/32 = 567.720<br /> <br /> Map: [<1 3 -1 8|, <0 -3 7 -11|]<br /> Wedgie: <<3 -7 11 -18 9 45||<br /> EDOs: 17, 19, 55c, 74cd, 93cd<br /> Badness: 0.0737</body></html>