Sensamagic clan

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Revision as of 14:50, 20 May 2012 by Wikispaces>genewardsmith (**Imported revision 337597096 - Original comment: **)
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This revision was by author genewardsmith and made on 2012-05-20 14:50:32 UTC.
The original revision id was 337597096.
The revision comment was:

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[[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: 1220703125/1162261467

POTE generator: ~27/25 = 146.476

Map: [<1 0 0|, <0 13 19|]
EDOs: 8, 41, 131, 172, 213c
Badness: 0.8605

==7-limit==
[[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

==13-limit==
Commas: 105/104, 144/143, 243/242, 245/242

POTE generator: ~11/9 = 351.025

Map: [<1 1 7 -1 2 4|, <0 2 -16 13 5 -1|]
EDOs: 17, 24, 41, 106df, 147df
Badness: 0.0310

=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

=Cohemiripple=
Commas: 245/243, 1323/1250

POTE generator: ~7/5 = 549.944

Map: [<1 7 11 12|, <0 -10 -16 -17|]
Wedgie: <<10 16 17 2 -1 -5||
EDOs: 24
Badness: 0.1902

==11-limit==
Commas: 77/75, 243/242, 245/242

POTE generator: ~7/5 = 549.945

Map: [<1 7 11 12 17|, <0 -10 -16 -17 -25|]
EDOs: 24
Badness: 0.0827

==13-limit==
Commas: 66/65, 77/75, 147/143, 351/350

POTE generator: ~7/5 = 549.958

Map: [<1 7 11 12 17 14|, <0 -10 -16 -17 -25 -19|]
EDOs: 24
Badness: 0.0499

=Superthird=
Commas: 245/243, 78125/76832

POTE generator: ~9/7 = 439.076

Map: [<1 13 15 25|, <0 -18 -20 -35|]
Wedgie: <<18 20 35 -10 5 25||
EDOs: 41, 317bc, 358bc, 399bc
Badness: 0.1394

==11-limit==
Commas: 100/99, 245/243, 78125/76832

POTE generator: ~9/7 = 439.152

Map: [<1 13 15 25 6|, <0 -18 -20 -35 -4|]
EDOs: 41, 153be, 194be, 235bce
Badness: 0.0709

==13-limit==
Commas: 100/99, 144/143, 196/195, 1375/1352

POTE generator: ~9/7 = 439.119

Map: [<1 13 15 25 6 24|, <0 -18 -20 -35 -4 -32|]
EDOs: 41
Badness: 0.0528



Original HTML content:

<html><head><title>Sensamagic clan</title></head><body><!-- ws:start:WikiTextTocRule:36:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><a href="#Bohpier">Bohpier</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Sensa">Sensa</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Salsa">Salsa</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --> | <a href="#Pycnic">Pycnic</a><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Cohemiripple">Cohemiripple</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Superthird">Superthird</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: -->
<!-- ws:end:WikiTextTocRule:55 --><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&gt; 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:&lt;h1&gt; --><h1 id="toc0"><a name="Bohpier"></a><!-- ws:end:WikiTextHeadingRule:0 -->Bohpier</h1>
 Comma: 1220703125/1162261467<br />
<br />
POTE generator: ~27/25 = 146.476<br />
<br />
Map: [&lt;1 0 0|, &lt;0 13 19|]<br />
EDOs: 8, 41, 131, 172, 213c<br />
Badness: 0.8605<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Bohpier-7-limit"></a><!-- ws:end:WikiTextHeadingRule:2 -->7-limit</h2>
<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: [&lt;1 0 0 0|, &lt;0 13 19 23|]<br />
<a class="wiki_link" href="/Wedgie">Wedgie</a>: &lt;&lt;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:4:&lt;h2&gt; --><h2 id="toc2"><a name="Bohpier-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
Commas: 100/99, 245/243, 1344/1331<br />
<br />
POTE generator: ~12/11 = 146.545<br />
<br />
Map: [&lt;1 0 0 0 0|, &lt;0 13 19 23 12|]<br />
EDOs: 41, 90e, 131e<br />
Badness: 0.0339<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Bohpier-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
Commas: 100/99, 144/143, 245/243, 275/273<br />
<br />
POTE generator: ~12/11 = 146.603<br />
<br />
Map: [&lt;1 0 0 0 0 0|, &lt;0 13 19 23 12 14|]<br />
EDOs: 41, 90ef, 131ef, 221bdeff<br />
Badness: 0.0249<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Bohpier-Music"></a><!-- ws:end:WikiTextHeadingRule:8 -->Music</h2>
By <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a><br />
<!-- ws:start:WikiTextUrlRule:231: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:231 --><br />
<!-- ws:start:WikiTextUrlRule:232: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:232 --><br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="Sensa"></a><!-- ws:end:WikiTextHeadingRule:10 -->Sensa</h1>
 Commas: 245/243, 65625/65536<br />
<br />
POTE generator: ~28/27 = 55.122<br />
<br />
Map: [&lt;1 2 2 4|, &lt;0 -9 7 -26|]<br />
Wedgie: &lt;&lt;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:12:&lt;h2&gt; --><h2 id="toc6"><a name="Sensa-11-limit"></a><!-- ws:end:WikiTextHeadingRule:12 -->11-limit</h2>
 Commas: 245/243, 385/384, 4000/3993<br />
<br />
POTE generator: ~28/27 = 55.126<br />
<br />
Map: [&lt;1 2 2 4 3|, &lt;0 -9 7 -26 10|]<br />
EDOs: 22, 43, 65, 87, 109, 196, 283<br />
Badness: 0.0358<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Sensa-13-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->13-limit</h2>
 Commas: 245/243, 352/351, 385/384, 625/624<br />
<br />
POTE generator: ~28/27 = 55.138<br />
<br />
Map: [&lt;1 2 2 4 3 2|, &lt;0 -9 7 -26 10 37|]<br />
EDOs: 22, 43, 65, 87, 109, 196, 283<br />
Badness: 0.0317<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Salsa"></a><!-- ws:end:WikiTextHeadingRule:16 -->Salsa</h1>
Commas: 245/243, 32805/32768<br />
<br />
POTE generator: ~128/105 = 351.049<br />
<br />
Map: [&lt;1 1 7 -1|, &lt;0 2 -16 13|]<br />
Wedgie: &lt;&lt;2 -16 13 -30 15 75||<br />
EDOs: 17, 24, 41, 106d, 147d, 188cd, 335cd<br />
Badness: 0.08015<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Salsa-11-limit"></a><!-- ws:end:WikiTextHeadingRule:18 -->11-limit</h2>
Commas: 243/242, 245/242, 385/384<br />
<br />
POTE generator: ~11/9 = 351.014<br />
<br />
Map: [&lt;1 1 7 -1 2|, &lt;0 2 -16 13 5|]<br />
EDOs: 17, 24, 41, 106d, 147d<br />
Badness: 0.0394<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Salsa-13-limit"></a><!-- ws:end:WikiTextHeadingRule:20 -->13-limit</h2>
Commas: 105/104, 144/143, 243/242, 245/242<br />
<br />
POTE generator: ~11/9 = 351.025<br />
<br />
Map: [&lt;1 1 7 -1 2 4|, &lt;0 2 -16 13 5 -1|]<br />
EDOs: 17, 24, 41, 106df, 147df<br />
Badness: 0.0310<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Pycnic"></a><!-- ws:end:WikiTextHeadingRule:22 -->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: [&lt;1 3 -1 8|, &lt;0 -3 7 -11|]<br />
Wedgie: &lt;&lt;3 -7 11 -18 9 45||<br />
EDOs: 17, 19, 55c, 74cd, 93cd<br />
Badness: 0.0737<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Cohemiripple"></a><!-- ws:end:WikiTextHeadingRule:24 -->Cohemiripple</h1>
Commas: 245/243, 1323/1250<br />
<br />
POTE generator: ~7/5 = 549.944<br />
<br />
Map: [&lt;1 7 11 12|, &lt;0 -10 -16 -17|]<br />
Wedgie: &lt;&lt;10 16 17 2 -1 -5||<br />
EDOs: 24<br />
Badness: 0.1902<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Cohemiripple-11-limit"></a><!-- ws:end:WikiTextHeadingRule:26 -->11-limit</h2>
Commas: 77/75, 243/242, 245/242<br />
<br />
POTE generator: ~7/5 = 549.945<br />
<br />
Map: [&lt;1 7 11 12 17|, &lt;0 -10 -16 -17 -25|]<br />
EDOs: 24<br />
Badness: 0.0827<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Cohemiripple-13-limit"></a><!-- ws:end:WikiTextHeadingRule:28 -->13-limit</h2>
Commas: 66/65, 77/75, 147/143, 351/350<br />
<br />
POTE generator: ~7/5 = 549.958<br />
<br />
Map: [&lt;1 7 11 12 17 14|, &lt;0 -10 -16 -17 -25 -19|]<br />
EDOs: 24<br />
Badness: 0.0499<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Superthird"></a><!-- ws:end:WikiTextHeadingRule:30 -->Superthird</h1>
Commas: 245/243, 78125/76832<br />
<br />
POTE generator: ~9/7 = 439.076<br />
<br />
Map: [&lt;1 13 15 25|, &lt;0 -18 -20 -35|]<br />
Wedgie: &lt;&lt;18 20 35 -10 5 25||<br />
EDOs: 41, 317bc, 358bc, 399bc<br />
Badness: 0.1394<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Superthird-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2>
Commas: 100/99, 245/243, 78125/76832<br />
<br />
POTE generator: ~9/7 = 439.152<br />
<br />
Map: [&lt;1 13 15 25 6|, &lt;0 -18 -20 -35 -4|]<br />
EDOs: 41, 153be, 194be, 235bce<br />
Badness: 0.0709<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Superthird-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2>
Commas: 100/99, 144/143, 196/195, 1375/1352<br />
<br />
POTE generator: ~9/7 = 439.119<br />
<br />
Map: [&lt;1 13 15 25 6 24|, &lt;0 -18 -20 -35 -4 -32|]<br />
EDOs: 41<br />
Badness: 0.0528</body></html>