Laconic family

Revision as of 12:14, 18 October 2011 by Wikispaces>keenanpepper (**Imported revision 266006216 - Original comment: **)

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This revision was by author keenanpepper and made on 2011-10-18 12:14:50 UTC.
The original revision id was 266006216.
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Original Wikitext content:

The Laconic family [[tempering out|tempers out]] the [[Laconic comma]], 2187/2000, which is the difference between three [[10_9|10/9]]'s and a [[3_2|3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in 16-EDO and 21-EDO. The only 7-limit extension that makes any sense to use is [[gorgo]], which also tempers out 1029/1024.

=Laconic= 
Comma: 2187/2000

[[POTE generator]]: ~10/9 = 227.426

Map: [<1 1 1|, <0 3 7|>
[[EDO]]s: [[5edo|5]], [[16edo|16]], [[21edo|21]], [[37edo|37]]b
[[Badness]]: 0.1618

==Gorgo== 
Commas: 36/35, 1029/1024

POTE generator: ~8/7 = 228.334

Map: [<1 1 1 3|, <0 3 7 -1|>
EDOs: 5, 16, 21, 37b
Badness: 0.0607

==11-limit== 
Commas: 36/35, 45/44, 1029/1024

POTE generator: ~8/7 = 227.373

Map: [<1 1 1 3 1|, <0 3 7 -1 13|>
EDOs: 16, 21, 37b
Badness: 0.0495

==13-limit== 
Commas: 27/26, 36/35, 45/55, 507/500

POTE generator: ~8/7 = 227.230

Map: [<1 1 1 3 1 2|, <0 3 7 -1 13 9|>
EDOs 16, 21, 37b
Badness: 0.0327

=Spartan= 
Commas: 36/35, 56/55, 1029/1024

POTE generator: ~8/7 = 229.535

Map: [<1 1 1 3 5|, <0 3 7 -1 -8|>
EDOs: 5, 21
Badness: 0.0627

Original HTML content:

<html><head><title>Laconic Family</title></head><body>The Laconic family <a class="wiki_link" href="/tempering%20out">tempers out</a> the <a class="wiki_link" href="/Laconic%20comma">Laconic comma</a>, 2187/2000, which is the difference between three <a class="wiki_link" href="/10_9">10/9</a>'s and a <a class="wiki_link" href="/3_2">3/2</a>. Although a higher-error temperament, it does pop up enough in the low-numbered EDOs to be useful, most notably in 16-EDO and 21-EDO. The only 7-limit extension that makes any sense to use is <a class="wiki_link" href="/gorgo">gorgo</a>, which also tempers out 1029/1024.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Laconic"></a><!-- ws:end:WikiTextHeadingRule:0 -->Laconic</h1>
 Comma: 2187/2000<br />
<br />
<a class="wiki_link" href="/POTE%20generator">POTE generator</a>: ~10/9 = 227.426<br />
<br />
Map: [&lt;1 1 1|, &lt;0 3 7|&gt;<br />
<a class="wiki_link" href="/EDO">EDO</a>s: <a class="wiki_link" href="/5edo">5</a>, <a class="wiki_link" href="/16edo">16</a>, <a class="wiki_link" href="/21edo">21</a>, <a class="wiki_link" href="/37edo">37</a>b<br />
<a class="wiki_link" href="/Badness">Badness</a>: 0.1618<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Laconic-Gorgo"></a><!-- ws:end:WikiTextHeadingRule:2 -->Gorgo</h2>
 Commas: 36/35, 1029/1024<br />
<br />
POTE generator: ~8/7 = 228.334<br />
<br />
Map: [&lt;1 1 1 3|, &lt;0 3 7 -1|&gt;<br />
EDOs: 5, 16, 21, 37b<br />
Badness: 0.0607<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Laconic-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2>
 Commas: 36/35, 45/44, 1029/1024<br />
<br />
POTE generator: ~8/7 = 227.373<br />
<br />
Map: [&lt;1 1 1 3 1|, &lt;0 3 7 -1 13|&gt;<br />
EDOs: 16, 21, 37b<br />
Badness: 0.0495<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Laconic-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2>
 Commas: 27/26, 36/35, 45/55, 507/500<br />
<br />
POTE generator: ~8/7 = 227.230<br />
<br />
Map: [&lt;1 1 1 3 1 2|, &lt;0 3 7 -1 13 9|&gt;<br />
EDOs 16, 21, 37b<br />
Badness: 0.0327<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Spartan"></a><!-- ws:end:WikiTextHeadingRule:8 -->Spartan</h1>
 Commas: 36/35, 56/55, 1029/1024<br />
<br />
POTE generator: ~8/7 = 229.535<br />
<br />
Map: [&lt;1 1 1 3 5|, &lt;0 3 7 -1 -8|&gt;<br />
EDOs: 5, 21<br />
Badness: 0.0627</body></html>