Laconic family: Difference between revisions

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**Imported revision 265829804 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
#redirect [[Syntonic–diatonic equivalence continuum #Laconic]]
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>2011-10-18 01:21:30 UTC</tt>.<br>
: The original revision id was <tt>265829804</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>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The Laconic family tempers out the Laconic comma, 2187/2000, which is the difference between three 10/9's and a 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.
 
=Laconic=
Comma: 2187/2000
 
POTE generator: ~10/9 = 227.426
 
Map: [&lt;1 1 1|, &lt;0 3 7|&gt;
EDOs: 5, 16, 21, 37b
Badness: 0.1618
 
==7-limit==
Commas: 36/35, 1029/1024
 
POTE generator: ~8/7 = 228.334
 
Map: [&lt;1 1 1 3|, &lt;0 3 7 -1|&gt;
EDOs: 5, 16, 21, 37b
Badness: 0.0607
 
==11-limit==
Commas: 36/35, 45/44, 1029/1024
 
POTE generator: ~8/7 = 227.373
 
Map: [&lt;1 1 1 3 1|, &lt;0 3 7 -1 13|&gt;
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: [&lt;1 1 1 3 1 2|, &lt;0 3 7 -1 13 9|&gt;
EDOs 16, 21, 37b
Badness: 0.0327
 
=Spartan=
Commas: 36/35, 56/55, 1029/1024
 
POTE generator: ~8/7 = 229.535
 
Map: [&lt;1 1 1 3 5|, &lt;0 3 7 -1 -8|&gt;
EDOs: 5, 21
Badness: 0.0627</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Laconic Family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The Laconic family tempers out the Laconic comma, 2187/2000, which is the difference between three 10/9's and a 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.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Laconic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Laconic&lt;/h1&gt;
Comma: 2187/2000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10/9 = 227.426&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1|, &amp;lt;0 3 7|&amp;gt;&lt;br /&gt;
EDOs: 5, 16, 21, 37b&lt;br /&gt;
Badness: 0.1618&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Laconic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
Commas: 36/35, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 228.334&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3|, &amp;lt;0 3 7 -1|&amp;gt;&lt;br /&gt;
EDOs: 5, 16, 21, 37b&lt;br /&gt;
Badness: 0.0607&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Laconic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
Commas: 36/35, 45/44, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 227.373&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3 1|, &amp;lt;0 3 7 -1 13|&amp;gt;&lt;br /&gt;
EDOs: 16, 21, 37b&lt;br /&gt;
Badness: 0.0495&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Laconic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
Commas: 27/26, 36/35, 45/55, 507/500&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 227.230&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3 1 2|, &amp;lt;0 3 7 -1 13 9|&amp;gt;&lt;br /&gt;
EDOs 16, 21, 37b&lt;br /&gt;
Badness: 0.0327&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Spartan"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Spartan&lt;/h1&gt;
Commas: 36/35, 56/55, 1029/1024&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~8/7 = 229.535&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 1 1 3 5|, &amp;lt;0 3 7 -1 -8|&amp;gt;&lt;br /&gt;
EDOs: 5, 21&lt;br /&gt;
Badness: 0.0627&lt;/body&gt;&lt;/html&gt;</pre></div>

Latest revision as of 14:24, 21 January 2025