Laconic family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
The Laconic family [[tempering_out|tempers out]] the [[Laconic_comma|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|gorgo]], which also tempers out 1029/1024.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-10-18 12:14:50 UTC</tt>.<br>
: The original revision id was <tt>266006216</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 [[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=  
=Laconic=
Comma: 2187/2000
Comma: 2187/2000


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


Map: [&lt;1 1 1|, &lt;0 3 7|&gt;
Map: [&lt;1 1 1|, &lt;0 3 7|&gt;
[[EDO]]s: [[5edo|5]], [[16edo|16]], [[21edo|21]], [[37edo|37]]b
[[Badness]]: 0.1618


==Gorgo==  
[[EDO|EDO]]s: [[5edo|5]], [[16edo|16]], [[21edo|21]], [[37edo|37]]b
 
[[Badness|Badness]]: 0.1618
 
==Gorgo==
Commas: 36/35, 1029/1024
Commas: 36/35, 1029/1024


Line 23: Line 18:


Map: [&lt;1 1 1 3|, &lt;0 3 7 -1|&gt;
Map: [&lt;1 1 1 3|, &lt;0 3 7 -1|&gt;
EDOs: 5, 16, 21, 37b
EDOs: 5, 16, 21, 37b
Badness: 0.0607
Badness: 0.0607


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


Line 32: Line 29:


Map: [&lt;1 1 1 3 1|, &lt;0 3 7 -1 13|&gt;
Map: [&lt;1 1 1 3 1|, &lt;0 3 7 -1 13|&gt;
EDOs: 16, 21, 37b
EDOs: 16, 21, 37b
Badness: 0.0495
Badness: 0.0495


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


Line 41: Line 40:


Map: [&lt;1 1 1 3 1 2|, &lt;0 3 7 -1 13 9|&gt;
Map: [&lt;1 1 1 3 1 2|, &lt;0 3 7 -1 13 9|&gt;
EDOs 16, 21, 37b
EDOs 16, 21, 37b
Badness: 0.0327
Badness: 0.0327


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


Line 50: Line 51:


Map: [&lt;1 1 1 3 5|, &lt;0 3 7 -1 -8|&gt;
Map: [&lt;1 1 1 3 5|, &lt;0 3 7 -1 -8|&gt;
EDOs: 5, 21
EDOs: 5, 21
Badness: 0.0627</pre></div>
 
<h4>Original HTML content:</h4>
Badness: 0.0627
<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 &lt;a class="wiki_link" href="/tempering%20out"&gt;tempers out&lt;/a&gt; the &lt;a class="wiki_link" href="/Laconic%20comma"&gt;Laconic comma&lt;/a&gt;, 2187/2000, which is the difference between three &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;'s and a &lt;a class="wiki_link" href="/3_2"&gt;3/2&lt;/a&gt;. 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 &lt;a class="wiki_link" href="/gorgo"&gt;gorgo&lt;/a&gt;, which also tempers out 1029/1024.&lt;br /&gt;
[[Category:family]]
&lt;br /&gt;
[[Category:laconic]]
&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;
&lt;a class="wiki_link" href="/POTE%20generator"&gt;POTE generator&lt;/a&gt;: ~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;
&lt;a class="wiki_link" href="/EDO"&gt;EDO&lt;/a&gt;s: &lt;a class="wiki_link" href="/5edo"&gt;5&lt;/a&gt;, &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/21edo"&gt;21&lt;/a&gt;, &lt;a class="wiki_link" href="/37edo"&gt;37&lt;/a&gt;b&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 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-Gorgo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Gorgo&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>

Revision as of 00:00, 17 July 2018

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. 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|>

EDOs: 5, 16, 21, 37b

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

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