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Dimcomp family: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Technical data page}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
The '''dimcomp family''' of [[rank-3 temperament|rank-3]] [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[dimcomp comma]] ({{monzo|legend=1| -1 -4 8 -4 }}, [[ratio]]: 390625/388962).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-10-26 03:54:48 UTC</tt>.<br>
: The original revision id was <tt>268658448</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 dimcomp family of rank three temperaments tempers out the dimcomp comma, 390625/388962.


=Dimcomp=
== Dimcomp ==
Commas: 390625/388962
[[Subgroup]]: 2.3.5.7


Map: [&lt;4 0 0 -1|, &lt;0 1 0 -1|, &lt;0 0 1 2|]
[[Comma list]]: 390625/388962
EDOs: 12, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952
Badness: 0.000783


==11-limit==
{{Mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }}
Commas: 1375/1372, 6250/6237
: mapping generators: ~25/21, ~3, ~5


Map: [&lt;4 0 0 -1 5|, &lt;0 1 0 -1 -3|, &lt;0 0 1 2 3|]
[[Optimal tuning]]s:  
EDOs: 12, 68, 72, 140, 152, 224, 364, 436, 588
* [[WE]]: ~25/21 = 300.0036{{c}}, ~3/2 = 702.0854{{c}}, ~5/4 = 385.6631{{c}}
Badness: 0.000624
: [[error map]]: {{val| +0.014 +0.145 -0.622 +0.454 }}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0885{{c}}, ~5/4 = 385.6745{{c}}
: error map: {{val| 0.000 +0.133 -0.639 +0.435 }}


==13-limit==
{{Optimal ET sequence|legend=1| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
Commas: 625/624, 1375/1372, 2080/2079


Map: [&lt;4 0 0 -1 5 -16|, &lt;0 1 0 -1 -3 -1|, &lt;0 0 1 2 3 4|]
[[Badness]] (Sintel): 3.45
EDOs: 68, 72, 140, 212, 224, 364, 436, 588, 660
Badness: 0.000820


=Octopus=
== Undecimal dimcomp ==
Commas: 540/539, 1375/1372, 4000/3993
[[Subgroup]]: 2.3.5.7.11


Map: [&lt;8 1 3 3 16 0|, &lt;0 3 4 5 3 0|, &lt;0 0 0 0 0 1|]
[[Comma list]]: 1375/1372, 6250/6237
EDOs: 72, 144, 152, 224
 
Badness: 0.001244</pre></div>
{{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }}
<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;Dimcomp family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The dimcomp family of rank three temperaments tempers out the dimcomp comma, 390625/388962.&lt;br /&gt;
[[Optimal tuning]]s:
&lt;br /&gt;
* [[WE]]: ~25/21 = 300.0093{{c}}, ~3/2 = 701.9976{{c}}, ~5/4 = 385.6591{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Dimcomp"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Dimcomp&lt;/h1&gt;
: [[error map]]: {{val| +0.037 +0.080 -0.580 +0.597 -0.176 }}
Commas: 390625/388962&lt;br /&gt;
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0009{{c}}, ~5/4 = 385.6895{{c}}
&lt;br /&gt;
: error map: {{val| 0.000 +0.046 -0.624 +0.552 -0.252 }}
Map: [&amp;lt;4 0 0 -1|, &amp;lt;0 1 0 -1|, &amp;lt;0 0 1 2|]&lt;br /&gt;
 
EDOs: 12, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952&lt;br /&gt;
{{Optimal ET sequence|legend=1| 12, …, 68, 72, 140, 152, 224, 364, 436, 588 }}
Badness: 0.000783&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 0.751
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Dimcomp-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
 
Commas: 1375/1372, 6250/6237&lt;br /&gt;
=== 13-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Map: [&amp;lt;4 0 0 -1 5|, &amp;lt;0 1 0 -1 -3|, &amp;lt;0 0 1 2 3|]&lt;br /&gt;
 
EDOs: 12, 68, 72, 140, 152, 224, 364, 436, 588&lt;br /&gt;
Comma list: 625/624, 1375/1372, 2080/2079
Badness: 0.000624&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Dimcomp-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
 
Commas: 625/624, 1375/1372, 2080/2079&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* WE: ~25/21 = 300.0140{{c}}, ~3/2 = 701.9679{{c}}, ~5/4 = 385.5977{{c}}
Map: [&amp;lt;4 0 0 -1 5 -16|, &amp;lt;0 1 0 -1 -3 -1|, &amp;lt;0 0 1 2 3 4|]&lt;br /&gt;
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.9549{{c}}, ~5/4 = 385.6140{{c}}
EDOs: 68, 72, 140, 212, 224, 364, 436, 588, 660&lt;br /&gt;
 
Badness: 0.000820&lt;br /&gt;
{{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Octopus"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Octopus&lt;/h1&gt;
Badness (Sintel): 0.767
Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
 
&lt;br /&gt;
== Octopod ==
Map: [&amp;lt;8 1 3 3 16 0|, &amp;lt;0 3 4 5 3 0|, &amp;lt;0 0 0 0 0 1|]&lt;br /&gt;
Octopod is [[octoid]] with an independent generator for [[prime interval|prime]] [[13/1|13]].
EDOs: 72, 144, 152, 224&lt;br /&gt;
 
Badness: 0.001244&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Subgroup]]: 2.3.5.7.11.13
 
[[Comma list]]: 540/539, 1375/1372, 4000/3993
 
{{Mapping|legend=1| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }}
: mapping generators: ~12/11, ~7/5, ~13
 
[[Optimal tuning]]s:
* [[WE]]: ~12/11 = 150.0093{{c}}, ~7/5 = 583.9356{{c}}, ~13/8 = 840.6906{{c}}
: [[error map]]: {{val| -0.055 -0.155 -0.592 +0.832 +0.380 -0.001 }}
* [[CWE]]: ~12/11 = 150.0000{{c}}, ~7/5 = 583.9477{{c}}, ~13/8 = 840.6394{{c}}
: error map: {{val| 0.000 -0.112 -0.523 +0.913 +0.525 +0.112 }}
 
{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }}
 
[[Badness]] (Sintel): 1.16
 
[[Category:Temperament families]]
[[Category:Dimcomp family| ]] <!-- main article -->
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Dimcomp_family"