Dimcomp family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 268658448 - Original comment: **
 
(15 intermediate revisions by 7 users not shown)
Line 1: Line 1:
<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]]s tempers out the [[dimcomp comma]], 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


Map: [&lt;4 0 0 -1 5|, &lt;0 1 0 -1 -3|, &lt;0 0 1 2 3|]
: mapping generators: ~25/21, ~3, ~5
EDOs: 12, 68, 72, 140, 152, 224, 364, 436, 588
Badness: 0.000624


==13-limit==
{{Optimal ET sequence|legend=1| 8d, 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]]: 0.783 × 10<sup>-3</sup>
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 ET sequence|legend=1| 68, 72, 140, 152, 224, 364, 436, 588 }}
&lt;br /&gt;
 
&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;
[[Badness]]: 0.624 × 10<sup>-3</sup>
Commas: 390625/388962&lt;br /&gt;
 
&lt;br /&gt;
=== 13-limit ===
Map: [&amp;lt;4 0 0 -1|, &amp;lt;0 1 0 -1|, &amp;lt;0 0 1 2|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
EDOs: 12, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952&lt;br /&gt;
 
Badness: 0.000783&lt;br /&gt;
Comma list: 625/624, 1375/1372, 2080/2079
&lt;br /&gt;
 
&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;
Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}
Commas: 1375/1372, 6250/6237&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
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;
Badness: 0.820 × 10<sup>-3</sup>
Badness: 0.000624&lt;br /&gt;
 
&lt;br /&gt;
== Octopod ==
&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;
Subgroup: 2.3.5.7.11.13
Commas: 625/624, 1375/1372, 2080/2079&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 540/539, 1375/1372, 4000/3993
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;
 
EDOs: 68, 72, 140, 212, 224, 364, 436, 588, 660&lt;br /&gt;
Mapping: {{mapping| 8 1 3 3 16 0 | 0 3 4 5 3 0 | 0 0 0 0 0 1 }}
Badness: 0.000820&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 72, 144, 152f, 224, 824d }}
&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;
 
Commas: 540/539, 1375/1372, 4000/3993&lt;br /&gt;
Badness: 1.244 × 10<sup>-3</sup>
&lt;br /&gt;
 
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;
[[Category:Temperament families]]
EDOs: 72, 144, 152, 224&lt;br /&gt;
[[Category:Pages with mostly numerical content]]
Badness: 0.001244&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:Dimcomp family| ]] <!-- main article -->
[[Category:Dimcomp| ]] <!-- key article -->
[[Category:Rank 3]]

Latest revision as of 00:31, 24 June 2025

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, 390625/388962.

Dimcomp

Subgroup: 2.3.5.7

Comma list: 390625/388962

Mapping: [⟨4 0 0 -1], ⟨0 1 0 -1], ⟨0 0 1 2]]

mapping generators: ~25/21, ~3, ~5

Optimal ET sequence: 8d, 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952

Badness: 0.783 × 10-3

Undecimal dimcomp

Subgroup: 2.3.5.7.11

Comma list: 1375/1372, 6250/6237

Mapping: [⟨4 0 0 -1 5], ⟨0 1 0 -1 -3], ⟨0 0 1 2 3]]

Optimal ET sequence: 68, 72, 140, 152, 224, 364, 436, 588

Badness: 0.624 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 1375/1372, 2080/2079

Mapping: [⟨4 0 0 -1 5 -16], ⟨0 1 0 -1 -3 -1], ⟨0 0 1 2 3 4]]

Optimal ET sequence: 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c

Badness: 0.820 × 10-3

Octopod

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 1375/1372, 4000/3993

Mapping: [⟨8 1 3 3 16 0], ⟨0 3 4 5 3 0], ⟨0 0 0 0 0 1]]

Optimal ET sequence: 72, 144, 152f, 224, 824d

Badness: 1.244 × 10-3

Retrieved from "https://en.xen.wiki/index.php?title=Dimcomp_family&oldid=200893"