Dimcomp family: Difference between revisions

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**Imported revision 268652836 - Original comment: **
 
+ intro to octopod
 
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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 03:12:22 UTC</tt>.<br>
: The original revision id was <tt>268652836</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</pre></div>
 
<h4>Original HTML content:</h4>
{{Mapping|legend=1| 4 0 0 -1 | 0 1 0 -1 | 0 0 1 2 }}
<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;
: mapping generators: ~25/21, ~3, ~5
&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;
[[Optimal tuning]]s:
Commas: 390625/388962&lt;br /&gt;
* [[WE]]: ~25/21 = 300.0036{{c}}, ~3/2 = 702.0854{{c}}, ~5/4 = 385.6631{{c}}
&lt;br /&gt;
: [[error map]]: {{val| +0.014 +0.145 -0.622 +0.454 }}
Map: [&amp;lt;4 0 0 -1|, &amp;lt;0 1 0 -1|, &amp;lt;0 0 1 2|]&lt;br /&gt;
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0885{{c}}, ~5/4 = 385.6745{{c}}
EDOs: 12, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952&lt;/body&gt;&lt;/html&gt;</pre></div>
: error map: {{val| 0.000 +0.133 -0.639 +0.435 }}
 
{{Optimal ET sequence|legend=1| 12, 44d, 48d, 56, 60, 68, 72, 140, 152, 212, 224, 364, 588, 952 }}
 
[[Badness]] (Sintel): 3.45
 
== Undecimal dimcomp ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 1375/1372, 6250/6237
 
{{Mapping|legend=1| 4 0 0 -1 5 | 0 1 0 -1 -3 | 0 0 1 2 3 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~25/21 = 300.0093{{c}}, ~3/2 = 701.9976{{c}}, ~5/4 = 385.6591{{c}}
: [[error map]]: {{val| +0.037 +0.080 -0.580 +0.597 -0.176 }}
* [[CWE]]: ~25/21 = 300.0000{{c}}, ~3/2 = 702.0009{{c}}, ~5/4 = 385.6895{{c}}
: error map: {{val| 0.000 +0.046 -0.624 +0.552 -0.252 }}
 
{{Optimal ET sequence|legend=1| 12, …, 68, 72, 140, 152, 224, 364, 436, 588 }}
 
[[Badness]] (Sintel): 0.751
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 625/624, 1375/1372, 2080/2079
 
Mapping: {{mapping| 4 0 0 -1 5 -16 | 0 1 0 -1 -3 -1 | 0 0 1 2 3 4 }}
 
Optimal tunings:
* WE: ~25/21 = 300.0140{{c}}, ~3/2 = 701.9679{{c}}, ~5/4 = 385.5977{{c}}
* CWE: ~25/21 = 300.0000{{c}}, ~3/2 = 701.9549{{c}}, ~5/4 = 385.6140{{c}}
 
{{Optimal ET sequence|legend=0| 68, 72, 140, 152f, 212, 224, 364, 436, 588, 660, 1024c }}
 
Badness (Sintel): 0.767
 
== Octopod ==
Octopod is [[octoid]] with an independent generator for [[prime interval|prime]] [[13/1|13]].
 
[[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]]

Latest revision as of 08:41, 12 February 2026

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 (monzo: [-1 -4 8 -4⟩, ratio: 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 tunings:

  • WE: ~25/21 = 300.0036 ¢, ~3/2 = 702.0854 ¢, ~5/4 = 385.6631 ¢
error map: ⟨+0.014 +0.145 -0.622 +0.454]
  • CWE: ~25/21 = 300.0000 ¢, ~3/2 = 702.0885 ¢, ~5/4 = 385.6745 ¢
error map: ⟨0.000 +0.133 -0.639 +0.435]

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

Badness (Sintel): 3.45

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 tunings:

  • WE: ~25/21 = 300.0093 ¢, ~3/2 = 701.9976 ¢, ~5/4 = 385.6591 ¢
error map: ⟨+0.037 +0.080 -0.580 +0.597 -0.176]
  • CWE: ~25/21 = 300.0000 ¢, ~3/2 = 702.0009 ¢, ~5/4 = 385.6895 ¢
error map: ⟨0.000 +0.046 -0.624 +0.552 -0.252]

Optimal ET sequence: 12, …, 68, 72, 140, 152, 224, 364, 436, 588

Badness (Sintel): 0.751

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 tunings:

  • WE: ~25/21 = 300.0140 ¢, ~3/2 = 701.9679 ¢, ~5/4 = 385.5977 ¢
  • CWE: ~25/21 = 300.0000 ¢, ~3/2 = 701.9549 ¢, ~5/4 = 385.6140 ¢

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

Badness (Sintel): 0.767

Octopod

Octopod is octoid with an independent generator for prime 13.

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]]

mapping generators: ~12/11, ~7/5, ~13

Optimal tunings:

  • WE: ~12/11 = 150.0093 ¢, ~7/5 = 583.9356 ¢, ~13/8 = 840.6906 ¢
error map: ⟨-0.055 -0.155 -0.592 +0.832 +0.380 -0.001]
  • CWE: ~12/11 = 150.0000 ¢, ~7/5 = 583.9477 ¢, ~13/8 = 840.6394 ¢
error map: ⟨0.000 -0.112 -0.523 +0.913 +0.525 +0.112]

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

Badness (Sintel): 1.16

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