Porcupine rank three 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 '''porcupine rank-3 family''' of [[temperament]]s [[tempering out|tempers out]] the porcupine comma or maximal diesis, [[250/243]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-13 01:02:52 UTC</tt>.<br>
: The original revision id was <tt>291887545</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">These are the rank three temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.  


==Sonic==
== Rank-3 porcupine ==
Commas: 55/54, 100/99
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 2 3 0 4|, &lt;0 -3 -5 0 -4|, &lt;0 0 0 1 0|]
[[Comma list]]: [[250/243]]
Generators: ~10/9 = 164.078, ~7 = 3367.841
EDOs: 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce
Badness: 0.000523


==Tikal==
{{Mapping|legend=1| 1 2 3 0 | 0 -3 -5 0 | 0 0 0 1 }}
Commas: 56/55, 250/243


Map: [&lt;1 2 3 0 0], &lt;0 -3 -5 0 5|, &lt;0 0 0 1 1|]
: mapping generators: ~2, ~10/9, ~7
POTE generators: ~10/9 = 161.519, ~7 = 3371.046
 
EDOs: 15, 37e, 52be
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552
Badness: 0.001973</pre></div>
 
<h4>Original HTML content:</h4>
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
<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;Porcupine rank three family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;These are the rank three temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. &lt;br /&gt;
 
&lt;br /&gt;
[[Badness]]: 0.535 × 10<sup>-3</sup>
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Sonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Sonic&lt;/h2&gt;
 
Commas: 55/54, 100/99&lt;br /&gt;
== Sonic ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7.11
Map: [&amp;lt;1 2 3 0 4|, &amp;lt;0 -3 -5 0 -4|, &amp;lt;0 0 0 1 0|]&lt;br /&gt;
 
Generators: ~10/9 = 164.078, ~7 = 3367.841&lt;br /&gt;
[[Comma list]]: 55/54, 100/99
EDOs: 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce&lt;br /&gt;
 
Badness: 0.000523&lt;br /&gt;
{{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Tikal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Tikal&lt;/h2&gt;
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/10 = 164.0777, ~7/4 = 967.8413
Commas: 56/55, 250/243&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
Map: [&amp;lt;1 2 3 0 0], &amp;lt;0 -3 -5 0 5|, &amp;lt;0 0 0 1 1|]&lt;br /&gt;
 
POTE generators: ~10/9 = 161.519, ~7 = 3371.046&lt;br /&gt;
[[Badness]]: 0.523 × 10<sup>-3</sup>
EDOs: 15, 37e, 52be&lt;br /&gt;
 
Badness: 0.001973&lt;/body&gt;&lt;/html&gt;</pre></div>
== Tikal ==
[[Subgroup]]: 2.3.5.7.11
 
[[Comma list]]: 56/55, 250/243
 
{{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }}
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 161.5193, ~7/4 = 971.0457
 
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}
 
[[Badness]]: 1.973 × 10<sup>-3</sup>
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Porcupine rank-3 family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 3]]

Latest revision as of 00:32, 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 porcupine rank-3 family of temperaments tempers out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

Rank-3 porcupine

Subgroup: 2.3.5.7

Comma list: 250/243

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

mapping generators: ~2, ~10/9, ~7

Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552

Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 73c

Badness: 0.535 × 10-3

Sonic

Subgroup: 2.3.5.7.11

Comma list: 55/54, 100/99

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

Optimal tuning (POTE): ~2 = 1\1, ~11/10 = 164.0777, ~7/4 = 967.8413

Optimal ET sequence: 7d, 8d, 14c, 15, 22, 37, 51, 88b

Badness: 0.523 × 10-3

Tikal

Subgroup: 2.3.5.7.11

Comma list: 56/55, 250/243

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

Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 161.5193, ~7/4 = 971.0457

Optimal ET sequence: 7d, 8d, 15, 30dee, 37ee, 52bee

Badness: 1.973 × 10-3

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