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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 '''immunity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[immunity comma]] ({{monzo|legend=1| 16 -13 2 }}, [[ratio]]: 1638400/1594323).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-07 17:33:08 UTC</tt>.<br>
: The original revision id was <tt>488046868</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">[[toc]]


=Immunity=
== Immunity ==
Comma: 1638400/1594323
The head of this family is immunity, which splits the perfect twelfth in halves, and [[5/4]] is found in 13 generator steps. Its [[ploidacot]] is alpha-dicot. It is a member of the [[syntonic–limmic equivalence continuum]] with equivalence number ''n'' = 2, meaning the [[Pythagorean limma]] is equated with a stack of two [[syntonic comma]]s.


POTE generator: ~729/640 = 247.070
[[Subgroup]]: 2.3.5


Map: [&lt;1 0 -8|, &lt;0 2 13|]
[[Comma list]]: 1638400/1594323
EDOs: 5, 29, 34
Badness: 0.18473


==7-limit==
{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}
Commas: 49/48, 2240/2187
: mapping generators: ~2, ~1280/729


POTE generator: ~8/7 = 247.555
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1198.9215{{c}}, ~1280/729 = 952.0734{{c}}
: [[error map]]: {{val| -1.079 +2.192 -0.731 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1280/729 = 952.8424{{c}}
: error map: {{val| 0.000 +3.730 +0.638 }}


Map: [&lt;1 0 -8 2|, &lt;0 2 13 1|]
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}
Wedgie: &lt;&lt;2 13 1 16 -4 -34||
EDOs: 5, 29, 34
Badness: 0.0776


==11-limit==
[[Badness]] (Sintel): 4.33
Commas: 49/48, 55/54, 896/891


POTE generator: ~8/7 = 247.926
=== Overview to extensions ===
The second comma of the comma list defines which 7-limit family member we are looking at:  
* Septimal immunity adds [[49/48]];
* Immunized adds [[64/63]];
* Immune adds [[225/224]].


Map: [&lt;1 0 -8 2 9|, &lt;0 2 13 1 -7|]
The immunity family boasts a very remarkable extension to the [[2.3.5.13 subgroup]], discussed in [[#Subgroup extensions]].  
EDOs: 5, 29, 63de, 92cde
Badness: 0.0527


==13-limit==
== Septimal immunity ==
Commas: 49/48, 55/54, 91/90, 896/891
{{See also| Semaphoresmic clan }}


POTE generator: ~8/7 = 247.97
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 0 -8 2 9 -9|, &lt;0 2 13 1 -7 16|]
[[Comma list]]: 49/48, 2240/2187
EDOs: 5, 29, 92cde
Badness: 0.0371


==Impunity==
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}
Commas: 49/48, 100/99, 1232/1215


POTE generator: ~8/7 = 247.773
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1201.4508{{c}}, ~7/4 = 953.5968{{c}}
: [[error map]]: {{val| +1.451 +5.239 -1.162 -12.327 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~7/4 = 952.5376{{c}}
: error map: {{val| 0.000 +3.120 -3.325 -16.288 }}


Map: [&lt;1 0 -8 2 -14|, &lt;0 2 13 1 22|]
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}
EDOs: 29, 63d, 92cd
Badness: 0.0552


===13-limit===
[[Badness]] (Sintel): 1.96
Commas: 49/48, 91/90, 100/99, 352/351


POTE generator: ~8/7 = 247.783
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 0 -8 2 -14 -9|, &lt;0 2 13 1 22 16|]
Comma list: 49/48, 55/54, 896/891
EDOs: 29, 63d, 92cd
Badness: 0.0332


=Immunized=
{{Mapping|legend=0| 1 0 -8 2 9 | 0 2 13 1 -7 }}
Commas: 64/63, 8748/8575


POTE generator: ~81/70 = 246.479
Optimal tunings:  
* WE: ~2 = 1202.6033{{c}}, ~7/4 = 954.1395{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.1429{{c}}


Map: [&lt;1 0 -8 6|, &lt;0 2 13 -4|]
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}
Wedgie: &lt;&lt;2 13 -4 16 -12 -46||
 
EDOs: 5, 34d, 39d, 73d
Badness (Sintel): 1.74
Badness: 0.0826</pre></div>
 
<h4>Original HTML content:</h4>
==== 13-limit ====
<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;Immunity family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:14:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Immunity"&gt;Immunity&lt;/a&gt;&lt;/div&gt;
Subgroup: 2.3.5.7.11.13
&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Immunity-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Immunity-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
Comma list: 49/48, 55/54, 91/90, 896/891
&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Immunity-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Immunity-Impunity"&gt;Impunity&lt;/a&gt;&lt;/div&gt;
{{Mapping|legend=0| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Immunity-Impunity-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
 
&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Immunized"&gt;Immunized&lt;/a&gt;&lt;/div&gt;
Optimal tunings:  
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;/div&gt;
* WE: ~2 = 1202.5640{{c}}, ~7/4 = 954.0648{{c}}
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.1117{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Immunity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Immunity&lt;/h1&gt;
 
Comma: 1638400/1594323&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}
&lt;br /&gt;
 
POTE generator: ~729/640 = 247.070&lt;br /&gt;
Badness (Sintel): 1.53
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -8|, &amp;lt;0 2 13|]&lt;br /&gt;
=== Impunity ===
EDOs: 5, 29, 34&lt;br /&gt;
Subgroup: 2.3.5.7.11
Badness: 0.18473&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 49/48, 100/99, 1232/1215
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Immunity-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h2&gt;
 
Commas: 49/48, 2240/2187&lt;br /&gt;
{{Mapping|legend=0| 1 0 -8 2 -14 | 0 2 13 1 22 }}
&lt;br /&gt;
 
POTE generator: ~8/7 = 247.555&lt;br /&gt;
Optimal tunings:  
&lt;br /&gt;
* WE: ~2 = 1201.6023{{c}}, ~7/4 = 953.4988{{c}}
Map: [&amp;lt;1 0 -8 2|, &amp;lt;0 2 13 1|]&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.3120{{c}}
Wedgie: &amp;lt;&amp;lt;2 13 1 16 -4 -34||&lt;br /&gt;
 
EDOs: 5, 29, 34&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}
Badness: 0.0776&lt;br /&gt;
 
&lt;br /&gt;
Badness (Sintel): 1.83
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Immunity-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit&lt;/h2&gt;
 
Commas: 49/48, 55/54, 896/891&lt;br /&gt;
==== 13-limit ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
POTE generator: ~8/7 = 247.926&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 49/48, 91/90, 100/99, 352/351
Map: [&amp;lt;1 0 -8 2 9|, &amp;lt;0 2 13 1 -7|]&lt;br /&gt;
 
EDOs: 5, 29, 63de, 92cde&lt;br /&gt;
{{Mapping|legend=0| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}
Badness: 0.0527&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:  
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Immunity-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;13-limit&lt;/h2&gt;
* WE: ~2 = 1200.5826{{c}}, ~7/4 = 952.4725{{c}}
Commas: 49/48, 55/54, 91/90, 896/891&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~7/4 = 952.3038{{c}}
&lt;br /&gt;
 
POTE generator: ~8/7 = 247.97&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -8 2 9 -9|, &amp;lt;0 2 13 1 -7 16|]&lt;br /&gt;
Badness (Sintel): 1.37
EDOs: 5, 29, 92cde&lt;br /&gt;
 
Badness: 0.0371&lt;br /&gt;
== Immunized ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Immunity-Impunity"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Impunity&lt;/h2&gt;
 
Commas: 49/48, 100/99, 1232/1215&lt;br /&gt;
[[Comma list]]: 64/63, 8748/8575
&lt;br /&gt;
 
POTE generator: ~8/7 = 247.773&lt;br /&gt;
{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -8 2 -14|, &amp;lt;0 2 13 1 22|]&lt;br /&gt;
[[Optimal tuning]]s:
EDOs: 29, 63d, 92cd&lt;br /&gt;
* [[WE]]: ~2 = 1196.6463{{c}}, ~140/81 = 950.8564{{c}}
Badness: 0.0552&lt;br /&gt;
: [[error map]]: {{val| -3.354 -0.242 +1.649 +7.626 }}
&lt;br /&gt;
* [[CWE]]: ~2 = 1200.0000{{c}}, ~140/81 = 953.3954{{c}}
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Immunity-Impunity-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;13-limit&lt;/h3&gt;
: error map: {{val| 0.000 +4.836 +7.827 +17.592 }}
Commas: 49/48, 91/90, 100/99, 352/351&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}
POTE generator: ~8/7 = 247.783&lt;br /&gt;
 
&lt;br /&gt;
[[Badness]] (Sintel): 2.09
Map: [&amp;lt;1 0 -8 2 -14 -9|, &amp;lt;0 2 13 1 22 16|]&lt;br /&gt;
 
EDOs: 29, 63d, 92cd&lt;br /&gt;
=== 11-limit ===
Badness: 0.0332&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc6"&gt;&lt;a name="Immunized"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Immunized&lt;/h1&gt;
Comma list: 64/63, 99/98, 1944/1925
Commas: 64/63, 8748/8575&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=0| 1 0 -8 6 13 | 0 2 13 -4 -12 }}
POTE generator: ~81/70 = 246.479&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
Map: [&amp;lt;1 0 -8 6|, &amp;lt;0 2 13 -4|]&lt;br /&gt;
* WE: ~2 = 1196.9902{{c}}, ~55/32 = 951.0056{{c}}
Wedgie: &amp;lt;&amp;lt;2 13 -4 16 -12 -46||&lt;br /&gt;
* CWE: ~2 = 1200.0000{{c}}, ~55/32 = 953.3755{{c}}
EDOs: 5, 34d, 39d, 73d&lt;br /&gt;
 
Badness: 0.0826&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}
 
Badness (Sintel): 1.70
 
== Immune ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 781250/750141
 
{{Mapping|legend=1| 1 2 5 9 | 0 -2 -13 -30 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.7353{{c}}, ~1000/567 = 952.2068{{c}}
: [[error map]]: {{val| -0.265 +2.459 -5.507 +2.939 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~1000/567 = 952.4061{{c}}
: error map: {{val| 0.000 +2.857 -5.034 +3.357 }}
 
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
 
[[Badness]] (Sintel): 3.67
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 225/224, 1331/1323
 
{{Mapping|legend=0| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}
 
Optimal tunings:
* WE: ~2 = 1199.7081{{c}}, ~121/70 = 952.1793{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~121/70 = 952.3983{{c}}
 
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
 
Badness (Sintel): 1.69
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 169/168, 225/224, 275/273
 
{{Mapping|legend=0| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}
 
Optimal tunings:
* WE: ~2 = 1199.8625{{c}}, ~26/15 = 952.2977{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.4008{{c}}
 
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
 
Badness (Sintel): 1.18
 
== Subgroup extensions ==
=== Immunity (2.3.5.13) ===
Immunity is naturally a [[2.3.5.13 subgroup|2.3.5.13-subgroup]] temperament as the generator serves as ~[[26/15]] (or its [[octave complement]] ~[[15/13]]), tempering out [[676/675]].
 
Subgroup: 2.3.5.13
 
Comma list: 676/675, 3200/3159
 
{{Mapping|legend=2| 1 0 -8 -9 | 0 2 13 16 }}
 
Optimal tunings:
* WE: ~2 = 1198.8955{{c}}, ~26/15 = 952.0049{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~26/15 = 952.7890{{c}}
 
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
 
Badness (Sintel): 0.858
 
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]
Retrieved from "https://en.xen.wiki/w/Immunity_family"