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Immunity 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 '''immunity family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[immunity comma]], 1638400/1594323 ({{monzo| 16 -13 2 }}).
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-02-07 17:32:39 UTC</tt>.<br>
: The original revision id was <tt>488046794</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">
=Immunity=
Comma: 1638400/1594323


POTE generator: ~729/640 = 247.070
== Immunity ==
Immunity is naturally a 2.3.5.13 [[subgroup temperament]] as the generator serves as ~26/15 (or its [[octave complement]] ~15/13), tempering out [[676/675]].  


Map: [&lt;1 0 -8|, &lt;0 2 13|]
[[Subgroup]]: 2.3.5
EDOs: 5, 29, 34
Badness: 0.18473


==7-limit==
[[Comma list]]: 1638400/1594323
Commas: 49/48, 2240/2187


POTE generator: ~8/7 = 247.555
{{Mapping|legend=1| 1 0 -8 | 0 2 13 }}


Map: [&lt;1 0 -8 2|, &lt;0 2 13 1|]
: mapping generators: ~2, ~1280/729
Wedgie: &lt;&lt;2 13 1 16 -4 -34||
EDOs: 5, 29, 34
Badness: 0.0776


==11-limit==
[[Optimal tuning]]s:
Commas: 49/48, 55/54, 896/891
* [[CTE]]: ~2 = 1200.000, ~1280/729 = 952.706
: [[error map]]: {{val| 0.000 +3.456 -1.141 }}
* [[POTE]]: ~2 = 1200.000, ~1280/729 = 952.930
: error map: {{val| 0.000 +3.905 +1.775 }}


POTE generator: ~8/7 = 247.926
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}


Map: [&lt;1 0 -8 2 9|, &lt;0 2 13 1 -7|]
[[Badness]] (Smith): 0.184738
EDOs: 5, 29, 63de, 92cde
Badness: 0.0527


==13-limit==
=== 2.3.5.13 subgroup ===
Commas: 49/48, 55/54, 91/90, 896/891
Subgroup: 2.3.5.13


POTE generator: ~8/7 = 247.97
Comma list: 676/675, 3200/3159


Map: [&lt;1 0 -8 2 9 -9|, &lt;0 2 13 1 -7 16|]
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
EDOs: 5, 29, 92cde
Badness: 0.0371


==Impunity==
Optimal tunings:
Commas: 49/48, 100/99, 1232/1215
* CTE: ~2 = 1200.000, ~26/15 = 952.643
* CWE: ~2 = 1200.000, ~26/15 = 952.789


POTE generator: ~8/7 = 247.773
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}


Map: [&lt;1 0 -8 2 -14|, &lt;0 2 13 1 22|]
Badness (Smith): 0.257
EDOs: 29, 63d, 92cd
Badness: 0.0552


===13-limit===
== Septimal immunity ==
Commas: 49/48, 91/90, 100/99, 352/351
{{See also| Semaphoresmic clan }}


POTE generator: ~8/7 = 247.783
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 0 -8 2 -14 -9|, &lt;0 2 13 1 22 16|]
[[Comma list]]: 49/48, 2240/2187
EDOs: 29, 63d, 92cd
Badness: 0.0332


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


POTE generator: ~81/70 = 246.479
[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1200.000, ~7/4 = 952.767
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
* [[POTE]]: ~2 = 1200.000, ~7/4 = 952.445
: error map: {{val| 0.000 +2.936 -4.525 -16.381 }}


Map: [&lt;1 0 -8 6|, &lt;0 2 13 -4|]
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}
Wedgie: &lt;&lt;2 13 -4 16 -12 -46||
 
EDOs: 5, 34d, 39d, 73d
[[Badness]] (Smith): 0.077631
Badness: 0.0826</pre></div>
 
<h4>Original HTML content:</h4>
=== 11-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;br /&gt;
Subgroup: 2.3.5.7.11
&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;
Comma list: 49/48, 55/54, 896/891
&lt;br /&gt;
 
POTE generator: ~729/640 = 247.070&lt;br /&gt;
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -8|, &amp;lt;0 2 13|]&lt;br /&gt;
Optimal tunings:  
EDOs: 5, 29, 34&lt;br /&gt;
* CTE: ~2 = 1200.000, ~7/4 = 952.442
Badness: 0.18473&lt;br /&gt;
* POTE: ~2 = 1200.000, ~7/4 = 952.074
&lt;br /&gt;
 
&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;
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}
Commas: 49/48, 2240/2187&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.052661
POTE generator: ~8/7 = 247.555&lt;br /&gt;
 
&lt;br /&gt;
==== 13-limit ====
Map: [&amp;lt;1 0 -8 2|, &amp;lt;0 2 13 1|]&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Wedgie: &amp;lt;&amp;lt;2 13 1 16 -4 -34||&lt;br /&gt;
 
EDOs: 5, 29, 34&lt;br /&gt;
Comma list: 49/48, 55/54, 91/90, 896/891
Badness: 0.0776&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}
&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;
Optimal tunings:
&lt;br /&gt;
* CTE: ~2 = 1200.000, ~7/4 = 952.472
POTE generator: ~8/7 = 247.926&lt;br /&gt;
* POTE: ~2 = 1200.000, ~7/4 = 952.031
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -8 2 9|, &amp;lt;0 2 13 1 -7|]&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}
EDOs: 5, 29, 63de, 92cde&lt;br /&gt;
 
Badness: 0.0527&lt;br /&gt;
Badness (Smith): 0.037078
&lt;br /&gt;
 
&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;
=== Impunity ===
Commas: 49/48, 55/54, 91/90, 896/891&lt;br /&gt;
Subgroup: 2.3.5.7.11
&lt;br /&gt;
 
POTE generator: ~8/7 = 247.97&lt;br /&gt;
Comma list: 49/48, 100/99, 1232/1215
&lt;br /&gt;
 
Map: [&amp;lt;1 0 -8 2 9 -9|, &amp;lt;0 2 13 1 -7 16|]&lt;br /&gt;
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}
EDOs: 5, 29, 92cde&lt;br /&gt;
 
Badness: 0.0371&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* CTE: ~2 = 1200.000, ~7/4 = 952.528
&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;
* POTE: ~2 = 1200.000, ~7/4 = 952.227
Commas: 49/48, 100/99, 1232/1215&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}
POTE generator: ~8/7 = 247.773&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.055243
Map: [&amp;lt;1 0 -8 2 -14|, &amp;lt;0 2 13 1 22|]&lt;br /&gt;
 
EDOs: 29, 63d, 92cd&lt;br /&gt;
==== 13-limit ====
Badness: 0.0552&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
&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;
Comma list: 49/48, 91/90, 100/99, 352/351
Commas: 49/48, 91/90, 100/99, 352/351&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}
POTE generator: ~8/7 = 247.783&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
Map: [&amp;lt;1 0 -8 2 -14 -9|, &amp;lt;0 2 13 1 22 16|]&lt;br /&gt;
* CTE: ~2 = 1200.000, ~7/4 = 952.529
EDOs: 29, 63d, 92cd&lt;br /&gt;
* POTE: ~2 = 1200.000, ~7/4 = 952.217
Badness: 0.0332&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}
&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;
 
Commas: 64/63, 8748/8575&lt;br /&gt;
Badness (Smith): 0.033196
&lt;br /&gt;
 
POTE generator: ~81/70 = 246.479&lt;br /&gt;
== Immunized ==
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
Map: [&amp;lt;1 0 -8 6|, &amp;lt;0 2 13 -4|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;2 13 -4 16 -12 -46||&lt;br /&gt;
[[Comma list]]: 64/63, 8748/8575
EDOs: 5, 34d, 39d, 73d&lt;br /&gt;
 
Badness: 0.0826&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Mapping|legend=1| 1 0 -8 6 | 0 2 13 -4 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~2 = 1200.000, ~140/81 = 953.001
: [[error map]]: {{val| 0.000 +4.047 +2.669 +19.170 }}
* [[POTE]]: ~2 = 1200.000, ~140/81 = 953.521
: error map: {{val| 0.000 +5.088 +9.463 +17.089 }}
 
{{Optimal ET sequence|legend=1| 5, 29d, 34d, 39d, 73dd, 112cddd }}
 
[[Badness]] (Smith): 0.082592
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 64/63, 99/98, 1944/1925
 
Mapping: {{mapping| 1 0 -8 6 13 | 0 2 13 -4 -12 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~55/32 = 953.271
* POTE: ~2 = 1200.000, ~55/32 = 953.397
 
{{Optimal ET sequence|legend=0| 5, 29de, 34d, 39d, 73dd }}
 
Badness (Smith): 0.051515
 
== 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:  
* [[CTE]]: ~2 = 1200.000, ~1000/567 = 952.386
: [[error map]]: {{val| 0.000 +2.818 -5.292 +2.763 }}
* [[POTE]]: ~2 = 1200.000, ~1000/567 = 952.417
: error map: {{val| 0.000 +2.879 -4.893 +3.683 }}
 
{{Optimal ET sequence|legend=1| 29, 34d, 63 }}
 
[[Badness]] (Smith): 0.144835
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 100/99, 225/224, 1331/1323
 
Mapping: {{mapping| 1 2 5 9 8 | 0 -2 -13 -30 -22 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~121/70 = 952.375
* POTE: ~2 = 1200.000, ~121/70 = 952.411
 
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
 
Badness (Smith): 0.050990
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 100/99, 169/168, 225/224, 275/273
 
Mapping: {{mapping| 1 2 5 9 8 7 | 0 -2 -13 -30 -22 -16 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~26/15 = 952.389
* POTE: ~2 = 1200.000, ~26/15 = 952.407
 
{{Optimal ET sequence|legend=0| 29, 34d, 63 }}
 
Badness (Smith): 0.028521
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Immunity family| ]] <!-- Main article -->
[[Category:Immunity| ]] <!-- Key article -->
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Immunity_family"