Immunity family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 309271806 - Original comment: **
 
(24 intermediate revisions by 11 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 '''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>2012-03-08 21:04:20 UTC</tt>.<br>
: The original revision id was <tt>309271806</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


=Immunized=
[[Optimal tuning]]s:
Commas: 64/63, 8748/8575
* [[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: ~81/70 = 246.479
{{Optimal ET sequence|legend=1| 5, …, 29, 34 }}


Map: [&lt;1 0 -8 6|, &lt;0 2 13 -4|]
[[Badness]] (Smith): 0.184738
Wedgie: &lt;&lt;2 13 -4 16 -12 -46||
 
EDOs: 5, 34d, 39d, 73d
=== 2.3.5.13 subgroup ===
Badness: 0.0826
Subgroup: 2.3.5.13
</pre></div>
 
<h4>Original HTML content:</h4>
Comma list: 676/675, 3200/3159
<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;
 
&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;
Sval mapping: {{mapping| 1 0 -8 -9 | 0 2 13 16 }}
Comma: 1638400/1594323&lt;br /&gt;
 
&lt;br /&gt;
Optimal tunings:
POTE generator: ~729/640 = 247.070&lt;br /&gt;
* CTE: ~2 = 1200.000, ~26/15 = 952.643
&lt;br /&gt;
* CWE: ~2 = 1200.000, ~26/15 = 952.789
Map: [&amp;lt;1 0 -8|, &amp;lt;0 2 13|]&lt;br /&gt;
 
EDOs: 5, 29, 34&lt;br /&gt;
{{Optimal ET sequence|legend=0| 5, …, 29, 34 }}
Badness: 0.18473&lt;br /&gt;
 
&lt;br /&gt;
Badness (Smith): 0.257
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit&lt;/h1&gt;
 
Commas: 49/48, 2240/2187&lt;br /&gt;
== Septimal immunity ==
&lt;br /&gt;
{{See also| Semaphoresmic clan }}
POTE generator: ~8/7 = 247.555&lt;br /&gt;
 
&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
Map: [&amp;lt;1 0 -8 2|, &amp;lt;0 2 13 1|]&lt;br /&gt;
 
Wedgie: &amp;lt;&amp;lt;2 13 1 16 -4 -34||&lt;br /&gt;
[[Comma list]]: 49/48, 2240/2187
EDOs: 5, 29, 34&lt;br /&gt;
 
Badness: 0.0776&lt;br /&gt;
{{Mapping|legend=1| 1 0 -8 2 | 0 2 13 1 }}
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Immunized"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Immunized&lt;/h1&gt;
[[Optimal tuning]]s:  
Commas: 64/63, 8748/8575&lt;br /&gt;
* [[CTE]]: ~2 = 1200.000, ~7/4 = 952.767
&lt;br /&gt;
: [[error map]]: {{val| 0.000 +3.580 -0.337 -16.058 }}
POTE generator: ~81/70 = 246.479&lt;br /&gt;
* [[POTE]]: ~2 = 1200.000, ~7/4 = 952.445
&lt;br /&gt;
: error map: {{val| 0.000 +2.936 -4.525 -16.381 }}
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;
{{Optimal ET sequence|legend=1| 5, …, 29, 34, 63d }}
EDOs: 5, 34d, 39d, 73d&lt;br /&gt;
 
Badness: 0.0826&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Badness]] (Smith): 0.077631
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 55/54, 896/891
 
Mapping: {{mapping| 1 0 -8 2 9 | 0 2 13 1 -7 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.442
* POTE: ~2 = 1200.000, ~7/4 = 952.074
 
{{Optimal ET sequence|legend=0| 5, 24c, 29, 63de }}
 
Badness (Smith): 0.052661
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 55/54, 91/90, 896/891
 
Mapping: {{mapping| 1 0 -8 2 9 -9 | 0 2 13 1 -7 16 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/4 = 952.472
* POTE: ~2 = 1200.000, ~7/4 = 952.031
 
{{Optimal ET sequence|legend=0| 5, 24cf, 29 }}
 
Badness (Smith): 0.037078
 
=== Impunity ===
Subgroup: 2.3.5.7.11
 
Comma list: 49/48, 100/99, 1232/1215
 
Mapping: {{mapping| 1 0 -8 2 -14 | 0 2 13 1 22 }}
 
Optimal tunings:  
* CTE: ~2 = 1200.000, ~7/4 = 952.528
* POTE: ~2 = 1200.000, ~7/4 = 952.227
 
{{Optimal ET sequence|legend=0| 5e, 24cee, 29 }}
 
Badness (Smith): 0.055243
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 49/48, 91/90, 100/99, 352/351
 
Mapping: {{mapping| 1 0 -8 2 -14 -9 | 0 2 13 1 22 16 }}
 
Optimal tunings:
* CTE: ~2 = 1200.000, ~7/4 = 952.529
* POTE: ~2 = 1200.000, ~7/4 = 952.217
 
{{Optimal ET sequence|legend=0| 5e, 24ceef, 29 }}
 
Badness (Smith): 0.033196
 
== Immunized ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 64/63, 8748/8575
 
{{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]]

Latest revision as of 00:39, 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 immunity family of temperaments tempers out the immunity comma, 1638400/1594323 ([16 -13 2⟩).

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.

Subgroup: 2.3.5

Comma list: 1638400/1594323

Mapping: [⟨1 0 -8], ⟨0 2 13]]

mapping generators: ~2, ~1280/729

Optimal tunings:

  • CTE: ~2 = 1200.000, ~1280/729 = 952.706
error map: ⟨0.000 +3.456 -1.141]
  • POTE: ~2 = 1200.000, ~1280/729 = 952.930
error map: ⟨0.000 +3.905 +1.775]

Optimal ET sequence: 5, …, 29, 34

Badness (Smith): 0.184738

2.3.5.13 subgroup

Subgroup: 2.3.5.13

Comma list: 676/675, 3200/3159

Sval mapping: [⟨1 0 -8 -9], ⟨0 2 13 16]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~26/15 = 952.643
  • CWE: ~2 = 1200.000, ~26/15 = 952.789

Optimal ET sequence: 5, …, 29, 34

Badness (Smith): 0.257

Septimal immunity

See also: Semaphoresmic clan

Subgroup: 2.3.5.7

Comma list: 49/48, 2240/2187

Mapping: [⟨1 0 -8 2], ⟨0 2 13 1]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~7/4 = 952.767
error map: ⟨0.000 +3.580 -0.337 -16.058]
  • POTE: ~2 = 1200.000, ~7/4 = 952.445
error map: ⟨0.000 +2.936 -4.525 -16.381]

Optimal ET sequence: 5, …, 29, 34, 63d

Badness (Smith): 0.077631

11-limit

Subgroup: 2.3.5.7.11

Comma list: 49/48, 55/54, 896/891

Mapping: [⟨1 0 -8 2 9], ⟨0 2 13 1 -7]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~7/4 = 952.442
  • POTE: ~2 = 1200.000, ~7/4 = 952.074

Optimal ET sequence: 5, 24c, 29, 63de

Badness (Smith): 0.052661

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 55/54, 91/90, 896/891

Mapping: [⟨1 0 -8 2 9 -9], ⟨0 2 13 1 -7 16]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~7/4 = 952.472
  • POTE: ~2 = 1200.000, ~7/4 = 952.031

Optimal ET sequence: 5, 24cf, 29

Badness (Smith): 0.037078

Impunity

Subgroup: 2.3.5.7.11

Comma list: 49/48, 100/99, 1232/1215

Mapping: [⟨1 0 -8 2 -14], ⟨0 2 13 1 22]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~7/4 = 952.528
  • POTE: ~2 = 1200.000, ~7/4 = 952.227

Optimal ET sequence: 5e, 24cee, 29

Badness (Smith): 0.055243

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 49/48, 91/90, 100/99, 352/351

Mapping: [⟨1 0 -8 2 -14 -9], ⟨0 2 13 1 22 16]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~7/4 = 952.529
  • POTE: ~2 = 1200.000, ~7/4 = 952.217

Optimal ET sequence: 5e, 24ceef, 29

Badness (Smith): 0.033196

Immunized

Subgroup: 2.3.5.7

Comma list: 64/63, 8748/8575

Mapping: [⟨1 0 -8 6], ⟨0 2 13 -4]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~140/81 = 953.001
error map: ⟨0.000 +4.047 +2.669 +19.170]
  • POTE: ~2 = 1200.000, ~140/81 = 953.521
error map: ⟨0.000 +5.088 +9.463 +17.089]

Optimal ET sequence: 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: [⟨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: 5, 29de, 34d, 39d, 73dd

Badness (Smith): 0.051515

Immune

Subgroup: 2.3.5.7

Comma list: 225/224, 781250/750141

Mapping: [⟨1 2 5 9], ⟨0 -2 -13 -30]]

Optimal tunings:

  • CTE: ~2 = 1200.000, ~1000/567 = 952.386
error map: ⟨0.000 +2.818 -5.292 +2.763]
  • POTE: ~2 = 1200.000, ~1000/567 = 952.417
error map: ⟨0.000 +2.879 -4.893 +3.683]

Optimal ET sequence: 29, 34d, 63

Badness (Smith): 0.144835

11-limit

Subgroup: 2.3.5.7.11

Comma list: 100/99, 225/224, 1331/1323

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: 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: [⟨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: 29, 34d, 63

Badness (Smith): 0.028521

Retrieved from "https://en.xen.wiki/index.php?title=Immunity_family&oldid=201208"