Vishnuzmic 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 '''vishnuzmic family''' of [[temperament]]s [[Tempering out|tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} = 6115295232/6103515625, a [[5-limit]] comma of about 3 [[cent]]s. It is the amount by which seven just chromatic semitones of [[25/24]] fall short of a just perfect fourth of [[4/3]], or in other words (4/3)/(25/24)<sup>7</sup>.
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-17 21:21:43 UTC</tt>.<br>
: The original revision id was <tt>293070464</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|flat]]


The //vishnuzmic family// of temperaments tempers out the vishnuzma, |23 6 -14&gt; = 6115295232/6103515625, a small 5-limit comma of size 3.338 cents. It is the amount by which seven [[25_24|just chromatic semitones]] of size 25/24 fall short of a [[4_3|just perfect fourth]] of 4/3, or in other words (4/3)/(25/24)^7.
== Vishnu ==
[[Subgroup]]: 2.3.5


Comma: 6115295232/6103515625
[[Comma list]]: 6115295232/6103515625


POTE generator: ~25/24 = 71.1432
{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}


Map: [&lt;2 4 5|, &lt;0 -7 -3|]
: mapping generators: ~78125/55296, ~25/24
EDOs: [[16edo|16]], [[18edo|18]], [[34edo|34]], [[50edo|50]], [[84edo|84]], [[118edo|118]], [[152edo|152]], [[270edo|270]], [[388edo|380]], [[422edo]], 506, 894, 1400
Badness: 0.0312


=Vishnu=
[[Optimal tuning]]s:
Commas: 4375/4374, 29360128/29296875
* [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556
* [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143


POTE generator: ~25/24 = 71.1075
{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}


Map: [&lt;2 4 5 10|, &lt;0 -7 -3 -37|]
[[Badness]]: 0.031181
EDOs: 118, 152, 270, [[1232edo|1232]], [[1502edo|1502]]
Badness: 0.0419


==11-limit==
== Septimal vishnu ==
Commas: 3025/3024, 4375/4374, 5632/5625
[[Subgroup]]: 2.3.5.7


POTE generator: ~25/24 = 71.1048
[[Comma list]]: 4375/4374, 29360128/29296875


Map: [&lt;2 4 5 10 10|, &lt;0 -7 -3 -37 -26|]
{{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}
EDOs: 118, 152, 270, [[422edo]], [[962edo|962]], 1232, 1502
Badness: 0.0142


==Ananta==
[[Optimal tuning]]s:
Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374
* [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175
* [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107


POTE generator: ~25/24 = 71.1170
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}


Map: [&lt;2 4 5 10 10 1|, &lt;0 -7 -3 -37 -26 54|]
[[Badness]]: 0.041912
EDOs: 118, 152, 270, 928, 1198, 1468
Badness: 0.0237


==Acyuta==
=== 11-limit ===
Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625
Subgroup: 2.3.5.7.11


POTE generator: ~25/24 = 71.1001
Comma list: 3025/3024, 4375/4374, 5632/5625


Map: [&lt;2 4 5 10 10 17|, &lt;0 -7 -3 -37 -26 -81|]
Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}
EDOs: 270, [[682edo|692]], 962
 
Badness: 0.0158</pre></div>
Optimal tunings:  
<h4>Original HTML content:</h4>
* CTE: ~99/70 = 1\2, ~25/24 = 71.1142
<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;Vishnuzmic family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:8:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt;&lt;a href="#Vishnu"&gt;Vishnu&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;
* POTE: ~99/70 = 1\2, ~25/24 = 71.105
&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;br /&gt;
 
The &lt;em&gt;vishnuzmic family&lt;/em&gt; of temperaments tempers out the vishnuzma, |23 6 -14&amp;gt; = 6115295232/6103515625, a small 5-limit comma of size 3.338 cents. It is the amount by which seven &lt;a class="wiki_link" href="/25_24"&gt;just chromatic semitones&lt;/a&gt; of size 25/24 fall short of a &lt;a class="wiki_link" href="/4_3"&gt;just perfect fourth&lt;/a&gt; of 4/3, or in other words (4/3)/(25/24)^7.&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}
&lt;br /&gt;
 
Comma: 6115295232/6103515625&lt;br /&gt;
Badness: 0.014180
&lt;br /&gt;
 
POTE generator: ~25/24 = 71.1432&lt;br /&gt;
==== Ananta ====
&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
Map: [&amp;lt;2 4 5|, &amp;lt;0 -7 -3|]&lt;br /&gt;
 
EDOs: &lt;a class="wiki_link" href="/16edo"&gt;16&lt;/a&gt;, &lt;a class="wiki_link" href="/18edo"&gt;18&lt;/a&gt;, &lt;a class="wiki_link" href="/34edo"&gt;34&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/84edo"&gt;84&lt;/a&gt;, &lt;a class="wiki_link" href="/118edo"&gt;118&lt;/a&gt;, &lt;a class="wiki_link" href="/152edo"&gt;152&lt;/a&gt;, &lt;a class="wiki_link" href="/270edo"&gt;270&lt;/a&gt;, &lt;a class="wiki_link" href="/388edo"&gt;380&lt;/a&gt;, &lt;a class="wiki_link" href="/422edo"&gt;422edo&lt;/a&gt;, 506, 894, 1400&lt;br /&gt;
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
Badness: 0.0312&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Vishnu"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Vishnu&lt;/h1&gt;
 
Commas: 4375/4374, 29360128/29296875&lt;br /&gt;
Optimal tuning:
&lt;br /&gt;
* CTE: ~99/70 = 1\2, ~25/24 = 71.1173
POTE generator: ~25/24 = 71.1075&lt;br /&gt;
* POTE: ~99/70 = 1\2, ~25/24 = 71.117
&lt;br /&gt;
 
Map: [&amp;lt;2 4 5 10|, &amp;lt;0 -7 -3 -37|]&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 118, 152, 270, 928, 1198, 1468 }}
EDOs: 118, 152, 270, &lt;a class="wiki_link" href="/1232edo"&gt;1232&lt;/a&gt;, &lt;a class="wiki_link" href="/1502edo"&gt;1502&lt;/a&gt;&lt;br /&gt;
 
Badness: 0.0419&lt;br /&gt;
Badness: 0.023678
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Vishnu-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
==== Acyuta ====
Commas: 3025/3024, 4375/4374, 5632/5625&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
POTE generator: ~25/24 = 71.1048&lt;br /&gt;
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
&lt;br /&gt;
 
Map: [&amp;lt;2 4 5 10 10|, &amp;lt;0 -7 -3 -37 -26|]&lt;br /&gt;
Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}
EDOs: 118, 152, 270, &lt;a class="wiki_link" href="/422edo"&gt;422edo&lt;/a&gt;, &lt;a class="wiki_link" href="/962edo"&gt;962&lt;/a&gt;, 1232, 1502&lt;br /&gt;
 
Badness: 0.0142&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* CTE: ~99/70 = 1\2, ~25/24 = 71.1079
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Vishnu-Ananta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Ananta&lt;/h2&gt;
* POTE: ~99/70 = 1\2, ~25/24 = 71.101
Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374&lt;br /&gt;
 
&lt;br /&gt;
Optimal ET sequence: {{Optimal ET sequence| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}
POTE generator: ~25/24 = 71.1170&lt;br /&gt;
 
&lt;br /&gt;
Badness: 0.015805
Map: [&amp;lt;2 4 5 10 10 1|, &amp;lt;0 -7 -3 -37 -26 54|]&lt;br /&gt;
 
EDOs: 118, 152, 270, 928, 1198, 1468&lt;br /&gt;
== Vishnean ==
Badness: 0.0237&lt;br /&gt;
[[Subgroup]]: 2.3.5.7
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Vishnu-Acyuta"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Acyuta&lt;/h2&gt;
[[Comma list]]: 126/125, 540225/524288
Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625&lt;br /&gt;
 
&lt;br /&gt;
{{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}
POTE generator: ~25/24 = 71.1001&lt;br /&gt;
 
&lt;br /&gt;
[[Optimal tuning]]s:  
Map: [&amp;lt;2 4 5 10 10 17|, &amp;lt;0 -7 -3 -37 -26 -81|]&lt;br /&gt;
* [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956
EDOs: 270, &lt;a class="wiki_link" href="/682edo"&gt;692&lt;/a&gt;, 962&lt;br /&gt;
* [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779
Badness: 0.0158&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}
 
[[Badness]]: 0.161398
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 126/125, 385/384, 1350/1331
 
Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}
 
Optimal tunings:  
* CTE: ~63/44 = 1\2, ~25/24 = 71.6218
* POTE: ~63/44 = 1\2, ~25/24 = 71.924
 
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}
 
Badness: 0.071990
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 126/125, 144/143, 847/845
 
Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}
 
Optimal tunings:
* CTE: ~55/39 = 1\2, ~25/24 = 71.6369
* POTE: ~55/39 = 1\2, ~25/24 = 71.926
 
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}
 
Badness: 0.040739
 
== Narayana ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 65625/65536, 321489/320000
 
{{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}
 
[[Optimal tuning]]s:
* [[CTE]]: ~567/400 = 1\2, ~25/24 = 71.2706
* [[POTE]]: ~567/400 = 1\2, ~25/24 = 71.265
 
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}
 
[[Badness]]: 0.094295
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 441/440, 8019/8000, 65625/65536
 
Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}
 
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.2609
* POTE: ~99/70 = 1\2, ~25/24 = 71.248
 
Optimal ET sequence: {{Optimal ET sequence| 34e, 84, 118, 202, 320 }}
 
Badness: 0.045908
 
== Quarvish ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 2401/2400, 6115295232/6103515625
 
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
 
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)
* [[POTE]]: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)
 
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
 
[[Badness]]: 0.045029
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 2401/2400, 9801/9800, 172032/171875
 
Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}
 
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~7/5 = 582.2122 (~99/98 = 17.7878)
* POTE: ~99/70 = 1\2, ~7/5 = 582.213 (~99/98 = 17.787)
 
Optimal ET sequence: {{Optimal ET sequence| 68, 134, 202, 270, 742, 1012 }}
 
Badness: 0.019868
 
== Decavish ==
The decavish temperament (50 &amp; 270) tempers out the wizma, {{monzo| -6 -8 2 5 }} = 420175/419904 and the [[linus comma]], {{monzo| 11 -10 -10 10 }} = 578509309952/576650390625.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 420175/419904, 2202927104/2197265625
 
{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}
 
: mapping generators: ~15/14, ~54/49
 
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 1\10, ~54/49 = 168.8587 (~25/24 = 71.1413, or ~36/35 = 48.8587)
* [[POTE]]: ~15/14 = 1\10, ~54/49 = 168.871 (~25/24 = 71.129, or ~36/35 = 48.871)
 
{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}
 
[[Badness]]: 0.114531
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 41503/41472, 172032/171875
 
Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}
 
Optimal tunings:
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.141, or ~36/35 = 48.859)
 
Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}
 
Badness: 0.036938
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
 
Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}
 
Optimal tunings:
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.151, or ~36/35 = 48.859)
 
Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}
 
Badness: 0.021906
 
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic| ]] <!-- key article -->
[[Category:Rank 2]]

Latest revision as of 00:38, 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 vishnuzmic family of temperaments tempers out the vishnuzma, [23 6 -14⟩ = 6115295232/6103515625, a 5-limit comma of about 3 cents. It is the amount by which seven just chromatic semitones of 25/24 fall short of a just perfect fourth of 4/3, or in other words (4/3)/(25/24)7.

Vishnu

Subgroup: 2.3.5

Comma list: 6115295232/6103515625

Mapping: [⟨2 4 5], ⟨0 -7 -3]]

mapping generators: ~78125/55296, ~25/24

Optimal tunings:

  • CTE: ~78125/55296 = 1\2, ~25/24 = 71.1556
  • POTE: ~78125/55296 = 1\2, ~25/24 = 71.143

Optimal ET sequence: 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc

Badness: 0.031181

Septimal vishnu

Subgroup: 2.3.5.7

Comma list: 4375/4374, 29360128/29296875

Mapping: [⟨2 4 5 10], ⟨0 -7 -3 -37]]

Optimal tunings:

  • CTE: ~10125/7168 = 1\2, ~25/24 = 71.1175
  • POTE: ~10125/7168 = 1\2, ~25/24 = 71.107

Optimal ET sequence: 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd

Badness: 0.041912

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4375/4374, 5632/5625

Mapping: [⟨2 4 5 10 10], ⟨0 -7 -3 -37 -26]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.1142
  • POTE: ~99/70 = 1\2, ~25/24 = 71.105

Optimal ET sequence: 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd

Badness: 0.014180

Ananta

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374

Mapping: [⟨2 4 5 10 10 1], ⟨0 -7 -3 -37 -26 54]]

Optimal tuning:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.1173
  • POTE: ~99/70 = 1\2, ~25/24 = 71.117

Optimal ET sequence: 118, 152, 270, 928, 1198, 1468

Badness: 0.023678

Acyuta

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625

Mapping: [⟨2 4 5 10 10 17], ⟨0 -7 -3 -37 -26 -81]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.1079
  • POTE: ~99/70 = 1\2, ~25/24 = 71.101

Optimal ET sequence: 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf

Badness: 0.015805

Vishnean

Subgroup: 2.3.5.7

Comma list: 126/125, 540225/524288

Mapping: [⟨2 4 5 5], ⟨0 -7 -3 5]]

Optimal tunings:

  • CTE: ~735/512 = 1\2, ~25/24 = 71.4956
  • POTE: ~735/512 = 1\2, ~25/24 = 71.779

Optimal ET sequence: 16, 34, 50, 134dd

Badness: 0.161398

11-limit

Subgroup: 2.3.5.7.11

Comma list: 126/125, 385/384, 1350/1331

Mapping: [⟨2 4 5 5 8], ⟨0 -7 -3 5 -9]]

Optimal tunings:

  • CTE: ~63/44 = 1\2, ~25/24 = 71.6218
  • POTE: ~63/44 = 1\2, ~25/24 = 71.924

Optimal ET sequence: 16, 34, 50

Badness: 0.071990

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 126/125, 144/143, 847/845

Mapping: [⟨2 4 5 5 8 8], ⟨0 -7 -3 5 -9 -5]]

Optimal tunings:

  • CTE: ~55/39 = 1\2, ~25/24 = 71.6369
  • POTE: ~55/39 = 1\2, ~25/24 = 71.926

Optimal ET sequence: 16, 34, 50

Badness: 0.040739

Narayana

Subgroup: 2.3.5.7

Comma list: 65625/65536, 321489/320000

Mapping: [⟨2 4 5 3], ⟨0 -7 -3 22]]

Optimal tunings:

  • CTE: ~567/400 = 1\2, ~25/24 = 71.2706
  • POTE: ~567/400 = 1\2, ~25/24 = 71.265

Optimal ET sequence: 34, 84, 118, 202, 320, 522

Badness: 0.094295

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 8019/8000, 65625/65536

Mapping: [⟨2 4 5 3 3], ⟨0 -7 -3 22 33]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~25/24 = 71.2609
  • POTE: ~99/70 = 1\2, ~25/24 = 71.248

Optimal ET sequence: 34e, 84, 118, 202, 320

Badness: 0.045908

Quarvish

Subgroup: 2.3.5.7

Comma list: 2401/2400, 6115295232/6103515625

Mapping: [⟨2 4 5 6], ⟨0 -28 -12 -13]]

Optimal tunings:

  • CTE: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)
  • POTE: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)

Optimal ET sequence: 68, 134, 202, 270, 742, 1012

Badness: 0.045029

11-limit

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800, 172032/171875

Mapping: [⟨2 4 5 6 6], ⟨0 -28 -12 -13 31]]

Optimal tunings:

  • CTE: ~99/70 = 1\2, ~7/5 = 582.2122 (~99/98 = 17.7878)
  • POTE: ~99/70 = 1\2, ~7/5 = 582.213 (~99/98 = 17.787)

Optimal ET sequence: 68, 134, 202, 270, 742, 1012

Badness: 0.019868

Decavish

The decavish temperament (50 & 270) tempers out the wizma, [-6 -8 2 5⟩ = 420175/419904 and the linus comma, [11 -10 -10 10⟩ = 578509309952/576650390625.

Subgroup: 2.3.5.7

Comma list: 420175/419904, 2202927104/2197265625

Mapping: [⟨10 6 19 14], ⟨0 7 3 10]]

mapping generators: ~15/14, ~54/49

Optimal tunings:

  • CTE: ~15/14 = 1\10, ~54/49 = 168.8587 (~25/24 = 71.1413, or ~36/35 = 48.8587)
  • POTE: ~15/14 = 1\10, ~54/49 = 168.871 (~25/24 = 71.129, or ~36/35 = 48.871)

Optimal ET sequence: 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c

Badness: 0.114531

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 41503/41472, 172032/171875

Mapping: [⟨10 6 19 14 36], ⟨0 7 3 10 -1]]

Optimal tunings:

  • CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
  • POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.141, or ~36/35 = 48.859)

Optimal ET sequence: 50, …, 220, 270, 860, 1130, 1400

Badness: 0.036938

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655

Mapping: [⟨10 6 19 14 36 37], ⟨0 7 3 10 -1 0]]

Optimal tunings:

  • CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
  • POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.151, or ~36/35 = 48.859)

Optimal ET sequence: 50, 220, 270, 590, 860, 1130

Badness: 0.021906

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