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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]]
Retrieved from "https://en.xen.wiki/w/Vishnuzmic_family"