Vishnu family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>genewardsmith
**Imported revision 248429539 - Original comment: **
m Recategorize
 
(40 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 '''vishnu family''' [[tempering out|tempers out]] the [[vishnu comma]] ({{monzo|legend=1| 23 6 -14 }}, [[ratio]]: 6 115 295 232 / 6 103 515 625), an [[unnoticeable comma]] of about 3.34 [[cent]]s in size.  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-25 11:35:16 UTC</tt>.<br>
: The original revision id was <tt>248429539</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">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.


Comma: 6115295232/6103515625
== Vishnu ==
The generator for the vishnu temperament is a [[25/24|classical chromatic semitone]], seven of which make a [[4/3|perfect fourth]], and [[5/4]] is found as a half-octave period minus three generators. Its [[ploidacot]] is diploid epsilon-heptacot. It is a member of the [[diaschismic–gothmic equivalence continuum]] with {{nowrap| ''n'' {{=}} 7/2 }}; thus it is most naturally used as a 34-form.


POTE generator: ~25/24 = 71.1432
[[Subgroup]]: 2.3.5


Map: [&lt;2 4 5|, &lt;0 -7 -3|]
[[Comma list]]: 6115295232/6103515625
EDOs: [[118edo|118]], [[152edo|152]], [[270edo|270]], [[928edo|928]], [[1198edo|1198]], [[1468edo|1468]]
Badness: 0.0312


=Vishnu=
{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}
Commas: 4375/4374, 29360128/29296875
: mapping generators: ~78125/55296, ~25/24


POTE generator: ~25/24 = 71.1075
[[Optimal tuning]]s:
* [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{c}}
: [[error map]]: {{val| -0.046 -0.030 +0.150 }}
* [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1482{{c}}
: error map: {{val| 0.000 +0.007 +0.242 }}


Map: [&lt;2 4 5 10|, &lt;0 -7 -3 -37|]
{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}
EDOs: 118, 152, 270, [[1232edo|1232]], [[1502edo|1502]]
Badness: 0.0419


==11-limit==
[[Badness]] (Sintel): 0.731
Commas: 3025/3024, 4375/4374, 5632/5625


POTE generator: ~25/24 = 71.1048
=== Overview to extensions ===
The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds [[4375/4374]]. Narayana (84 & 118) adds [[65625/65536]]. Vishnean (16 & 50) adds [[126/125]]. There is also an unnamed 50 & 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu.  


Map: [&lt;2 4 5 10 10|, &lt;0 -7 -3 -37 -26|]
Trivish (84 & 186) adds [[250047/250000]], splitting the semi-octave period in three. Quarvish (68 & 270) adds [[2401/2400]], splitting the generator in four. Decavish (50 & 220) adds [[420175/419904]], splitting the semi-octave period in five.  
EDOs: 118, 152, 270, [[962edo|962]], 1232, 1502
Badness: 0.0142


==Ananta==
== Septimal vishnu ==
Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374
Septimal vishnu may be described as the {{nowrap| 118 & 152 }} temperament, tempering out 4375/4374, the [[ragisma]], and 29360128/29296875, the [[quasiorwellisma]], aside from the vishnu comma. [[270edo]] is an excellent tuning for this temperament, with generator 16\270 (71.{{overline|1}} cents), but it can be tuned to [[422edo]], [[692edo]], or [[962edo]]. It extends naturally to the [[11-limit]] by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]].


POTE generator: ~25/24 = 71.1170
[[Subgroup]]: 2.3.5.7


Map: [&lt;2 4 5 10 10 1|, &lt;0 -7 -3 -37 -26 54|]
[[Comma list]]: 4375/4374, 29360128/29296875
EDOs: 118, 152, 270, 928, 1198, 1468
Badness: 0.0237


==Acyuta==
{{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}
Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625


POTE generator: ~25/24 = 71.1001
[[Optimal tuning]]s:  
* [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{c}}
: [[error map]]: {{val| -0.103 +0.129 +0.125 -0.092 }}
* [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1106{{c}}
: error map: {{val| 0.000 +0.271 +0.354 +0.081 }}


Map: [&lt;2 4 5 10 10 17|, &lt;0 -7 -3 -37 -26 -81|]
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}
EDOs: 270, [[682edo|692]], 962
 
Badness: 0.0158</pre></div>
[[Badness]] (Sintel): 1.06
<h4>Original HTML 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;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;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;
=== 11-limit ===
&lt;br /&gt;
Subgroup: 2.3.5.7.11
Comma: 6115295232/6103515625&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 3025/3024, 4375/4374, 5632/5625
POTE generator: ~25/24 = 71.1432&lt;br /&gt;
 
&lt;br /&gt;
Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}
Map: [&amp;lt;2 4 5|, &amp;lt;0 -7 -3|]&lt;br /&gt;
 
EDOs: &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="/928edo"&gt;928&lt;/a&gt;, &lt;a class="wiki_link" href="/1198edo"&gt;1198&lt;/a&gt;, &lt;a class="wiki_link" href="/1468edo"&gt;1468&lt;/a&gt;&lt;br /&gt;
Optimal tunings:  
Badness: 0.0312&lt;br /&gt;
* WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{c}}
&lt;br /&gt;
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1077{{c}}
&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 ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502 }}
&lt;br /&gt;
 
POTE generator: ~25/24 = 71.1075&lt;br /&gt;
Badness (Sintel): 0.469
&lt;br /&gt;
 
Map: [&amp;lt;2 4 5 10|, &amp;lt;0 -7 -3 -37|]&lt;br /&gt;
==== Acyuta ====
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;
Subgroup: 2.3.5.7.11.13
Badness: 0.0419&lt;br /&gt;
 
&lt;br /&gt;
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
&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;
 
Commas: 3025/3024, 4375/4374, 5632/5625&lt;br /&gt;
Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}
&lt;br /&gt;
 
POTE generator: ~25/24 = 71.1048&lt;br /&gt;
Optimal tunings:
&lt;br /&gt;
* WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{c}}
Map: [&amp;lt;2 4 5 10 10|, &amp;lt;0 -7 -3 -37 -26|]&lt;br /&gt;
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1028{{c}}
EDOs: 118, 152, 270, &lt;a class="wiki_link" href="/962edo"&gt;962&lt;/a&gt;, 1232, 1502&lt;br /&gt;
 
Badness: 0.0142&lt;br /&gt;
{{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}
&lt;br /&gt;
 
&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;
Badness (Sintel): 0.653
Commas: 1001/1000, 3025/3024, 4096/4095, 4375/4374&lt;br /&gt;
 
&lt;br /&gt;
==== Ananta ====
POTE generator: ~25/24 = 71.1170&lt;br /&gt;
Subgroup: 2.3.5.7.11.13
&lt;br /&gt;
 
Map: [&amp;lt;2 4 5 10 10 1|, &amp;lt;0 -7 -3 -37 -26 54|]&lt;br /&gt;
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
EDOs: 118, 152, 270, 928, 1198, 1468&lt;br /&gt;
 
Badness: 0.0237&lt;br /&gt;
Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}
&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;
Optimal tuning:  
Commas: 1716/1715, 2080/2079, 3025/3024, 5632/5625&lt;br /&gt;
* WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{c}}
&lt;br /&gt;
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1170{{c}}
POTE generator: ~25/24 = 71.1001&lt;br /&gt;
 
&lt;br /&gt;
{{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}
Map: [&amp;lt;2 4 5 10 10 17|, &amp;lt;0 -7 -3 -37 -26 -81|]&lt;br /&gt;
 
EDOs: 270, &lt;a class="wiki_link" href="/682edo"&gt;692&lt;/a&gt;, 962&lt;br /&gt;
Badness (Sintel): 0.978
Badness: 0.0158&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Narayana ==
Named by [[Xenllium]] in 2021, narayana tempers out 65625/65536, the [[horwell comma]], as well as 321489/320000, the [[varunisma]], and may be described as the {{nowrap| 84 & 118 }} temperament.  
 
[[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:  
* [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{c}}
: [[error map]]: {{val| +0.228 -0.447 +0.422 -0.362 }}
* [[CWE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2659{{c}}
: error map: {{val| 0.000 -0.816 -0.111 -0.976 }}
 
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}
 
[[Badness]] (Sintel): 2.39
 
=== 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:
* WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2501{{c}}
 
{{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}
 
Badness (Sintel): 1.52
 
== Vishnean ==
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the [[starling comma]].
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 126/125, 540225/524288
 
{{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}
 
[[Optimal tuning]]s:  
* [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{c}}
: [[error map]]: {{val| +1.751 -1.637 +2.413 -5.031 }}
* [[CWE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.7141{{c}}
: error map: {{val| 0.000 -3.954 -1.456 -10.255 }}
 
{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}
 
[[Badness]] (Sintel): 4.08
 
=== 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:
* WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{c}}
* CWE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.8588{{c}}
 
{{Optimal ET sequence|legend=0| 16, 34, 50 }}
 
Badness (Sintel): 2.38
 
=== 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:
* WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.8699{{c}}
 
{{Optimal ET sequence|legend=0| 16, 34, 50 }}
 
Badness (Sintel): 1.68
 
== Trivish ==
Trivish tempers out 250047/250000, the [[landscape comma]], with a 1/6-octave period. It may be described as the {{nowrap| 84 & 186 }} temperament. It is more significant in the [[11-limit]], where it tempers out the [[kalisma]] and the [[olympia]]. In the [[13-limit]], the generator can be taken as a [[~]][[14/13]]. [[270edo]] is an obvious tuning for it, but it can be tuned to [[354edo]], [[624edo]] or [[894edo]]. It was named by [[Flora Canou]] in 2026 for the fact that it splits the period of vishnu in three.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 250047/250000, 134217728/133984375
 
{{Mapping|legend=1| 6 5 12 22 | 0 7 3 -8 }}
: mapping generators: ~18375/16384, ~2205/2048
 
[[Optimal tuning]]s:
* [[WE]]: ~18375/16384 = 199.9885{{c}}, ~2205/2048 = 128.8583{{c}}
: [[error map]]: {{val| -0.069 -0.005 +0.123 +0.054 }}
* [[CWE]]: ~18375/16384 = 200.0000{{c}}, ~2205/2048 = 128.8643{{c}}
: error map: {{val| 0.000 +0.095 +0.279 +0.256 }}
 
{{Optimal ET sequence|legend=1| 84, 186, 270, 624, 894, 1164 }}
 
[[Badness]] (Sintel): 1.51
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 131072/130977, 151263/151250
 
Mapping: {{mapping| 6 5 12 22 33 | 0 7 3 -8 -19 }}
 
Optimal tunings:
* WE: ~55/49 = 199.9885{{c}}, ~320/297 = 128.8582{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~320/297 = 128.8661{{c}}
 
{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894, 1164 }}
 
Badness (Sintel): 0.807
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 1716/1715, 2080/2079, 4096/4095, 34398/34375
 
Mapping: {{mapping| 6 5 12 22 33 28 | 0 7 3 -8 -19 -9 }}
 
Optimal tunings:
* WE: ~55/49 = 199.9922{{c}}, ~14/13 = 128.8565{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8621{{c}}
 
{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894, 2058f }}
 
Badness (Sintel): 0.791
 
=== 2.3.5.7.11.13.19 subgroup ===
Subgroup: 2.3.5.7.11.13.19
 
Comma list: 1521/1520, 1716/1715, 2080/2079, 2376/2375, 3250/3249
 
Mapping: {{mapping| 6 5 12 22 33 28 30 | 0 7 3 -8 -19 -9 -7 }}
 
Optimal tunings:
* WE: ~55/49 = 199.9909{{c}}, ~14/13 = 128.8564{{c}}
* CWE: ~55/49 = 200.0000{{c}}, ~14/13 = 128.8630{{c}}
 
{{Optimal ET sequence|legend=0| 84, 186, 270, 624, 894 }}
 
Badness (Sintel): 0.591
 
== Quarvish ==
Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 & 270 }} temperament.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 2401/2400, 6115295232/6103515625
 
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
: mapping generators: ~78125/55296, ~110592/109375
 
[[Optimal tuning]]s:
* [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{c}}
: [[error map]]: {{val| -0.025 -0.020 +0.189 -0.123 }}
* [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~110592/109375 = 17.7873{{c}}
: error map: {{val| 0.000 +0.002 +0.239 -0.060 }}
 
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
 
[[Badness]] (Sintel): 1.14
 
=== 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:
* WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~99/98 = 17.7870{{c}}
 
{{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}
 
Badness (Sintel): 0.657
 
== Decavish ==
Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 220 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave.
 
[[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:
* [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{c}})
: [[error map]]: {{val| -0.043 +0.071 +0.197 -0.242 }}
* [[CWE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8658{{c}} (~36/35 = 48.8658{{c}})
: error map: {{val| 0.000 +0.106 +0.284 -0.168 }}
 
{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}
 
[[Badness]] (Sintel): 2.90
 
=== 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:
* WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8589{{c}} (~36/35 = 48.8589{{c}})
 
{{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}
 
Badness (Sintel): 1.22
 
=== 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:
* WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{c}})
* CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8506{{c}} (~36/35 = 48.8506{{c}})
 
{{Optimal ET sequence|legend=0| 50, …, 220, 270, 590, 860, 1130 }}
 
Badness (Sintel): 0.905
 
== References ==
<references/>
 
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Temperament families]]
[[Category:Catalogs of rank-2 temperaments]]

Latest revision as of 12:25, 14 August 2026

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 vishnu family tempers out the vishnu comma (monzo: [23 6 -14⟩, ratio: 6 115 295 232 / 6 103 515 625), an unnoticeable comma of about 3.34 cents in size.

Vishnu

The generator for the vishnu temperament is a classical chromatic semitone, seven of which make a perfect fourth, and 5/4 is found as a half-octave period minus three generators. Its ploidacot is diploid epsilon-heptacot. It is a member of the diaschismic–gothmic equivalence continuum with n = 7/2; thus it is most naturally used as a 34-form.

Subgroup: 2.3.5

Comma list: 6115295232/6103515625

Mapping: [⟨2 4 5], ⟨0 -7 -3]]

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

Optimal tunings:

  • WE: ~78125/55296 = 599.9771 ¢, ~25/24 = 71.1405 ¢
error map: ⟨-0.046 -0.030 +0.150]
  • CWE: ~78125/55296 = 600.0000 ¢, ~25/24 = 71.1482 ¢
error map: ⟨0.000 +0.007 +0.242]

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

Badness (Sintel): 0.731

Overview to extensions

The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 & 152) adds 4375/4374. Narayana (84 & 118) adds 65625/65536. Vishnean (16 & 50) adds 126/125. There is also an unnamed 50 & 84 temperament, which tempers out 225/224. These all use the same generators as classical vishnu.

Trivish (84 & 186) adds 250047/250000, splitting the semi-octave period in three. Quarvish (68 & 270) adds 2401/2400, splitting the generator in four. Decavish (50 & 220) adds 420175/419904, splitting the semi-octave period in five.

Septimal vishnu

Septimal vishnu may be described as the 118 & 152 temperament, tempering out 4375/4374, the ragisma, and 29360128/29296875, the quasiorwellisma, aside from the vishnu comma. 270edo is an excellent tuning for this temperament, with generator 16\270 (71.1 cents), but it can be tuned to 422edo, 692edo, or 962edo. It extends naturally to the 11-limit by identifying a stack of four 5/4's as 11/9, tempering out 5632/5625.

Subgroup: 2.3.5.7

Comma list: 4375/4374, 29360128/29296875

Mapping: [⟨2 4 5 10], ⟨0 -7 -3 -37]]

Optimal tunings:

  • WE: ~10125/7168 = 599.9486 ¢, ~25/24 = 71.1014 ¢
error map: ⟨-0.103 +0.129 +0.125 -0.092]
  • CWE: ~10125/7168 = 600.0000 ¢, ~25/24 = 71.1106 ¢
error map: ⟨0.000 +0.271 +0.354 +0.081]

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

Badness (Sintel): 1.06

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:

  • WE: ~99/70 = 599.9549 ¢, ~25/24 = 71.0994 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.1077 ¢

Optimal ET sequence: 34d, 84de, 118, 152, 270, 962, 1232, 1502

Badness (Sintel): 0.469

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:

  • WE: ~99/70 = 599.9475 ¢, ~25/24 = 71.0947 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.1028 ¢

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

Badness (Sintel): 0.653

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:

  • WE: ~99/70 = 599.9940 ¢, ~25/24 = 71.1163 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.1170 ¢

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

Badness (Sintel): 0.978

Narayana

Named by Xenllium in 2021, narayana tempers out 65625/65536, the horwell comma, as well as 321489/320000, the varunisma, and may be described as the 84 & 118 temperament.

Subgroup: 2.3.5.7

Comma list: 65625/65536, 321489/320000

Mapping: [⟨2 4 5 3], ⟨0 -7 -3 22]]

Optimal tunings:

  • WE: ~567/400 = 600.1141 ¢, ~25/24 = 71.2783 ¢
error map: ⟨+0.228 -0.447 +0.422 -0.362]
  • CWE: ~567/400 = 600.0000 ¢, ~25/24 = 71.2659 ¢
error map: ⟨0.000 -0.816 -0.111 -0.976]

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

Badness (Sintel): 2.39

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:

  • WE: ~99/70 = 600.0992 ¢, ~25/24 = 71.2593 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~25/24 = 71.2501 ¢

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

Badness (Sintel): 1.52

Vishnean

Named by Petr Pařízek in 2011[1], vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the starling comma.

Subgroup: 2.3.5.7

Comma list: 126/125, 540225/524288

Mapping: [⟨2 4 5 5], ⟨0 -7 -3 5]]

Optimal tunings:

  • WE: ~735/512 = 600.8754 ¢, ~25/24 = 71.8834 ¢
error map: ⟨+1.751 -1.637 +2.413 -5.031]
  • CWE: ~735/512 = 600.0000 ¢, ~25/24 = 71.7141 ¢
error map: ⟨0.000 -3.954 -1.456 -10.255]

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

Badness (Sintel): 4.08

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:

  • WE: ~63/44 = 600.7144 ¢, ~25/24 = 72.0091 ¢
  • CWE: ~63/44 = 600.0000 ¢, ~25/24 = 71.8588 ¢

Optimal ET sequence: 16, 34, 50

Badness (Sintel): 2.38

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:

  • WE: ~55/39 = 600.5983 ¢, ~25/24 = 71.9975 ¢
  • CWE: ~55/39 = 600.0000 ¢, ~25/24 = 71.8699 ¢

Optimal ET sequence: 16, 34, 50

Badness (Sintel): 1.68

Trivish

Trivish tempers out 250047/250000, the landscape comma, with a 1/6-octave period. It may be described as the 84 & 186 temperament. It is more significant in the 11-limit, where it tempers out the kalisma and the olympia. In the 13-limit, the generator can be taken as a ~14/13. 270edo is an obvious tuning for it, but it can be tuned to 354edo, 624edo or 894edo. It was named by Flora Canou in 2026 for the fact that it splits the period of vishnu in three.

Subgroup: 2.3.5.7

Comma list: 250047/250000, 134217728/133984375

Mapping: [⟨6 5 12 22], ⟨0 7 3 -8]]

mapping generators: ~18375/16384, ~2205/2048

Optimal tunings:

  • WE: ~18375/16384 = 199.9885 ¢, ~2205/2048 = 128.8583 ¢
error map: ⟨-0.069 -0.005 +0.123 +0.054]
  • CWE: ~18375/16384 = 200.0000 ¢, ~2205/2048 = 128.8643 ¢
error map: ⟨0.000 +0.095 +0.279 +0.256]

Optimal ET sequence: 84, 186, 270, 624, 894, 1164

Badness (Sintel): 1.51

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 131072/130977, 151263/151250

Mapping: [⟨6 5 12 22 33], ⟨0 7 3 -8 -19]]

Optimal tunings:

  • WE: ~55/49 = 199.9885 ¢, ~320/297 = 128.8582 ¢
  • CWE: ~55/49 = 200.0000 ¢, ~320/297 = 128.8661 ¢

Optimal ET sequence: 84, 186, 270, 624, 894, 1164

Badness (Sintel): 0.807

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1716/1715, 2080/2079, 4096/4095, 34398/34375

Mapping: [⟨6 5 12 22 33 28], ⟨0 7 3 -8 -19 -9]]

Optimal tunings:

  • WE: ~55/49 = 199.9922 ¢, ~14/13 = 128.8565 ¢
  • CWE: ~55/49 = 200.0000 ¢, ~14/13 = 128.8621 ¢

Optimal ET sequence: 84, 186, 270, 624, 894, 2058f

Badness (Sintel): 0.791

2.3.5.7.11.13.19 subgroup

Subgroup: 2.3.5.7.11.13.19

Comma list: 1521/1520, 1716/1715, 2080/2079, 2376/2375, 3250/3249

Mapping: [⟨6 5 12 22 33 28 30], ⟨0 7 3 -8 -19 -9 -7]]

Optimal tunings:

  • WE: ~55/49 = 199.9909 ¢, ~14/13 = 128.8564 ¢
  • CWE: ~55/49 = 200.0000 ¢, ~14/13 = 128.8630 ¢

Optimal ET sequence: 84, 186, 270, 624, 894

Badness (Sintel): 0.591

Quarvish

Quarvish tempers out 2401/2400, the breedsma, and may be described as the 68 & 270 temperament.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 6115295232/6103515625

Mapping: [⟨2 4 5 6], ⟨0 -28 -12 -13]]

mapping generators: ~78125/55296, ~110592/109375

Optimal tunings:

  • WE: ~78125/55296 = 599.9874 ¢, ~110592/109375 = 17.7862 ¢
error map: ⟨-0.025 -0.020 +0.189 -0.123]
  • CWE: ~78125/55296 = 600.0000 ¢, ~110592/109375 = 17.7873 ¢
error map: ⟨0.000 +0.002 +0.239 -0.060]

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

Badness (Sintel): 1.14

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:

  • WE: ~99/70 = 599.9884 ¢, ~99/98 = 17.7865 ¢
  • CWE: ~99/70 = 600.0000 ¢, ~99/98 = 17.7870 ¢

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

Badness (Sintel): 0.657

Decavish

Decavish tempers out the wizma as well as the linus comma, and may be described as the 50 & 220 temperament. It was named by Xenllium in 2021 for the fact that its period is 1/10 octave.

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:

  • WE: ~15/14 = 119.9957 ¢, ~54/49 = 168.8645 ¢ (~36/35 = 48.8689 ¢)
error map: ⟨-0.043 +0.071 +0.197 -0.242]
  • CWE: ~15/14 = 120.0000 ¢, ~54/49 = 168.8658 ¢ (~36/35 = 48.8658 ¢)
error map: ⟨0.000 +0.106 +0.284 -0.168]

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

Badness (Sintel): 2.90

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:

  • WE: ~15/14 = 119.9997 ¢, ~54/49 = 168.8587 ¢ (~36/35 = 48.8590 ¢)
  • CWE: ~15/14 = 120.0000 ¢, ~54/49 = 168.8589 ¢ (~36/35 = 48.8589 ¢)

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

Badness (Sintel): 1.22

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:

  • WE: ~15/14 = 120.0037 ¢, ~54/49 = 168.8537 ¢ (~36/35 = 48.8500 ¢)
  • CWE: ~15/14 = 120.0000 ¢, ~54/49 = 168.8506 ¢ (~36/35 = 48.8506 ¢)

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

Badness (Sintel): 0.905

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
Retrieved from "https://en.xen.wiki/index.php?title=Vishnu_family&oldid=235703"