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Vishnu family: Difference between revisions

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m Units, misc. cleanup, - redundant category
Switch to Sintel's badness, WE & CWE tunings
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1556{{c}}
* [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{c}}
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~25/24 = 71.143{{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 }}


{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}
{{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}


[[Badness]] (Smith): 0.031181
[[Badness]] (Sintel): 0.731


== Septimal vishnu ==
== Septimal vishnu ==
Line 26: Line 28:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1175{{c}}
* [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{c}}
* [[POTE]]: ~10125/7168 = 600.000{{c}}, ~25/24 = 71.107{{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 }}


{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}


[[Badness]] (Smith): 0.041912
[[Badness]] (Sintel): 1.06


=== 11-limit ===
=== 11-limit ===
Line 41: Line 45:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1142{{c}}
* WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.105{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1077{{c}}


{{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}
{{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502 }}


Badness (Smith): 0.014180
Badness (Sintel): 0.469


==== Ananta ====
==== Ananta ====
Line 56: Line 60:


Optimal tuning:  
Optimal tuning:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1173{{c}}
* WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.117{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1170{{c}}


{{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}
{{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}


Badness (Smith): 0.023678
Badness (Sintel): 0.978


==== Acyuta ====
==== Acyuta ====
Line 71: Line 75:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1079{{c}}
* WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.101{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1028{{c}}


{{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}
{{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}


Badness (Smith): 0.015805
Badness (Sintel): 0.653


== Vishnean ==
== Vishnean ==
Line 86: Line 90:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.4956{{c}}
* [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{c}}
* [[POTE]]: ~735/512 = 600.000{{c}}, ~25/24 = 71.779{{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 }}
{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}


[[Badness]] (Smith): 0.161398
[[Badness]] (Sintel): 4.08


=== 11-limit ===
=== 11-limit ===
Line 101: Line 107:


Optimal tunings:  
Optimal tunings:  
* CTE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.6218{{c}}
* WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{c}}
* POTE: ~63/44 = 600.000{{c}}, ~25/24 = 71.924{{c}}
* CWE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.8588{{c}}


{{Optimal ET sequence|legend=0| 16, 34, 50 }}
{{Optimal ET sequence|legend=0| 16, 34, 50 }}


Badness (Smith): 0.071990
Badness (Sintel): 2.38


=== 13-limit ===
=== 13-limit ===
Line 116: Line 122:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.6369{{c}}
* WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{c}}
* POTE: ~55/39 = 600.000{{c}}, ~25/24 = 71.926{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.8699{{c}}


{{Optimal ET sequence|legend=0| 16, 34, 50 }}
{{Optimal ET sequence|legend=0| 16, 34, 50 }}


Badness (Smith): 0.040739
Badness (Sintel): 1.68


== Narayana ==
== Narayana ==
Line 131: Line 137:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2706{{c}}
* [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{c}}
* [[POTE]]: ~567/400 = 600.000{{c}}, ~25/24 = 71.265{{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 }}
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}


[[Badness]] (Smith): 0.094295
[[Badness]] (Sintel): 2.39


=== 11-limit ===
=== 11-limit ===
Line 146: Line 154:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2609{{c}}
* WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.248{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2501{{c}}


{{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}
{{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}


Badness (Smith): 0.045908
Badness (Sintel): 1.52


== Quarvish ==
== Quarvish ==
Line 159: Line 167:


{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}
: mapping generators: ~78125/55296, ~110592/109375


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~7/5 = 582.2115{{c}} (~110592/109375 = 17.7885{{c}})
* [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{c}}
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~110592/109375 = 17.787{{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 }}
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}


[[Badness]] (Smith): 0.045029
[[Badness]] (Sintel): 1.14


=== 11-limit ===
=== 11-limit ===
Line 176: Line 187:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 600.0000{{c}}, ~7/5 = 582.2122{{c}} (~99/98 = 17.7878{{c}})
* WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{c}}
* POTE: ~99/70 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~99/98 = 17.787{{c}})
* CWE: ~99/70 = 600.0000{{c}}, ~99/98 = 17.7870{{c}}


{{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}
{{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}


Badness (Smith): 0.019868
Badness (Sintel): 0.657


== Decavish ==
== Decavish ==
The decavish temperament (50 & 270) tempers out the wizma, {{monzo| -6 -8 2 5 }} = 420175/419904 and the [[linus comma]], {{monzo| 11 -10 -10 10 }} = 578509309952/576650390625.
Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 & 270 }} temperament.  


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 194: Line 205:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8587{{c}} (~25/24 = 71.1413{{c}}, or ~36/35 = 48.8587{{c}})
* [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{c}})
* [[POTE]]: ~15/14 = 120.000{{c}}, ~54/49 = 168.871{{c}} (~25/24 = 71.129{{c}}, or ~36/35 = 48.871{{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 }}
{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}


[[Badness]] (Smith): 0.114531
[[Badness]] (Sintel): 2.90


=== 11-limit ===
=== 11-limit ===
Line 209: Line 222:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{c}})
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.141{{c}}, or ~36/35 = 48.859{{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 }}
{{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}


Badness (Smith): 0.036938
Badness (Sintel): 1.22


=== 13-limit ===
=== 13-limit ===
Line 224: Line 237:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{c}})
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.151{{c}}, or ~36/35 = 48.859{{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 }}
{{Optimal ET sequence|legend=0| 50, …, 220, 270, 590, 860, 1130 }}


Badness (Smith): 0.021906
Badness (Sintel): 0.905


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Vishnu_family"