Xenharmonic Wiki

Vishnuzmic family: Difference between revisions

← Older edit
VisualWikitext
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,160 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
 
(5 intermediate revisions by 3 users not shown)
Line 1: Line 1:
The '''vishnuzmic family''' of temperaments tempers out the [[vishnuzma]], {{Monzo| 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)<sup>7</sup>.
{{Technical data page}}
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>.


== Vishnu ==
== Vishnu ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


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


[[Mapping]]: [{{val| 2 4 5 }}, {{val| 0 -7 -3 }}]
{{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}


[[POTE generator]]: ~25/24 = 71.143
: mapping generators: ~78125/55296, ~25/24
 
[[Optimal tuning]]s:
* [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556
* [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143


{{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 }}
Line 15: Line 20:


== Septimal vishnu ==
== Septimal vishnu ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 4375/4374, 29360128/29296875
[[Comma list]]: 4375/4374, 29360128/29296875


[[Mapping]]: [{{val| 2 4 5 10 }}, {{val| 0 -7 -3 -37 }}]
{{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}


{{Multival|legend=1| 14 6 74 -23 78 155 }}
[[Optimal tuning]]s:
* [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175
* [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107


[[POTE generator]]: ~25/24 = 71.107
{{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}
 
{{Optimal ET sequence|legend=1| 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc }}


[[Badness]]: 0.041912
[[Badness]]: 0.041912
Line 34: Line 39:
Comma list: 3025/3024, 4375/4374, 5632/5625
Comma list: 3025/3024, 4375/4374, 5632/5625


Mapping: [{{val| 2 4 5 10 10 }}, {{val| 0 -7 -3 -37 -26 }}]
Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}


POTE generator: ~25/24 = 71.105
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.1142
* POTE: ~99/70 = 1\2, ~25/24 = 71.105


{{Optimal ET sequence|legend=1| 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}
Optimal ET sequence: {{Optimal ET sequence| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}


Badness: 0.014180
Badness: 0.014180
Line 47: Line 54:
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374
Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374


Mapping: [{{val| 2 4 5 10 10 1 }}, {{val| 0 -7 -3 -37 -26 54 }}]
Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}


POTE generator: ~25/24 = 71.117
Optimal tuning:
* CTE: ~99/70 = 1\2, ~25/24 = 71.1173
* POTE: ~99/70 = 1\2, ~25/24 = 71.117


{{Optimal ET sequence|legend=1| 118, 152, 270, 928, 1198, 1468 }}
Optimal ET sequence: {{Optimal ET sequence| 118, 152, 270, 928, 1198, 1468 }}


Badness: 0.023678
Badness: 0.023678
Line 60: Line 69:
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625
Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625


Mapping: [{{val| 2 4 5 10 10 17 }}, {{val| 0 -7 -3 -37 -26 -81 }}]
Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}


POTE generator: ~25/24 = 71.101
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.1079
* POTE: ~99/70 = 1\2, ~25/24 = 71.101


{{Optimal ET sequence|legend=1| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}
Optimal ET sequence: {{Optimal ET sequence| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}


Badness: 0.015805
Badness: 0.015805


== Vishnean ==
== Vishnean ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 126/125, 540225/524288
[[Comma list]]: 126/125, 540225/524288


[[Mapping]]: [{{val| 2 4 5 5 }}, {{val| 0 -7 -3 5 }}]
{{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}
 
{{Multival|legend=1| 14 6 -10 -23 -55 -40 }}


[[POTE generator]]: ~25/24 = 71.779
[[Optimal tuning]]s:
* [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956
* [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779


{{Optimal ET sequence|legend=1| 16, 34, 50 }}
{{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}


[[Badness]]: 0.161398
[[Badness]]: 0.161398
Line 88: Line 99:
Comma list: 126/125, 385/384, 1350/1331
Comma list: 126/125, 385/384, 1350/1331


Mapping: [{{val| 2 4 5 5 8 }}, {{val| 0 -7 -3 5 -9 }}]
Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}


POTE generator: ~25/24 = 71.924
Optimal tunings:
* CTE: ~63/44 = 1\2, ~25/24 = 71.6218
* POTE: ~63/44 = 1\2, ~25/24 = 71.924


{{Optimal ET sequence|legend=1| 16, 34, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}


Badness: 0.071990
Badness: 0.071990
Line 101: Line 114:
Comma list: 105/104, 126/125, 144/143, 847/845
Comma list: 105/104, 126/125, 144/143, 847/845


Mapping: [{{val| 2 4 5 5 8 8 }}, {{val| 0 -7 -3 5 -9 -5 }}]
Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}


POTE generator: ~25/24 = 71.926
Optimal tunings:
* CTE: ~55/39 = 1\2, ~25/24 = 71.6369
* POTE: ~55/39 = 1\2, ~25/24 = 71.926


{{Optimal ET sequence|legend=1| 16, 34, 50 }}
Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}


Badness: 0.040739
Badness: 0.040739


== Narayana ==
== Narayana ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 65625/65536, 321489/320000
[[Comma list]]: 65625/65536, 321489/320000


[[Mapping]]: [{{val| 2 4 5 3 }}, {{val| 0 -7 -3 22 }}]
{{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}
 
{{Multival|legend=1| 14 6 -44 -23 -109 -119 }}


[[POTE generator]]: ~25/24 = 71.265
[[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 }}
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}
Line 129: Line 144:
Comma list: 441/440, 8019/8000, 65625/65536
Comma list: 441/440, 8019/8000, 65625/65536


Mapping: [{{val| 2 4 5 3 3 }}, {{val| 0 -7 -3 22 33 }}]
Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}


POTE generator: ~25/24 = 71.248
Optimal tunings:
* CTE: ~99/70 = 1\2, ~25/24 = 71.2609
* POTE: ~99/70 = 1\2, ~25/24 = 71.248


{{Optimal ET sequence|legend=1| 34e, 84, 118, 202, 320 }}
Optimal ET sequence: {{Optimal ET sequence| 34e, 84, 118, 202, 320 }}


Badness: 0.045908
Badness: 0.045908


== Quarvish ==
== Quarvish ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 2401/2400, 6115295232/6103515625
[[Comma list]]: 2401/2400, 6115295232/6103515625


[[Mapping]]: [{{val| 2 4 5 6 }}, {{val| 0 -28 -12 -13 }}]
{{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}


{{Multival|legend=1| 56 24 26 -92 -116 -7 }}
[[Optimal tuning]]s:
 
* [[CTE]]: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)
[[POTE generator]]: ~7/5 = 582.213
* [[POTE]]: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)


{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
Line 157: Line 174:
Comma list: 2401/2400, 9801/9800, 172032/171875
Comma list: 2401/2400, 9801/9800, 172032/171875


Mapping: [{{val| 2 4 5 6 6 }}, {{val| 0 -28 -12 -13 31 }}]
Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}


POTE generator: ~7/5 = 582.213
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|legend=1| 68, 134, 202, 270, 742, 1012 }}
Optimal ET sequence: {{Optimal ET sequence| 68, 134, 202, 270, 742, 1012 }}


Badness: 0.019868
Badness: 0.019868


== Decavish ==
== Decavish ==
The ''decavish'' temperament (50&amp;270) tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904 and the [[15/14 equal-step tuning|linus comma]], {{monzo|11 -10 -10 10}} = 578509309952/576650390625.
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 420175/419904, 2202927104/2197265625
[[Comma list]]: 420175/419904, 2202927104/2197265625


[[Mapping]]: [{{val| 10 13 22 24 }}, {{val| 0 7 3 10 }}]
{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}


{{Multival|legend=1| 70 30 100 -115 -38 148 }}
: mapping generators: ~15/14, ~54/49


[[POTE generator]]: ~25/24 = 71.129
[[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 }}
{{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}


[[Badness]]: 0.114531
[[Badness]]: 0.114531
Line 187: Line 208:
Comma list: 9801/9800, 41503/41472, 172032/171875
Comma list: 9801/9800, 41503/41472, 172032/171875


Mapping: [{{val| 10 13 22 24 35 }}, {{val| 0 7 3 10 -1 }}]
Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}


POTE generator: ~25/24 = 71.141
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|legend=1| 50, 220, 270, 860, 1130, 1400, 3070cd, 4470cde }}
Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}


Badness: 0.036938
Badness: 0.036938
Line 200: Line 223:
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655


Mapping: [{{val| 10 13 22 24 35 37 }}, {{val| 0 7 3 10 -1 0 }}]
Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}


POTE generator: ~25/24 = 71.151
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|legend=1| 50, 220, 270, 590, 860, 1130 }}
Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}


Badness: 0.021906
Badness: 0.021906


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Vishnuzmic]]
[[Category:Pages with mostly numerical content]]
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnuzmic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Vishnuzmic_family"