Vishnu family: Difference between revisions

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m FloraC moved page Vishnuzmic family to Vishnu family: The temp's name is *vishnu*
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{{Technical data page}}
{{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>.
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), 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 ==
Line 8: Line 8:


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


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1556{{c}}
* [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~25/24 = 71.143{{c}}


{{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]]: 0.031181
[[Badness]] (Smith): 0.031181


== Septimal vishnu ==
== Septimal vishnu ==
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[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175
* [[CTE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1175{{c}}
* [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107
* [[POTE]]: ~10125/7168 = 600.000{{c}}, ~25/24 = 71.107{{c}}


{{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]]: 0.041912
[[Badness]] (Smith): 0.041912


=== 11-limit ===
=== 11-limit ===
Line 42: Line 41:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1142
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1142{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.105
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.105{{c}}


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


Badness: 0.014180
Badness (Smith): 0.014180


==== Ananta ====
==== Ananta ====
Line 57: Line 56:


Optimal tuning:  
Optimal tuning:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1173
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1173{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.117
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.117{{c}}


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


Badness: 0.023678
Badness (Smith): 0.023678


==== Acyuta ====
==== Acyuta ====
Line 72: Line 71:


Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.1079
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1079{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.101
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.101{{c}}


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


Badness: 0.015805
Badness (Smith): 0.015805


== Vishnean ==
== Vishnean ==
Line 87: Line 86:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956
* [[CTE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.4956{{c}}
* [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779
* [[POTE]]: ~735/512 = 600.000{{c}}, ~25/24 = 71.779{{c}}


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


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


=== 11-limit ===
=== 11-limit ===
Line 102: Line 101:


Optimal tunings:  
Optimal tunings:  
* CTE: ~63/44 = 1\2, ~25/24 = 71.6218
* CTE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.6218{{c}}
* POTE: ~63/44 = 1\2, ~25/24 = 71.924
* POTE: ~63/44 = 600.000{{c}}, ~25/24 = 71.924{{c}}


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


Badness: 0.071990
Badness (Smith): 0.071990


=== 13-limit ===
=== 13-limit ===
Line 117: Line 116:


Optimal tunings:  
Optimal tunings:  
* CTE: ~55/39 = 1\2, ~25/24 = 71.6369
* CTE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.6369{{c}}
* POTE: ~55/39 = 1\2, ~25/24 = 71.926
* POTE: ~55/39 = 600.000{{c}}, ~25/24 = 71.926{{c}}


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


Badness: 0.040739
Badness (Smith): 0.040739


== Narayana ==
== Narayana ==
Line 132: Line 131:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~567/400 = 1\2, ~25/24 = 71.2706
* [[CTE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2706{{c}}
* [[POTE]]: ~567/400 = 1\2, ~25/24 = 71.265
* [[POTE]]: ~567/400 = 600.000{{c}}, ~25/24 = 71.265{{c}}


{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}
{{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}


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


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~25/24 = 71.2609
* CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2609{{c}}
* POTE: ~99/70 = 1\2, ~25/24 = 71.248
* POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.248{{c}}


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


Badness: 0.045908
Badness (Smith): 0.045908


== Quarvish ==
== Quarvish ==
Line 162: Line 161:


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)
* [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~7/5 = 582.2115{{c}} (~110592/109375 = 17.7885{{c}})
* [[POTE]]: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)
* [[POTE]]: ~78125/55296 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~110592/109375 = 17.787{{c}})


{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}
{{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}


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


=== 11-limit ===
=== 11-limit ===
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Optimal tunings:  
Optimal tunings:  
* CTE: ~99/70 = 1\2, ~7/5 = 582.2122 (~99/98 = 17.7878)
* CTE: ~99/70 = 600.0000{{c}}, ~7/5 = 582.2122{{c}} (~99/98 = 17.7878{{c}})
* POTE: ~99/70 = 1\2, ~7/5 = 582.213 (~99/98 = 17.787)
* POTE: ~99/70 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~99/98 = 17.787{{c}})


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


Badness: 0.019868
Badness (Smith): 0.019868


== Decavish ==
== 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.
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.


[[Subgroup]]: 2.3.5.7
[[Subgroup]]: 2.3.5.7
Line 192: Line 191:


{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}
{{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}
: mapping generators: ~15/14, ~54/49
: mapping generators: ~15/14, ~54/49


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
* [[CTE]]: ~15/14 = 1\10, ~54/49 = 168.8587 (~25/24 = 71.1413, or ~36/35 = 48.8587)
* [[CTE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8587{{c}} (~25/24 = 71.1413{{c}}, or ~36/35 = 48.8587{{c}})
* [[POTE]]: ~15/14 = 1\10, ~54/49 = 168.871 (~25/24 = 71.129, or ~36/35 = 48.871)
* [[POTE]]: ~15/14 = 120.000{{c}}, ~54/49 = 168.871{{c}} (~25/24 = 71.129{{c}}, or ~36/35 = 48.871{{c}})


{{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]] (Smith): 0.114531


=== 11-limit ===
=== 11-limit ===
Line 211: Line 209:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.141, or ~36/35 = 48.859)
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.141{{c}}, or ~36/35 = 48.859{{c}})


Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}
{{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}


Badness: 0.036938
Badness (Smith): 0.036938


=== 13-limit ===
=== 13-limit ===
Line 226: Line 224:


Optimal tunings:  
Optimal tunings:  
* CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)
* CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})
* POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.151, or ~36/35 = 48.859)
* POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.151{{c}}, or ~36/35 = 48.859{{c}})


Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}
{{Optimal ET sequence|legend=0| 50, 220, 270, 590, 860, 1130 }}


Badness: 0.021906
Badness (Smith): 0.021906


[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Vishnuzmic family| ]] <!-- main article -->
[[Category:Vishnu family| ]] <!-- main article -->
[[Category:Vishnuzmic| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Revision as of 06:49, 18 June 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), 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 = 600.0000 ¢, ~25/24 = 71.1556 ¢
  • POTE: ~78125/55296 = 600.000 ¢, ~25/24 = 71.143 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.1175 ¢
  • POTE: ~10125/7168 = 600.000 ¢, ~25/24 = 71.107 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.1142 ¢
  • POTE: ~99/70 = 600.000 ¢, ~25/24 = 71.105 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.1173 ¢
  • POTE: ~99/70 = 600.000 ¢, ~25/24 = 71.117 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.1079 ¢
  • POTE: ~99/70 = 600.000 ¢, ~25/24 = 71.101 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.4956 ¢
  • POTE: ~735/512 = 600.000 ¢, ~25/24 = 71.779 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.6218 ¢
  • POTE: ~63/44 = 600.000 ¢, ~25/24 = 71.924 ¢

Optimal ET sequence: 16, 34, 50

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.6369 ¢
  • POTE: ~55/39 = 600.000 ¢, ~25/24 = 71.926 ¢

Optimal ET sequence: 16, 34, 50

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.2706 ¢
  • POTE: ~567/400 = 600.000 ¢, ~25/24 = 71.265 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~25/24 = 71.2609 ¢
  • POTE: ~99/70 = 600.000 ¢, ~25/24 = 71.248 ¢

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

Badness (Smith): 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 = 600.0000 ¢, ~7/5 = 582.2115 ¢ (~110592/109375 = 17.7885 ¢)
  • POTE: ~78125/55296 = 600.000 ¢, ~7/5 = 582.213 ¢ (~110592/109375 = 17.787 ¢)

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

Badness (Smith): 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 = 600.0000 ¢, ~7/5 = 582.2122 ¢ (~99/98 = 17.7878 ¢)
  • POTE: ~99/70 = 600.000 ¢, ~7/5 = 582.213 ¢ (~99/98 = 17.787 ¢)

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

Badness (Smith): 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 = 120.0000 ¢, ~54/49 = 168.8587 ¢ (~25/24 = 71.1413 ¢, or ~36/35 = 48.8587 ¢)
  • POTE: ~15/14 = 120.000 ¢, ~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 (Smith): 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 = 120.0000 ¢, ~54/49 = 168.8583 ¢ (~25/24 = 71.1417 ¢, or ~36/35 = 48.8583 ¢)
  • POTE: ~15/14 = 120.000 ¢, ~54/49 = 168.859 ¢ (~25/24 = 71.141 ¢, or ~36/35 = 48.859 ¢)

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

Badness (Smith): 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 = 120.0000 ¢, ~54/49 = 168.8583 ¢ (~25/24 = 71.1417 ¢, or ~36/35 = 48.8583 ¢)
  • POTE: ~15/14 = 120.000 ¢, ~54/49 = 168.859 ¢ (~25/24 = 71.151 ¢, or ~36/35 = 48.859 ¢)

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

Badness (Smith): 0.021906

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