Vishnuzmic family: Difference between revisions
"Vishnu" was the proposed 5-limit name it seems |
Add narayana temperament |
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[[Mapping]]: [{{val| 2 4 5 10 }}, {{val| 0 -7 -3 -37 }}] | [[Mapping]]: [{{val| 2 4 5 10 }}, {{val| 0 -7 -3 -37 }}] | ||
{{Multival|legend=1|14 6 74 -23 78 155}} | {{Multival|legend=1| 14 6 74 -23 78 155 }} | ||
[[POTE generator]]: ~25/24 = 71.107 | [[POTE generator]]: ~25/24 = 71.107 | ||
| Line 75: | Line 75: | ||
[[Mapping]]: [{{val| 2 4 5 5 }}, {{val| 0 -7 -3 5 }}] | [[Mapping]]: [{{val| 2 4 5 5 }}, {{val| 0 -7 -3 5 }}] | ||
{{Multival|legend=1|14 6 -10 -23 -55 -40}} | {{Multival|legend=1| 14 6 -10 -23 -55 -40 }} | ||
[[POTE generator]]: ~25/24 = 71.779 | [[POTE generator]]: ~25/24 = 71.779 | ||
| Line 108: | Line 108: | ||
Badness: 0.040739 | Badness: 0.040739 | ||
== Narayana == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 321489/320000 | |||
[[Mapping]]: [{{val| 2 4 5 3 }}, {{val| 0 -7 -3 22 }}] | |||
{{Multival|legend=1| 14 6 -44 -23 -109 -119 }} | |||
[[POTE generator]]: ~25/24 = 71.265 | |||
{{Val list|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: [{{val| 2 4 5 3 3 }}, {{val| 0 -7 -3 22 33 }}] | |||
POTE generator: ~25/24 = 71.248 | |||
Vals: {{Val list| 34e, 84, 118, 202, 320 }} | |||
Badness: 0.045908 | |||
== Quarvish == | == Quarvish == | ||
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[[Mapping]]: [{{val| 2 4 5 6 }}, {{val| 0 -28 -12 -13 }}] | [[Mapping]]: [{{val| 2 4 5 6 }}, {{val| 0 -28 -12 -13 }}] | ||
{{Multival|legend=1|56 24 26 -92 -116 -7}} | {{Multival|legend=1| 56 24 26 -92 -116 -7 }} | ||
[[POTE generator]]: ~7/5 = 582.213 | [[POTE generator]]: ~7/5 = 582.213 | ||
| Line 146: | Line 174: | ||
[[Mapping]]: [{{val| 10 13 22 24 }}, {{val| 0 7 3 10 }}] | [[Mapping]]: [{{val| 10 13 22 24 }}, {{val| 0 7 3 10 }}] | ||
{{Multival|legend=1|70 30 100 -115 -38 148}} | {{Multival|legend=1| 70 30 100 -115 -38 148 }} | ||
[[POTE generator]]: ~25/24 = 71.129 | [[POTE generator]]: ~25/24 = 71.129 | ||
Revision as of 02:41, 25 September 2021
The vishnuzmic family of temperaments tempers out the vishnuzma, [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)7.
Vishnu
Subgroup: 2.3.5
Comma list: 6115295232/6103515625
Mapping: [⟨2 4 5], ⟨0 -7 -3]]
POTE generator: ~25/24 = 71.143
Badness: 0.031181
Septimal vishnu
Subgroup: 2.3.5.7
Comma list: 4375/4374, 29360128/29296875
Mapping: [⟨2 4 5 10], ⟨0 -7 -3 -37]]
Wedgie: ⟨⟨ 14 6 74 -23 78 155 ]]
POTE generator: ~25/24 = 71.107
Badness: 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]]
POTE generator: ~25/24 = 71.105
Vals: Template:Val list
Badness: 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]]
POTE generator: ~25/24 = 71.117
Vals: Template:Val list
Badness: 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]]
POTE generator: ~25/24 = 71.101
Vals: Template:Val list
Badness: 0.015805
Vishnean
Subgroup: 2.3.5.7
Comma list: 126/125, 540225/524288
Mapping: [⟨2 4 5 5], ⟨0 -7 -3 5]]
Wedgie: ⟨⟨ 14 6 -10 -23 -55 -40 ]]
POTE generator: ~25/24 = 71.779
Badness: 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]]
POTE generator: ~25/24 = 71.924
Vals: Template:Val list
Badness: 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]]
POTE generator: ~25/24 = 71.926
Vals: Template:Val list
Badness: 0.040739
Narayana
Subgroup: 2.3.5.7
Comma list: 65625/65536, 321489/320000
Mapping: [⟨2 4 5 3], ⟨0 -7 -3 22]]
Wedgie: ⟨⟨ 14 6 -44 -23 -109 -119 ]]
POTE generator: ~25/24 = 71.265
Badness: 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]]
POTE generator: ~25/24 = 71.248
Vals: Template:Val list
Badness: 0.045908
Quarvish
Subgroup: 2.3.5.7
Comma list: 2401/2400, 6115295232/6103515625
Mapping: [⟨2 4 5 6], ⟨0 -28 -12 -13]]
Wedgie: ⟨⟨ 56 24 26 -92 -116 -7 ]]
POTE generator: ~7/5 = 582.213
Badness: 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]]
POTE generator: ~7/5 = 582.213
Vals: Template:Val list
Badness: 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 13 22 24], ⟨0 7 3 10]]
Wedgie: ⟨⟨ 70 30 100 -115 -38 148 ]]
POTE generator: ~25/24 = 71.129
Badness: 0.114531
11-limit
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 41503/41472, 172032/171875
Mapping: [⟨10 13 22 24 35], ⟨0 7 3 10 -1]]
POTE generator: ~25/24 = 71.141
Vals: Template:Val list
Badness: 0.036938
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655
Mapping: [⟨10 13 22 24 35 37], ⟨0 7 3 10 -1 0]]
POTE generator: ~25/24 = 71.151
Vals: Template:Val list
Badness: 0.021906