Luna family: Difference between revisions
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[[Comma list]]: 48828125/48771072, 67108864/66976875 | [[Comma list]]: 48828125/48771072, 67108864/66976875 | ||
[[Mapping]]: [{{val|1 4 2 -5}}, {{val|0 -30 4 97}}] | [[Mapping]]: [{{val| 1 4 2 -5 }}, {{val| 0 -30 4 97 }}] | ||
Mapping generators: ~2, ~200/189 | |||
{{Multival|legend=1| 30 -4 -97 -76 -238 -214 }} | {{Multival|legend=1| 30 -4 -97 -76 -238 -214 }} | ||
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[[POTE generator]]: ~200/189 = 96.591 | [[POTE generator]]: ~200/189 = 96.591 | ||
{{Val list|legend=1| 87, 236, 323, 410, 733 }} | {{Val list|legend=1| 87, 236, 323, 410, 733, 1056, 1789bd, 2845bdd }} | ||
[[Badness]]: 0.179304 | [[Badness]]: 0.179304 | ||
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Comma list: 5632/5625, 14641/14580, 131072/130977 | Comma list: 5632/5625, 14641/14580, 131072/130977 | ||
Mapping: [{{val|1 4 2 -5 7}}, {{val|0 -30 4 97 -44}}] | Mapping: [{{val| 1 4 2 -5 7 }}, {{val| 0 -30 4 97 -44 }}] | ||
POTE generator: ~200/189 = 96.587 | POTE generator: ~200/189 = 96.587 | ||
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Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580 | Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580 | ||
Mapping: [{{val|1 4 2 -5 7 7}}, {{val|0 -30 4 97 -44 -41}}] | Mapping: [{{val| 1 4 2 -5 7 7 }}, {{val| 0 -30 4 97 -44 -41 }}] | ||
POTE generator: ~143/135 = 96.586 | POTE generator: ~143/135 = 96.586 | ||
Revision as of 13:35, 24 September 2021
The luna family tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of [38 -2 -15⟩.
Temperaments discussed elsewhere include:
- subneutral, {2401/2400, 274877906944/274658203125} → Breedsmic temperaments #Subneutral
Luna
Subgroup: 2.3.5
Comma list: 274877906944/274658203125
Mapping: [⟨1 4 2], ⟨0 -15 2]]
POTE generator: ~262144/234375 = 193.201
Badness: 0.020576
Hemithirds
Subgroup: 2.3.5.7
Comma list: 1029/1024, 3136/3125
Mapping: [⟨1 4 2 2], ⟨0 -15 2 5]]
Wedgie: ⟨⟨ 15 -2 -5 -38 -50 -6 ]]
POTE generator: ~28/25 = 193.244
- [[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [11/5 -1/10 0 1/10⟩, [5/2 -1/4 0 1/4⟩]
- Eigenmonzos (unchanged intervals): 2, 7/6
- [[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [82/35 -4/35 0 2/35⟩, [20/7 -2/7 0 1/7⟩]
- Eigenmonzos (unchanged intervals): 2, 7/6
Badness: 0.044284
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 3136/3125
Mapping: [⟨1 4 2 2 7], ⟨0 -15 2 5 -22]]
POTE generator: ~28/25 = 193.227
Minimax tuning:
- 11-odd-limit
- [[1 0 0 0 0⟩, [11/9 0 0 -5/9 5/9⟩, [64/27 0 0 2/27 -2/27⟩, [79/27 0 0 5/27 -5/27⟩, [79/27 0 0 -22/27 22/27⟩]
- Eigenmonzos (unchanged intervals): 2, 11/7
Vals: Template:Val list
Badness: 0.019003
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384, 625/624
Mapping: [⟨1 4 2 2 7 0], ⟨0 -15 2 5 -22 23]]
POTE generator: ~28/25 = 193.166
Vals: Template:Val list
Badness: 0.021738
Lunatic
Subgroup: 2.3.5.7
Comma list: 4375/4374, 274877906944/274658203125
Mapping: [⟨1 4 2 21], ⟨0 -15 2 -113]]
Wedgie: ⟨⟨ 15 -2 113 -38 137 268 ]]
POTE generator: ~262144/234375 = 193.196
Badness: 0.037966
11-limit
Subgroup: 2.3.5.7.11
Comma list: 4375/4374, 12005/11979, 172032/171875
Mapping: [⟨1 4 2 21 14], ⟨0 -15 2 -113 -140]]
POTE generator: ~352/315 = 193.200
Vals: Template:Val list
Badness: 0.058588
Hemiluna
Subgroup: 2.3.5.7
Comma list: 48828125/48771072, 67108864/66976875
Mapping: [⟨1 4 2 -5], ⟨0 -30 4 97]]
Mapping generators: ~2, ~200/189
Wedgie: ⟨⟨ 30 -4 -97 -76 -238 -214 ]]
POTE generator: ~200/189 = 96.591
Badness: 0.179304
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 14641/14580, 131072/130977
Mapping: [⟨1 4 2 -5 7], ⟨0 -30 4 97 -44]]
POTE generator: ~200/189 = 96.587
Vals: Template:Val list
Badness: 0.100077
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 4096/4095, 14641/14580
Mapping: [⟨1 4 2 -5 7 7], ⟨0 -30 4 97 -44 -41]]
POTE generator: ~143/135 = 96.586
Vals: Template:Val list
Badness: 0.046151
Semiluna
Subgroup: 2.3.5.7
Comma list: 4802000/4782969, 95703125/95551488
Mapping: [⟨2 8 4 23], ⟨0 -15 2 -54]]
Wedgie: ⟨⟨ 30 -4 108 -76 87 262 ]]
POTE generator: ~2187/1960 = 193.1725
Badness: 0.192167
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 14641/14580
Mapping: [⟨2 8 4 23 14], ⟨0 -15 2 -54 -22]]
POTE generator: ~121/108 = 193.1732
Vals: Template:Val list
Badness: 0.067783