Luna family: Difference between revisions
m Removing from Category:Regular temperament theory using Cat-a-lot |
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[[Minimax tuning]]: | [[Minimax tuning]]: | ||
* [[7-odd-limit]] | * [[7-odd-limit]]: ~28/25 = {{monzo| 1/10 -1/20 0 1/20 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 5/2 3/4 0 -3/4 }}, {{monzo| 11/5 -1/10 0 1/10 }}, {{monzo| 5/2 -1/4 0 1/4 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 7/6 | : [[Eigenmonzo]]s (unchanged intervals): 2, 7/6 | ||
* [[9-odd-limit]] | * [[9-odd-limit]]: ~28/25 = {{monzo| 6/35 -2/35 0 1/35 }} | ||
: [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | : [{{monzo| 1 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 }}, {{monzo| 82/35 -4/35 0 2/35 }}, {{monzo| 20/7 -2/7 0 1/7 }}] | ||
: [[Eigenmonzo]]s (unchanged intervals): 2, 7 | : [[Eigenmonzo]]s (unchanged intervals): 2, 9/7 | ||
{{Val list|legend=1| 25, 31, 87, 118 }} | {{Val list|legend=1| 25, 31, 87, 118 }} | ||
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Minimax tuning: | Minimax tuning: | ||
* 11-odd-limit | * 11-odd-limit: ~28/25 = {{monzo| 5/27 0 0 1/27 -1/27 }} | ||
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}] | : [{{monzo| 1 0 0 0 0 }}, {{monzo| 11/9 0 0 -5/9 5/9 }}, {{monzo| 64/27 0 0 2/27 -2/27 }}, {{monzo| 79/27 0 0 5/27 -5/27 }}, {{monzo| 79/27 0 0 -22/27 22/27 }}] | ||
: Eigenmonzos (unchanged intervals): 2, 11/7 | : Eigenmonzos (unchanged intervals): 2, 11/7 | ||
Optimal GPV sequence: {{Val list| 25e, 31, 87, 118 }} | |||
Badness: 0.019003 | Badness: 0.019003 | ||
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POTE generator: ~28/25 = 193.166 | POTE generator: ~28/25 = 193.166 | ||
Optimal GPV sequence: {{Val list| 31, 56, 87, 118, 205d }} | |||
Badness: 0.021738 | Badness: 0.021738 | ||
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POTE generator: ~352/315 = 193.200 | POTE generator: ~352/315 = 193.200 | ||
Optimal GPV sequence: {{Val list| 118, 323e, 441, 559, 1000e }} | |||
Badness: 0.058588 | Badness: 0.058588 | ||
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POTE generator: ~200/189 = 96.587 | POTE generator: ~200/189 = 96.587 | ||
Optimal GPV sequence: {{Val list| 87, 236, 323, 410 }} | |||
Badness: 0.100077 | Badness: 0.100077 | ||
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POTE generator: ~143/135 = 96.586 | POTE generator: ~143/135 = 96.586 | ||
Optimal GPV sequence: {{Val list| 87, 236, 323, 410 }} | |||
Badness: 0.046151 | Badness: 0.046151 | ||
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POTE generator: ~121/108 = 193.1732 | POTE generator: ~121/108 = 193.1732 | ||
Optimal GPV sequence: {{Val list| 56d, 118, 292, 410 }} | |||
Badness: 0.067783 | Badness: 0.067783 | ||
Revision as of 07:46, 21 March 2022
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
- 7-odd-limit: ~28/25 = [1/10 -1/20 0 1/20⟩
- [[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
- 9-odd-limit: ~28/25 = [6/35 -2/35 0 1/35⟩
- [[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, 9/7
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: ~28/25 = [5/27 0 0 1/27 -1/27⟩
- [[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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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]]
Mapping generators: ~10125/7168, ~2187/1960
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
Optimal GPV sequence: Template:Val list
Badness: 0.067783