Luna family: Difference between revisions
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The '''luna family''' tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}; | The '''luna family''' tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of {{monzo| 38 -2 -15 }}; | ||
= Luna = | == Luna == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 14: | Line 14: | ||
[[Badness]]: 0.020576 | [[Badness]]: 0.020576 | ||
= Hemithirds = | == Hemithirds == | ||
{{main| Hemithirds }} | {{main| Hemithirds }} | ||
{{see also| Hemimean clan #Hemithirds }} | {{see also| Hemimean clan #Hemithirds }} | ||
| Line 40: | Line 40: | ||
[[Badness]]: 0.044284 | [[Badness]]: 0.044284 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 58: | Line 58: | ||
Badness: 0.019003 | Badness: 0.019003 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 71: | Line 71: | ||
Badness: 0.021738 | Badness: 0.021738 | ||
= Lunatic = | == Lunatic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 86: | Line 86: | ||
[[Badness]]: 0.037966 | [[Badness]]: 0.037966 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 99: | Line 99: | ||
Badness: 0.058588 | Badness: 0.058588 | ||
= Semiluna = | == Semiluna == | ||
{{see also| Canousmic temperaments #Semiluna }} | {{see also| Canousmic temperaments #Semiluna }} | ||
| Line 116: | Line 116: | ||
[[Badness]]: 0.192167 | [[Badness]]: 0.192167 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Revision as of 21:36, 1 June 2021
The luna family tempers out the hemithirds comma aka luna comma, 274877906944/274658203125, which has a monzo of [38 -2 -15⟩;
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: 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: 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: 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
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