Cataharry family: Difference between revisions

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Line 6: Line 6:
[[Comma list]]: [[19683/19600]]
[[Comma list]]: [[19683/19600]]


[[Mapping]]: [<1 0 0 -2|, <0 2 0 9|, <0 0 1 -1|]
[[Mapping]]: [{{val| 1 0 0 -2 }}, {{val| 0 2 0 9 }}, {{val| 0 0 1 -1 }}]


Mapping generators: ~2, ~140/81, ~5
Mapping generators: ~2, ~140/81, ~5
Line 12: Line 12:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* 7- and [[9-odd-limit]]:  
* 7- and [[9-odd-limit]]:  
: [|1 0 0 0>, |4/9 0 2/9 2/9>, |0 0 1 0>, |0 0 0 1>]
: [{{monzo| 1 0 0 0 }}, {{monzo| 4/9 0 2/9 2/9 }}, {{monzo| 0 0 1 0 }}, {{monzo| 0 0 0 1 }}]
: Eigenmonzos: 2, 8/7, 5/4
: Eigenmonzos: 2, 8/7, 5/4


Line 24: Line 24:
[[Comma list]]: 540/539, 8019/8000
[[Comma list]]: 540/539, 8019/8000


[[Mapping]]: [<1 0 0 -2 6|, <0 2 0 9 -12|, <0 0 1 -1 3|]
[[Mapping]]: [{{val| 1 0 0 -2 6 }}, {{val| 0 2 0 9 -12 }}, {{val| 0 0 1 -1 3 }}]


Mapping generators: ~2, ~140/81, ~5
Mapping generators: ~2, ~140/81, ~5
Line 30: Line 30:
[[Minimax tuning]]:  
[[Minimax tuning]]:  
* [[11-odd-limit]]
* [[11-odd-limit]]
: [|1 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3>, |5 0 7/2 -2 -3/2>, |5 0 5/2 -1 -3/2>, |5 0 5/2 -2 -1/2>]
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo| 5 0 7/2 -2 -3/2 }}, {{monzo| 5 0 5/2 -1 -3/2 }}, {{monzo| 5 0 5/2 -2 -1/2 }}]
: Eigenmonzos: 2, 11/10, 7/5
: Eigenmonzos: 2, 11/10, 7/5


Line 42: Line 42:
Comma list: 351/350, 540/539, 676/675
Comma list: 351/350, 540/539, 676/675


Mapping: [<1 0 0 -2 6 -1|, <0 2 0 9 -12 3|, <0 0 1 -1 3 1|]
Mapping: [{{val| 1 0 0 -2 6 -1 }}, {{val| 0 2 0 9 -12 3 }}, {{val| 0 0 1 -1 3 1 }}]


Mapping generators: ~2, ~26/15, ~5
Mapping generators: ~2, ~26/15, ~5


Map to lattice: [<0 -2 -3 -6 3 -6|, <0 0 -1 1 -3 -1|]
Map to lattice: [{{val| 0 -2 -3 -6 3 -6 }}, {{val| 0 0 -1 1 -3 -1 }}]


Lattice basis:  
Lattice basis:  
Line 52: Line 52:
: Angle (15/13, 26/25) = 81.6476
: Angle (15/13, 26/25) = 81.6476


[[Minimax tuning]]:  
Minimax tuning:  
* 13- and 15-odd-limit
* 13- and 15-odd-limit
: [|1 0 0 0 0 0>, |8/3 0 4/3 -2/3 -2/3 0>, |5 0 7/2 -2 -3/2 0>, |5 0 5/2 -1 -3/2 0>, |5 0 5/2 -2 -1/2 0>, |8 0 11/2 -3 -5/2 0>]
: [{{monzo| 1 0 0 0 0 0 }}, {{monzo| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo| 5 0 7/2 -2 -3/2 0 }}, {{monzo| 5 0 5/2 -1 -3/2 0 }}, {{monzo| 5 0 5/2 -2 -1/2 0 }}, {{monzo| 8 0 11/2 -3 -5/2 0 }}]
: Eigenmonzos: 2, 11/10, 7/5
: Eigenmonzos: 2, 11/10, 7/5


Line 92: Line 92:
[[Comma list]]: 176/175, 19683/19600
[[Comma list]]: 176/175, 19683/19600


[[Mapping]]: [<1 0 0 -2 -6|, <0 2 0 9 9|, <0 0 1 -1 1|]
[[Mapping]]: [{{val| 1 0 0 -2 -6 }}, {{val| 0 2 0 9 9 }}, {{val| 0 0 1 -1 1 }}]


{{Val list|legend=1| 24, 34d, 53, 58, 111, 357cd, 468cd }}
{{Val list|legend=1| 24, 34d, 53, 58, 111, 357cd, 468cd }}
Line 103: Line 103:
Comma list: 176/175, 351/350, 676/675
Comma list: 176/175, 351/350, 676/675


Mapping: [<1 0 0 -2 -6 -1|, <0 2 0 9 9 3|, <0 0 1 -1 1 1|]
Mapping: [{{val| 1 0 0 -2 -6 -1 }}, {{val| 0 2 0 9 9 3 }}, {{val| 0 0 1 -1 1 1 }}]


Vals: {{Val list| 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf }}
Vals: {{Val list| 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf }}
Line 114: Line 114:
[[Category:Rank 3]]
[[Category:Rank 3]]


{{todo|review}}
{{todo| review }}

Revision as of 11:42, 6 June 2021

The cataharry family of rank-3 temperaments tempers out the cataharry comma, 19683/19600.

Cataharry

Subgroup: 2.3.5.7

Comma list: 19683/19600

Mapping: [⟨1 0 0 -2], ⟨0 2 0 9], ⟨0 0 1 -1]]

Mapping generators: ~2, ~140/81, ~5

Minimax tuning:

[[1 0 0 0⟩, [4/9 0 2/9 2/9⟩, [0 0 1 0⟩, [0 0 0 1⟩]
Eigenmonzos: 2, 8/7, 5/4

Template:Val list

Projection pairs: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7

Albus

Subgroup: 2.3.5.7.11

Comma list: 540/539, 8019/8000

Mapping: [⟨1 0 0 -2 6], ⟨0 2 0 9 -12], ⟨0 0 1 -1 3]]

Mapping generators: ~2, ~140/81, ~5

Minimax tuning:

[[1 0 0 0 0⟩, [8/3 0 4/3 -2/3 -2/3⟩, [5 0 7/2 -2 -3/2⟩, [5 0 5/2 -1 -3/2⟩, [5 0 5/2 -2 -1/2⟩]
Eigenmonzos: 2, 11/10, 7/5

Template:Val list

Badness: 0.621 × 10-3

Madagascar

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 676/675

Mapping: [⟨1 0 0 -2 6 -1], ⟨0 2 0 9 -12 3], ⟨0 0 1 -1 3 1]]

Mapping generators: ~2, ~26/15, ~5

Map to lattice: [⟨0 -2 -3 -6 3 -6], ⟨0 0 -1 1 -3 -1]]

Lattice basis:

15/13 length = 0.3019, 26/25 length = 0.9477
Angle (15/13, 26/25) = 81.6476

Minimax tuning:

  • 13- and 15-odd-limit
[[1 0 0 0 0 0⟩, [8/3 0 4/3 -2/3 -2/3 0⟩, [5 0 7/2 -2 -3/2 0⟩, [5 0 5/2 -1 -3/2 0⟩, [5 0 5/2 -2 -1/2 0⟩, [8 0 11/2 -3 -5/2 0⟩]
Eigenmonzos: 2, 11/10, 7/5

Vals: Template:Val list

Badness: 0.560 × 10-3

Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11

Projection pairs: 3 676/225 7 1357375919744/192216796875 11 16218292236328125/1491077447838784 13 8788/675 to 2.5.13/3

Scales: madagascar19

Snape

Subgroup: 2.3.5.7.11

Comma list: 441/440, 19683/19600

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 441/440, 729/728

Hagrid

Subgroup: 2.3.5.7.11

Comma list: 243/242, 9801/9800

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 351/350, 729/728

Draco

Subgroup: 2.3.5.7.11

Comma list: 176/175, 19683/19600

Mapping: [⟨1 0 0 -2 -6], ⟨0 2 0 9 9], ⟨0 0 1 -1 1]]

Template:Val list

Badness: 1.934 × 10-3

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 676/675

Mapping: [⟨1 0 0 -2 -6 -1], ⟨0 2 0 9 9 3], ⟨0 0 1 -1 1 1]]

Vals: Template:Val list

Badness: 0.999 × 10-3

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