Cataharry family: Difference between revisions
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The '''cataharry family''' of rank three temperaments tempers out the [[cataharry comma]], 19683/19600. | The '''cataharry family''' of rank three temperaments tempers out the [[cataharry comma]], 19683/19600. | ||
= Cataharry = | == Cataharry == | ||
Comma: 19683/19600 | Comma: 19683/19600 | ||
| Line 19: | Line 19: | ||
[[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7 | [[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7 | ||
= Albus = | == Albus == | ||
Commas: 540/539, 8019/8000 | Commas: 540/539, 8019/8000 | ||
| Line 38: | Line 38: | ||
Badness: 0.000621 | Badness: 0.000621 | ||
== Madagascar == | === Madagascar === | ||
Commas: 351/350, 540/539, 676/675 | Commas: 351/350, 540/539, 676/675 | ||
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* [[madagascar19]] | * [[madagascar19]] | ||
= Snape = | == Snape == | ||
Commas: 441/440, 19683/19600 | Commas: 441/440, 19683/19600 | ||
== 13-limit == | === 13-limit === | ||
Commas: 351/350, 441/440, 729/728 | Commas: 351/350, 441/440, 729/728 | ||
= Hagrid = | == Hagrid == | ||
Commas: 243/242, 9801/9800 | Commas: 243/242, 9801/9800 | ||
== 13-limit == | === 13-limit === | ||
Commas: 243/242, 351/350, 729/728 | Commas: 243/242, 351/350, 729/728 | ||
= Draco = | == Draco == | ||
Commas: 176/175, 19683/19600 | Commas: 176/175, 19683/19600 | ||
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Badness: 0.001934 | Badness: 0.001934 | ||
== 13-limit == | === 13-limit === | ||
Commas: 176/175, 351/350, 676/675 | Commas: 176/175, 351/350, 676/675 | ||
Revision as of 21:24, 1 June 2021
The cataharry family of rank three temperaments tempers out the cataharry comma, 19683/19600.
Cataharry
Comma: 19683/19600
7 and 9 limit minimax
[|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
Map: [<1 0 0 -2|, <0 2 0 9|, <0 0 1 -1|]
Generators: 2, 140/81, 5
EDOs: 19, 24, 48, 53, 58, 72, 130, 202, 457, 587, 659, 717
Projection pairs: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7
Albus
Commas: 540/539, 8019/8000
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
Map: [<1 0 0 -2 6|, <0 2 0 9 -12|, <0 0 1 -1 3|]
Generators: 2, 140/81, 5
EDOs: 19, 53, 58, 72, 130, 183, 255, 385, 640
Badness: 0.000621
Madagascar
Commas: 351/350, 540/539, 676/675
13 and 15 limit minimax
[|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
Lattice basis: 15/13 0.3019 26/25 0.9477
Angle(15/13, 26/25) = 81.6476
Map to lattice: [<0 -2 -3 -6 3 -6|, <0 0 -1 1 -3 -1|]
Map: [<1 0 0 -2 6 -1|, <0 2 0 9 -12 3|, <0 0 1 -1 3 1|]
Generators: 2, 26/15, 5
EDOs: 19, 53, 58, 72, 111, 130, 183, 313
Badness: 0.000560
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
Snape
Commas: 441/440, 19683/19600
13-limit
Commas: 351/350, 441/440, 729/728
Hagrid
Commas: 243/242, 9801/9800
13-limit
Commas: 243/242, 351/350, 729/728
Draco
Commas: 176/175, 19683/19600
Map: [<1 0 0 -2 -6|, <0 2 0 9 9|, <0 0 1 -1 1|]
EDOs: 24, 34d, 53, 58, 111, 357cd, 468cd
Badness: 0.001934
13-limit
Commas: 176/175, 351/350, 676/675
Map: [<1 0 0 -2 -6 -1|, <0 2 0 9 9 3|, <0 0 1 -1 1 1|]
EDOs: 24, 34d, 53, 58, 77, 111, 357cdf, 468cdf
Badness: 0.000999