Gamelismic family

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Gamelan

Gamelan temperament is the rank three 7-limit temperament tempering out 1029/1024.

Comma: c = 1029/1024

7-limit minimax tuning: 3, 5, and 7 1/4c flat

9-limit minimax tuning: 3 1/7c flat, 5 and 7 2/7c flat

TOP-RMS: <1200.486 1901.833 2786.314 3367.676|

Minkowski lattice basis: 8/7 length 0.5192, 5/4 length = log2(5)

Angle(8/7, 5/4) = 90 degrees

Map to lattice: [<0 3 0 -1|, <0 0 1 0|]

Map: [<1 1 0 3|, <0 3 0 -1|,<0 0 1 0|]

EDOs: 5, 10, 15, 26, 31, 41, 72, 118, 159, 190

Badness: 0.000176

Projection pair: 3 1024/343 to 2.5.7

Portent

Portent has a normal comma list [1029/1024, 385/384] and also tempers out 441/440.

Commas: c = 1029/1024, e = 385/384

Minimax: 3 1/7c flat, 5 and 7 2/7c flat, 11 e-3/7c flat

[|1 0 0 0 0>, |10/7 6/7 0 -3/7 0>, |39/14 4/7 1/2 -2/7 -1/2>, |20/7 -2/7 0 1/7 0>, |39/14 4/7 -1/2 -2/7 1/2>]

Eigenmonzos: 2, 11/10, 9/7

Minkowski lattice basis: 8/7 length 0.46467, 12/11 length 1.931

Angle(8/7, 12/11) = 86.657 degrees

Map to lattice: [<0 3 1 -1 3|, <0 0 1 0 -1|]

Map: [<1 1 0 3 5|, <0 3 0 -1 4| <0 0 1 0 -1|]

Generators: 2, 8/7, 5

EDOs: 10, 15, 26, 31, 41, 46, 57, 72, 77, 103, 118, 149, 159, 190

Badness: 0.000234

Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7

Portending

Commas: 325/324, 364/363, 441/440

Map: [<1 1 0 3 5 6|, <0 3 0 -1 4 12| <0 0 1 0 -1 -2|]

EDOs: 15, 26, 41, 46, 72, 87, 159, 477cdf

Badness: 0.000627

Portentous

Commas: 385/384, 441/440, 625/624

Map: [<1 1 0 3 5 -5|, <0 3 0 -1 4 -3| <0 0 1 0 -1 4|]

EDOs: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef

Badness: 0.000662

Ominous

Commas: 351/350, 385/384, 441/440

Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 -10| <0 0 1 0 -1 2|]

EDOs: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef

Badness: 0.000751

17-limit

Commas: 273/272, 351/350, 441/440, 561/560

Minimax tuning

[|1 0 0 0 0 0 0>, |7/4 9/10 0 0 -3/10 -3/20 0>, |5/2 7/5 0 0 -4/5 1/10 0>, |11/4 -3/10 0 0 1/10 1/20 0>, |7/2 -1/5 0 0 2/5 -3/10 0>, |7/2 -1/5 0 0 -3/5 7/10 0>, |4 2/5 0 0 -4/5 3/5 0>]

Eigenmonzos: 2, 13/11, 11/9

Lattice basis: 8/7 0.3859 6/5 1.1303

Angle(8/7, 6/5) = 98.6015

Map to lattice: [<0 1 1 0 0 -1 0|, <0 -1 -1 0 -1 2 1|]

Map: [<1 1 0 3 5 1 1|, <0 3 0 -1 4 -10 -8|,

<0 0 1 0 -1 2 2|]

Generators: 2, 8/7, 5

EDOs: 26, 31, 46, 72, 103, 149, 175f, 221ef

Badness: 0.000612

Momentous

Commas: 196/195, 352/351, 385/384

Map: [<1 1 0 3 5 7|, <0 3 0 -4 1 -5|, <0 0 1 0 -1 -1|]

EDOs: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def

Badness: 0.000832

Foreboding

Commas: 105/104, 144/143, 275/273

Map: [<1 1 0 3 5 1|, <0 3 0 -1 4 2|, <0 0 1 0 -1 1|]

EDOs: 5, 10, 15, 26, 31, 41, 72f, 185cf

Badness: 0.000873

Gamel

Commas: 1029/1024, 540/539

Map: [<1 1 0 3 -1|, <0 3 0 -1 11|, <0 0 1 0 1|]

EDOs: 10, 31, 41, 72

Badness: 0.000853