Gamelismic family
The gamelismic family of temperaments are rank-3 temperaments tempering out 1029/1024.
Gamelan
Comma list: c = 1029/1024
Mapping: [⟨1 1 0 3], ⟨0 3 0 -1],⟨0 0 1 0]]
Map to lattice: [⟨0 3 0 -1], ⟨0 0 1 0]]
- 8/7 length = 0.5192, 5/4 length = log25
- Angle (8/7, 5/4) = 90 degrees
- 7-odd-limit: 3, 5, and 7 1/4c flat
- [[1 0 0 0⟩, [5/2 3/4 0 -3/4⟩, [5/2 -1/4 1 -3/4⟩, [5/2 -1/4 0 1/4⟩]
- Eigenmonzos: 2, 7/6, 6/5
- 9-odd-limit: 3 1/7c flat, 5 and 7 2/7c flat
- [[1 0 0 0⟩, [10/7 6/7 0 -3/7⟩, [10/7 -1/7 1 -3/7⟩, [20/7 -2/7 0 1/7⟩]
- Eigenmonzos: 2, 6/5, 9/7
TE tuning map: ⟨1200.486 1901.833 2786.314 3367.676]
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