Gamelismic family
The gamelismic family of rank-3 temperaments tempers out the gamelisma, 1029/1024. The head of this family, gamelismic, tempers out 1029/1024 alone in the full 7-limit, so it has the same 2.3.7-subgroup structure as slendric but giving prime 5 an independent generator.
See Gamelismic clan for the rank-2 temperament without the last generator of gamelismic, and its various extensions.
Gamelismic
Subgroup: 2.3.5.7
Comma list: 1029/1024
Mapping: [⟨1 1 0 3], ⟨0 3 0 -1], ⟨0 0 1 0]]
- mapping generators: ~2, ~8/7, ~5
Mapping 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
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6875, ~5/4 = 385.1853
Minimax tuning: c = 1029/1024
- 7-odd-limit: 3, 5, and 7 1/4-comma 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⟩]
- eigenmonzo (unchanged-interval) basis: 2.7/3.5/3
- 9-odd-limit: 3 1/7-comma flat, 5 and 7 2/7-comma 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⟩]
- eigenmonzo (unchanged-interval) basis: 2.5/3.9/7
TE tuning map: ⟨1200.486 1901.833 2786.314 3367.676]
Optimal ET sequence: 5, 10, 15, 26, 31, 41, 72, 118, 159, 190
Badness: 0.176 × 10-3
Projection pair: 3 1024/343 to 2.5.7
Scales: portent26
Portent
Portent has a normal comma list [1029/1024, 385/384] and also tempers out 441/440.
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440
Mapping: [⟨1 1 0 3 5], ⟨0 3 0 -1 4], ⟨0 0 1 0 -1]]
Mapping to lattice: [⟨0 3 1 -1 3], ⟨0 0 1 0 -1]]
Minkowski lattice basis:
- 8/7 length = 0.46467, 12/11 length = 1.931
- Angle (8/7, 12/11) = 86.657 degrees
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6884, ~5/4 = 385.1618
Minimax tuning: c = 1029/1024, e = 385/384
- 11-odd-limit: 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⟩]
- eigenmonzo (unchanged-interval) basis: 2.11/5, 9/7
Optimal ET sequence: 10, 15, 26, 31, 41, 72, 118, 159, 190
Badness: 0.234 × 10-3
Projection pairs: 3 1024/343 11 131072/12005 to 2.5.7
Scales: portent26
Portending
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384
Mapping: [⟨1 1 0 3 5 6], ⟨0 3 0 -1 4 12], ⟨0 0 1 0 -1 -2]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.9128, ~5/4 = 384.7278
Optimal ET sequence: 15, 26, 41, 46, 72, 87, 159, 477cdf
Badness: 0.627 × 10-3
Complexity spectrum: 8/7, 4/3, 11/8, 6/5, 14/11, 7/6, 10/9, 12/11, 5/4, 13/11, 9/8, 7/5, 11/9, 9/7, 18/13, 13/12, 16/15, 11/10, 15/14, 16/13, 14/13, 15/11, 13/10, 15/13
Portentous
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 625/624
Mapping: [⟨1 1 0 3 5 -5], ⟨0 3 0 -1 4 -3], ⟨0 0 1 0 -1 4]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6843, ~5/4 = 384.9830
Optimal ET sequence: 15, 31, 56, 72, 87, 103, 159, 190, 262df, 349f, 452cdef, 611cdef
Badness: 0.662 × 10-3
Ominous
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 385/384, 441/440
Mapping: [⟨1 1 0 3 5 1], ⟨0 3 0 -1 4 -10], ⟨0 0 1 0 -1 2]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4088, ~5/4 = 385.3825
Optimal ET sequence: 26, 31, 46, 72, 103, 149, 221ef, 324bdef, 473bdef
Badness: 0.751 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 351/350, 385/384, 441/440
Mapping: [⟨1 1 0 3 5 1 1], ⟨0 3 0 -1 4 -10 -8], ⟨0 0 1 0 -1 2 2]]
Mapping to lattice: [⟨0 1 1 0 0 -1 0], ⟨0 -1 -1 0 -1 2 1]]
Lattice basis:
- 8/7 length = 0.3859, 6/5 length = 1.1303
- Angle (8/7, 6/5) = 98.6015
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4313, ~5/4 = 385.2890
Minimax tuning:
- 17-odd-limit
- [[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⟩]
- eigenmonzo (unchanged-interval) basis: 2.11/9.13/9
Optimal ET sequence: 26, 31, 46, 72, 103, 149, 175f, 221ef
Badness: 0.612 × 10-3
Momentous
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 385/384
Mapping: [⟨1 1 0 3 5 7], ⟨0 3 0 -4 1 -5], ⟨0 0 1 0 -1 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.4088, ~5/4 = 385.3825
Optimal ET sequence: 10, 31, 41, 46, 77, 87, 118, 164, 205d, 574def
Badness: 0.832 × 10-3
Foreboding
Subgroup: 2.3.5.7.11.13
Comma list: 105/104, 144/143, 275/273
Mapping: [⟨1 1 0 3 5 1], ⟨0 3 0 -1 4 2], ⟨0 0 1 0 -1 1]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.3664, ~5/4 = 382.3425
Optimal ET sequence: 5, 10, 15, 26, 31, 41, 72f, 185cf
Badness: 0.873 × 10-3
Portannic
Subgroup: 2.3.5.7.11.13
Comma list: 385/384, 441/440, 10985/10976
Mapping: [⟨1 1 2 3 3 4], ⟨0 3 0 -1 4 -1], ⟨0 0 3 0 -3 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6434, ~14/13 = 128.3440
Optimal ET sequence: 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 570ddeff, 832bcdddeefff
Badness: 1.783 × 10-3
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 385/384, 441/440, 8624/8619
Mapping: [⟨1 1 2 3 3 4 4], ⟨0 3 0 -1 4 -1 1], ⟨0 0 3 0 -3 -1 -1]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.6803, ~14/13 = 128.4149
Optimal ET sequence: 10, 36e, 46, 93e, 102, 103, 149, 159, 262df, 308def
Badness: 1.303 × 10-3
Gamel
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1029/1024
Mapping: [⟨1 1 0 3 -1], ⟨0 3 0 -1 11], ⟨0 0 1 0 1]]
Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 233.2909, ~5/4 = 384.2120
Optimal ET sequence: 10, 31, 41, 72
Badness: 0.853 × 10-3