Gravity family
The gravity family tempers out graviton, the 5-limit comma 129140163/128000000 = [-13 17 -6⟩. The graviton equals (81/80)4/(25/24), so that four 81/80 commas come to a classic chromatic semitone. The generator of gravity temperament is a grave fifth of 40/27, and hence the name. It is part of the syntonic-chromatic equivalence continuum, whereby (81/80)k = 25/24.
Full 7-limit extensions of gravity include gravid (58 & 65), marvo (65d & 72), zarvo (65 & 72), and harry (58 & 72), all considered below. A notable subgroup extension is larry.
Gravity
Subgroup: 2.3.5
Comma list: 129140163/128000000
Mapping: [⟨1 5 12], ⟨0 -6 -17]]
Mapping generators: ~2, ~40/27
POTE generator: ~40/27 = 683.156
Vals: 7, 37cc, 44c, 51c, 58, 65, 137, 202, 267, 469
Badness: 0.093184
Larry
Subgroup: 2.3.5.11
Comma list: 243/242, 4000/3993
Sval mapping: [⟨1 5 12 12], ⟨0 -6 -17 -15]]
Gencom mapping: [⟨1 5 12 0 12], ⟨0 -6 -17 0 -15]]
Gencom: [2 40/27; 243/242 4000/3993]
POTE generator: ~40/27 = 683.166
Vals: 7, 37ccee, 44ce, 51ce, 58, 65, 137, 202
Badness: 0.0125
Harry
- Main article: Harry
- See also: Breedsmic temperaments #Harry
Harry temperament can be described as 58&72 temperament, tempering out 7-limit commas 2401/2400 and 19683/19600; 11-limit commas 243/242, 441/440 and 4000/3993, leading to a period of a half octave and a generator of minor semitone tempered between 21/20 and 22/21. Harry temperament also equates 14/13 with 27/25 in the 13-limit, 17/16 with 18/17 and 13/11 with 20/17 in the 17-limit.
Subgroup: 2.3.5.7
Comma list: 2401/2400, 19683/19600
Mapping: [⟨2 4 7 7], ⟨0 -6 -17 -10]]
Wedgie: ⟨⟨12 34 20 26 -2 -49]]
POTE generator: ~21/20 = 83.156
Vals: 14c, 58, 72, 130, 202, 534, 736b, 938b
Badness: 0.034077
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 441/440, 4000/3993
Mapping: [⟨2 4 7 7 9], ⟨0 -6 -17 -10 -15]]
POTE generator: ~21/20 = 83.167
Badness: 0.015867
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 243/242, 351/350, 364/363, 441/440
Mapping: [⟨2 4 7 7 9 11], ⟨0 -6 -17 -10 -15 -26]]
POTE generator: ~21/20 = 83.116
Vals: 14cf, 58, 72, 130, 332f, 462ef
Badness: 0.013046
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 221/220, 243/242, 289/288, 351/350, 441/440
Mapping: [⟨2 4 7 7 9 11 9], ⟨0 -6 -17 -10 -15 -26 -6]]
POTE generator: ~21/20 = 83.168
Badness: 0.012657
Gravid
Subgroup: 2.3.5.7
Comma list: 126/125, 1605632/1594323
Mapping: [⟨1 -1 -5 -14], ⟨0 6 17 39]]
Wedgie: ⟨⟨6 17 39 13 45 43]]
POTE generator: ~27/20 = 517.140
Badness: 0.131153
11-limit
Subgroup: 2.3.5.7.11
Comma list: 126/125, 243/242, 896/891
Mapping: [⟨1 -1 -5 -14 -3], ⟨0 6 17 39 15]]
POTE generator: ~27/20 = 517.155
Badness: 0.047283
Marvo
Subgroup: 2.3.5.7
Comma list: 225/224, 78125000/78121827
Mapping: [⟨1 5 12 29], ⟨0 -6 -17 -46]]
Wedgie: ⟨⟨6 17 46 13 56 59]]
POTE generator: ~27/20 = 516.694
Vals: 65d, 72, 137, 209, 281, 569bcc
Badness: 0.097627
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 243/242, 4000/3993
Mapping: [⟨1 5 12 29 12], ⟨0 -6 -17 -46 -15]]
POTE generator: ~27/20 = 516.699
Vals: 65d, 72, 281, 353c, 425bc, 497bc
Badness: 0.031685
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 243/242, 351/350, 1625/1617
Mapping: [⟨1 5 12 29 12 39], ⟨0 -6 -17 -46 -15 -62]]
POTE generator: ~27/20 = 516.730
Vals: 65d, 72, 137, 209, 281f, 490bcf
Badness: 0.026882
Zarvo
Subgroup: 2.3.5.7
Comma list: 4375/4374, 33075/32768
Mapping: [⟨1 -1 -5 14], ⟨0 6 17 -26]]
Wedgie: ⟨⟨6 17 -26 13 -58 -108]]
POTE generator: ~27/20 = 516.702
Vals: 65, 72, 281d, 353cd, 425bcdd, 497bcdd
Badness: 0.096840
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384, 4000/3993
Mapping: [⟨1 -1 -5 14 -3], ⟨0 6 17 -26 15]]
POTE generator: ~27/20 = 516.691
Badness: 0.034773
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 243/242, 325/324, 385/384
Mapping: [⟨1 -1 -5 14 -3 8], ⟨0 6 17 -26 15 -10]]
POTE generator: ~27/20 = 516.667
Badness: 0.027584