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.
Gravity
Subgroup: 2.3.5
Comma list: 129140163/128000000
Mapping: [⟨1 5 12], ⟨0 -6 -17]]
Mapping generators: ~2, ~40/27
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.844
Badness: 0.093184
Overview to extensions
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.
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]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.834
Optimal GPV sequence: Template:Val list
Badness: 0.0125
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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.694
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]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.699
Optimal GPV sequence: Template:Val list
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]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.730
Optimal GPV sequence: Template:Val list
Badness: 0.026882
Zarvo
Subgroup: 2.3.5.7
Comma list: 4375/4374, 33075/32768
Mapping: [⟨1 5 12 -12], ⟨0 -6 -17 26]]
Wedgie: ⟨⟨ 6 17 -26 13 -58 -108 ]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.702
Badness: 0.096840
11-limit
Subgroup: 2.3.5.7.11
Comma list: 243/242, 385/384, 4000/3993
Mapping: [⟨1 5 12 -12 12], ⟨0 -6 -17 26 -15]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.691
Optimal GPV sequence: Template:Val list
Badness: 0.034773
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 243/242, 325/324, 385/384
Mapping: [⟨1 5 12 -12 12 -2], ⟨0 -6 -17 26 -15 10]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 516.667
Optimal GPV sequence: Template:Val list
Badness: 0.027584
Gravid
Subgroup: 2.3.5.7
Comma list: 126/125, 1605632/1594323
Mapping: [⟨1 5 12 25], ⟨0 -6 -17 -39]]
Wedgie: ⟨⟨ 6 17 39 13 45 43 ]]
Optimal tuning (POTE): ~2 = 1\1, ~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 5 12 25 12], ⟨0 -6 -17 -39 -15]]
Optimal tuning (POTE): ~2 = 1\1, ~27/20 = 517.155
Optimal GPV sequence: Template:Val list
Badness: 0.047283
Harry
Harry 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 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]]
Mapping generators: ~567/400, ~21/20
Wedgie: ⟨⟨ 12 34 20 26 -2 -49 ]]
Optimal tuning (POTE): ~567/400 = 1\2, ~27/20 = 516.844 (~21/20 = 83.156)
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]]
Optimal tuning (POTE): ~99/70 = 1\2, ~27/20 = 516.833 (~21/20 = 83.167)
Optimal GPV sequence: Template:Val list
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]]
Optimal tuning (POTE): ~55/39 = 1\2, ~27/20 = 516.884 (~21/20 = 83.116)
Optimal GPV sequence: Template:Val list
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]]
Optimal tuning (POTE): ~17/12 = 1\2, ~27/20 = 516.832 (~21/20 = 83.168)
Optimal GPV sequence: Template:Val list
Badness: 0.012657