Ripple family
The ripple family of temperaments tempers out the ripple comma, 6561/6250 = [-1 8 -5⟩, which equates a stack of five 27/25's with 4/3.
Ripple
The generator of ripple is a semitone representing 27/25, five of which give 4/3, and eight of which give 8/5. As one might expect, 12edo is about as accurate as it can be tuned.
Subgroup: 2.3.5
Comma list: 6561/6250
Mapping: [⟨1 2 3], ⟨0 -5 -8]]
- mapping generators: ~2, ~27/25
Optimal tuning (POTE): ~2 = 1200.000, ~27/25 = 100.838
- 5-odd-limit diamond monotone: [92.308, 109.091] (1\13 to 1\11)
- 5-odd-limit diamond tradeoff: [99.609, 105.214]
Optimal ET sequence: 11c, 12, 71b, 83b, 95b, 107bc, 119bc
Badness (Smith): 0.138948
Septimal ripple
Subgroup: 2.3.5.7
Comma list: 36/35, 2560/2401
Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]
Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 99.483
Badness (Smith): 0.059735
11-limit
Subgroup: 2.3.5.7.11
Comma list: 36/35, 80/77, 126/121
Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 99.385
Optimal ET sequence: 12
Badness (Smith): 0.038811
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 36/35, 40/39, 66/65, 147/143
Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]
Optimal tuning (POTE): ~2 = 1200.000, ~21/20 = 98.572
Optimal ET sequence: 12f
Badness (Smith): 0.031639
Hemiripple
Subgroup: 2.3.5.7
Comma list: 49/48, 6561/6250
Mapping: [⟨1 2 3 3], ⟨0 -10 -16 -5]]
Wedgie: ⟨⟨ 10 16 5 2 -20 -33 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~36/35 = 50.826
Optimal ET sequence: 23d, 24, 47d, 71bdd
Badness (Smith): 0.175113
11-limit
Subgroup: 2.3.5.7.11
Comma list: 49/48, 121/120, 567/550
Mapping: [⟨1 2 3 3 4], ⟨0 -10 -16 -5 -13]]
Optimal tuning (POTE): ~2 = 1200.000, ~36/35 = 50.826
Optimal ET sequence: 23de, 24, 47de, 71bdde
Badness (Smith): 0.066834
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 49/48, 66/65, 121/120, 351/350
Mapping: [⟨1 2 3 3 4 4], ⟨0 -10 -16 -5 -13 -7]]
Optimal tuning (POTE): ~2 = 1200.000, ~36/35 = 50.635
Optimal ET sequence: 23de, 24, 47de, 71bdde
Badness (Smith): 0.046588
Cohemiripple
Subgroup: 2.3.5.7
Comma list: 245/243, 1323/1250
Mapping: [⟨1 7 11 12], ⟨0 -10 -16 -17]]
Wedgie: ⟨⟨ 10 16 17 2 -1 -5 ]]
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 549.944
Optimal ET sequence: 11cd, 13cd, 24
Badness (Smith): 0.190208
11-limit
Subgroup: 2.3.5.7.11
Comma list: 77/75, 243/242, 245/242
Mapping: [⟨1 7 11 12 17], ⟨0 -10 -16 -17 -25]]
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 549.945
Optimal ET sequence: 11cdee, 13cdee, 24
Badness (Smith): 0.082716
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 66/65, 77/75, 147/143, 243/242
Mapping: [⟨1 7 11 12 17 14], ⟨0 -10 -16 -17 -25 -19]]
Optimal tuning (POTE): ~2 = 1200.000, ~7/5 = 549.958
Optimal ET sequence: 11cdeef, 13cdeef, 24
Badness (Smith): 0.049933