Ripple family

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The ripple family tempers out the ripple, 6561/6250 = [-1 8 -5, which equates a stack of four 10/9's with 8/5. As one might expect, 12edo is about as accurate as it can be.

Ripple

Subgroup: 2.3.5

Comma list: 6561/6250

Mapping[1 2 3], 0 -5 -8]]

Optimal tuning (POTE): ~2 = 1\1, ~27/25 = 100.838

Tuning ranges:

  • 5-odd-limit diamond monotone: [92.308, 109.091] (1\13 to 1\11)
  • 5-odd-limit diamond tradeoff: [99.609, 105.214]
  • 5-odd-limit diamond monotone and tradeoff: [99.609, 105.214]

Optimal ET sequence11c, 12, 71b, 83b, 95b, 107bc, 119bc

Badness: 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 = 1\1, ~21/20 = 99.483

Optimal ET sequence12

Badness: 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 = 1\1, ~21/20 = 99.385

Optimal ET sequence12

Badness: 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 = 1\1, ~21/20 = 98.572

Optimal ET sequence12f

Badness: 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 = 1\1, ~36/35 = 50.826

Optimal ET sequence23d, 24, 47d, 71bdd

Badness: 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 = 1\1, ~36/35 = 50.826

Optimal ET sequence23de, 24, 47de, 71bdde

Badness: 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 = 1\1, ~36/35 = 50.635

Optimal ET sequence23de, 24, 47de, 71bdde

Badness: 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 = 1\1, ~7/5 = 549.944

Optimal ET sequence11cd, 13cd, 24

Badness: 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 = 1\1, ~7/5 = 549.945

Optimal ET sequence11cdee, 13cdee, 24

Badness: 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 = 1\1, ~7/5 = 549.958

Optimal ET sequence11cdeef, 13cdeef, 24

Badness: 0.049933