Ripple family

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

Period: 1\1

Optimal (POTE) generators: ~27/25 = 100.838

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

Comma list: 6561/6250

Mapping: [⟨1 2 3], ⟨0 -5 -8]]

Badness: 0.1389

7-limit

See also: Mint temperaments § Ripple

Period: 1\1

Optimal (POTE) generators: ~21/20 = 99.483

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

Comma list: 36/35, 2560/2401

Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]

Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]

Badness: 0.0597

11-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 99.385

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

Comma list: 36/35, 80/77, 126/121

Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]

Badness: 0.0388

13-limit

Period: 1\1

Optimal (POTE) generators: ~21/20 = 98.572

EDO generators: 1\11, 1\12, 1\13

Scales:

Technical data

Comma list: 36/35, 40/39, 66/65, 147/143

Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]

Badness: 0.0316

Hemiripple

See also: Slendro clan § Hemiripple

Period: 1\1

Optimal (POTE) generator: ~36/35 = 50.826

EDO generators: 1\23, 1\24

Scales (Scala files):

Technical data

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]]

Badness: 0.1751

11-limit

Period: 1\1

Optimal (POTE) generator: ~36/35 = 50.826

EDO generators: 1\23, 1\24

Scales (Scala files):

Technical data

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]]

Badness: 0.0668

13-limit

Period: 1\1

Optimal (POTE) generator: ~36/35 = 50.635

EDO generators: 1\23, 1\24

Scales (Scala files):

Technical data

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]]

Badness: 0.0466

Cohemiripple

See also: Sensamagic clan § Cohemiripple

Subgroup: 2.3.5.7

Comma list: 245/243, 1323/1250

POTE generator: ~7/5 = 549.944

Mapping: [⟨1 7 11 12], ⟨0 -10 -16 -17]]

Wedgie: ⟨⟨ 10 16 17 2 -1 -5 ]]

Badness: 0.1902

11-limit

Subgroup: 2.3.5.7.11

Comma list: 77/75, 243/242, 245/242

POTE generator: ~7/5 = 549.945

Mapping: [⟨1 7 11 12 17], ⟨0 -10 -16 -17 -25]]

Badness: 0.0827

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 77/75, 147/143, 243/242

POTE generator: ~7/5 = 549.958

Mapping: [⟨1 7 11 12 17 14], ⟨0 -10 -16 -17 -25 -19]]

Badness: 0.0499