Ripple family: Difference between revisions
Created page with "The '''ripple family''' tempers out the ripple, 6561/6250 = {{monzo| -1 8 -5 }}, which equates a stack of four 10/9's with 8/5. As one might expect, 12edo is about..." |
→Cohemiripple: +data copied from sensamagic clan |
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= Cohemiripple = | = Cohemiripple = | ||
{{see also| Sensamagic clan #Cohemiripple }} | {{see also| Sensamagic clan #Cohemiripple }} | ||
Subgroup: 2.3.5.7 | |||
Comma list: 245/243, 1323/1250 | |||
POTE generator: ~7/5 = 549.944 | |||
Mapping: [{{val| 1 7 11 12 }}, {{val| 0 -10 -16 -17 }}] | |||
{{Multival|legend=1| 10 16 17 2 -1 -5 }} | |||
{{Val list|legend=1| 11cd, 13cd, 24 }} | |||
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: [{{val| 1 7 11 12 17 }}, {{val| 0 -10 -16 -17 -25 }}] | |||
{{Val list|legend=1| 11cdee, 13cdee, 24 }} | |||
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: [{{val| 1 7 11 12 17 14 }}, {{val| 0 -10 -16 -17 -25 -19 }}] | |||
{{Val list|legend=1| 11cdeef, 13cdeef, 24 }} | |||
Badness: 0.0499 | |||
[[Category:Theory]] | [[Category:Theory]] | ||
Revision as of 02:33, 17 March 2021
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:
7-limit
Period: 1\1
Optimal (POTE) generators: ~21/20 = 99.483
EDO generators: 1\11, 1\12, 1\13
Scales:
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:
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:
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
Period: 1\1
Optimal (POTE) generator: ~36/35 = 50.826
Scales (Scala files):
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
Scales (Scala files):
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
Scales (Scala files):
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
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