Ripple family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
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== Ripple ==
== Ripple ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma list]]: 6561/6250
[[Comma list]]: 6561/6250


[[Mapping]]: [{{val| 1 2 3 }}, {{val| 0 -5 -8 }}]
{{Mapping|legend=1| 1 2 3 | 0 -5 -8 }}


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


[[Tuning ranges]]:  
[[Tuning ranges]]:  
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{{see also| Mint temperaments #Ripple }}
{{see also| Mint temperaments #Ripple }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 36/35, 2560/2401
[[Comma list]]: 36/35, 2560/2401


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -5 -8 -2 }}


{{Multival|legend=1| 5 8 2 1 -11 -18 }}
{{Multival|legend=1| 5 8 2 1 -11 -18 }}


[[POTE generator]]: ~21/20 = 99.483
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 99.483


{{Optimal ET sequence|legend=1| 12 }}
{{Optimal ET sequence|legend=1| 12 }}
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Comma list: 36/35, 80/77, 126/121
Comma list: 36/35, 80/77, 126/121


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -5 -8 -2 -6 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -5 -8 -2 -6 }}


POTE generator: ~21/20 = 99.385
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 99.385


{{Optimal ET sequence|legend=1| 12 }}
{{Optimal ET sequence|legend=1| 12 }}
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Comma list: 36/35, 40/39, 66/65, 147/143
Comma list: 36/35, 40/39, 66/65, 147/143


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -5 -8 -2 -6 -3 }}]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -5 -8 -2 -6 -3 }}


POTE generator: ~21/20 = 98.572
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 98.572


{{Optimal ET sequence|legend=1| 12f }}
{{Optimal ET sequence|legend=1| 12f }}
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== Hemiripple ==
== Hemiripple ==
{{see also| Slendro clan #Hemiripple }}
{{See also| Slendro clan #Hemiripple }}


Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 49/48, 6561/6250
[[Comma list]]: 49/48, 6561/6250


[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -10 -16 -5 }}]
{{Mapping|legend=1| 1 2 3 3 | 0 -10 -16 -5 }}


{{Multival|legend=1| 10 16 5 2 -20 -33 }}
{{Multival|legend=1| 10 16 5 2 -20 -33 }}


[[POTE generator]]: ~36/35 = 50.826
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~36/35 = 50.826


{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}
{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}
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Comma list: 49/48, 121/120, 567/550
Comma list: 49/48, 121/120, 567/550


Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -10 -16 -5 -13 }}]
Mapping: {{mapping| 1 2 3 3 4 | 0 -10 -16 -5 -13 }}


POTE generator: ~36/35 = 50.826
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.826


{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
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Comma list: 49/48, 66/65, 121/120, 351/350
Comma list: 49/48, 66/65, 121/120, 351/350


Mapping: [{{val| 1 2 3 3 4 4 }}, {{val| 0 -10 -16 -5 -13 -7 }}]
Mapping: {{mapping| 1 2 3 3 4 4 | 0 -10 -16 -5 -13 -7 }}


POTE generator: ~36/35 = 50.635
Optimal tuning (POTE): ~2 = 1\1, ~36/35 = 50.635


{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}
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== Cohemiripple ==
== Cohemiripple ==
{{see also| Sensamagic clan #Cohemiripple }}
{{See also| Sensamagic clan #Cohemiripple }}


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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[[Comma list]]: 245/243, 1323/1250
[[Comma list]]: 245/243, 1323/1250


[[Mapping]]: [{{val| 1 7 11 12 }}, {{val| 0 -10 -16 -17 }}]
{{Mapping|legend=1| 1 7 11 12 | 0 -10 -16 -17 }}


{{Multival|legend=1| 10 16 17 2 -1 -5 }}
{{Multival|legend=1| 10 16 17 2 -1 -5 }}


[[POTE generator]]: ~7/5 = 549.944
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 549.944


{{Optimal ET sequence|legend=1| 11cd, 13cd, 24 }}
{{Optimal ET sequence|legend=1| 11cd, 13cd, 24 }}
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Comma list: 77/75, 243/242, 245/242
Comma list: 77/75, 243/242, 245/242


Mapping: [{{val| 1 7 11 12 17 }}, {{val| 0 -10 -16 -17 -25 }}]
Mapping: {{mapping| 1 7 11 12 17 | 0 -10 -16 -17 -25 }}


POTE generator: ~7/5 = 549.945
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.945


{{Optimal ET sequence|legend=1| 11cdee, 13cdee, 24 }}
{{Optimal ET sequence|legend=1| 11cdee, 13cdee, 24 }}
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Comma list: 66/65, 77/75, 147/143, 243/242
Comma list: 66/65, 77/75, 147/143, 243/242


Mapping: [{{val| 1 7 11 12 17 14 }}, {{val| 0 -10 -16 -17 -25 -19 }}]
Mapping: {{mapping| 1 7 11 12 17 14 | 0 -10 -16 -17 -25 -19 }}


POTE generator: ~7/5 = 549.958
Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 549.958


{{Optimal ET sequence|legend=1| 11cdeef, 13cdeef, 24 }}
{{Optimal ET sequence|legend=1| 11cdeef, 13cdeef, 24 }}

Revision as of 10:44, 6 August 2023

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 sequence: 11c, 12, 71b, 83b, 95b, 107bc, 119bc

Badness: 0.138948

Septimal ripple

See also: Mint temperaments § 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 sequence: 12

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 sequence: 12

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 sequence: 12f

Badness: 0.031639

Hemiripple

See also: Slendro clan § 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 sequence: 23d, 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 sequence: 23de, 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 sequence: 23de, 24, 47de, 71bdde

Badness: 0.046588

Cohemiripple

See also: Sensamagic clan § 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 sequence: 11cd, 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 sequence: 11cdee, 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 sequence: 11cdeef, 13cdeef, 24

Badness: 0.049933

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