Ripple family: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,032 edits
mNo edit summary
Cmloegcmluin (talk | contribs)
autopatrolled, emailconfirmed
5,171 edits
"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 15: Line 15:
* 5-odd-limit diamond monotone and tradeoff: [99.609, 105.214]  
* 5-odd-limit diamond monotone and tradeoff: [99.609, 105.214]  


{{Val list|legend=1| 11c, 12, 71b, 83b, 95b, 107bc, 119bc }}
{{Optimal ET sequence|legend=1| 11c, 12, 71b, 83b, 95b, 107bc, 119bc }}


[[Badness]]: 0.138948
[[Badness]]: 0.138948
Line 32: Line 32:
[[POTE generator]]: ~21/20 = 99.483
[[POTE generator]]: ~21/20 = 99.483


{{Val list|legend=1| 12 }}
{{Optimal ET sequence|legend=1| 12 }}


[[Badness]]: 0.059735
[[Badness]]: 0.059735
Line 45: Line 45:
POTE generator: ~21/20 = 99.385
POTE generator: ~21/20 = 99.385


Optimal GPV sequence: {{Val list| 12 }}
{{Optimal ET sequence|legend=1| 12 }}


Badness: 0.038811
Badness: 0.038811
Line 58: Line 58:
POTE generator: ~21/20 = 98.572
POTE generator: ~21/20 = 98.572


Optimal GPV sequence: {{Val list| 12f }}
{{Optimal ET sequence|legend=1| 12f }}


Badness: 0.031639
Badness: 0.031639
Line 75: Line 75:
[[POTE generator]]: ~36/35 = 50.826
[[POTE generator]]: ~36/35 = 50.826


{{Val list|legend=1| 23d, 24, 47d, 71bdd }}
{{Optimal ET sequence|legend=1| 23d, 24, 47d, 71bdd }}


[[Badness]]: 0.175113
[[Badness]]: 0.175113
Line 88: Line 88:
POTE generator: ~36/35 = 50.826
POTE generator: ~36/35 = 50.826


Optimal GPV sequence: {{Val list| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}


Badness: 0.066834
Badness: 0.066834
Line 101: Line 101:
POTE generator: ~36/35 = 50.635
POTE generator: ~36/35 = 50.635


Optimal GPV sequence: {{Val list| 23de, 24, 47de, 71bdde }}
{{Optimal ET sequence|legend=1| 23de, 24, 47de, 71bdde }}


Badness: 0.046588
Badness: 0.046588
Line 118: Line 118:
[[POTE generator]]: ~7/5 = 549.944
[[POTE generator]]: ~7/5 = 549.944


{{Val list|legend=1| 11cd, 13cd, 24 }}
{{Optimal ET sequence|legend=1| 11cd, 13cd, 24 }}


[[Badness]]: 0.190208
[[Badness]]: 0.190208
Line 131: Line 131:
POTE generator: ~7/5 = 549.945
POTE generator: ~7/5 = 549.945


Optimal GPV sequence: {{Val list| 11cdee, 13cdee, 24 }}
{{Optimal ET sequence|legend=1| 11cdee, 13cdee, 24 }}


Badness: 0.082716
Badness: 0.082716
Line 144: Line 144:
POTE generator: ~7/5 = 549.958
POTE generator: ~7/5 = 549.958


Optimal GPV sequence: {{Val list| 11cdeef, 13cdeef, 24 }}
{{Optimal ET sequence|legend=1| 11cdeef, 13cdeef, 24 }}


Badness: 0.049933
Badness: 0.049933

Revision as of 16:12, 7 May 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]]

POTE generator: ~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 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~7/5 = 549.958

Optimal ET sequence: 11cdeef, 13cdeef, 24

Badness: 0.049933

Retrieved from "https://en.xen.wiki/index.php?title=Ripple_family&oldid=112486"