Ripple family: Difference between revisions
m Edo list reviewed |
m +subgroup data |
||
| Line 2: | Line 2: | ||
= Ripple = | = Ripple = | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 6561/6250 | [[Comma list]]: 6561/6250 | ||
| Line 15: | Line 17: | ||
= 7-limit = | = 7-limit = | ||
{{see also| Mint temperaments #Ripple }} | {{see also| Mint temperaments #Ripple }} | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 36/35, 2560/2401 | [[Comma list]]: 36/35, 2560/2401 | ||
| Line 29: | Line 33: | ||
== 11-limit == | == 11-limit == | ||
Subgroup: 2.3.5.7.11 | |||
Comma list: 36/35, 80/77, 126/121 | Comma list: 36/35, 80/77, 126/121 | ||
| Line 41: | Line 47: | ||
== 13-limit == | == 13-limit == | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 36/35, 40/39, 66/65, 147/143 | Comma list: 36/35, 40/39, 66/65, 147/143 | ||
| Line 146: | Line 154: | ||
</div></div> | </div></div> | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Ripple]] | [[Category:Ripple]] | ||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
Revision as of 09:03, 9 April 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
Subgroup: 2.3.5
Comma list: 6561/6250
Mapping: [⟨1 2 3], ⟨0 -5 -8]]
POTE generator: ~27/25 = 100.838
Badness: 0.1389
7-limit
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
Badness: 0.0597
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
Badness: 0.0388
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
Badness: 0.0316
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
Badness: 0.1751
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
Badness: 0.0668
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
Badness: 0.0466
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
Badness: 0.1902
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
Badness: 0.0827
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
Badness: 0.0499