Ripple family: Difference between revisions
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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 as accurate as it can be. | 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 as accurate as it can be. | ||
= Ripple = | == Ripple == | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 18: | Line 18: | ||
[[Badness]]: 0.1389 | [[Badness]]: 0.1389 | ||
= 7-limit = | == 7-limit == | ||
{{see also| Mint temperaments #Ripple }} | {{see also| Mint temperaments #Ripple }} | ||
| Line 35: | Line 35: | ||
[[Badness]]: 0.0597 | [[Badness]]: 0.0597 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 49: | Line 49: | ||
Badness: 0.0388 | Badness: 0.0388 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 63: | Line 63: | ||
Badness: 0.0316 | Badness: 0.0316 | ||
= Hemiripple = | == Hemiripple == | ||
{{see also| Slendro clan #Hemiripple }} | {{see also| Slendro clan #Hemiripple }} | ||
| Line 80: | Line 80: | ||
[[Badness]]: 0.1751 | [[Badness]]: 0.1751 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 94: | Line 94: | ||
Badness: 0.0668 | Badness: 0.0668 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 108: | Line 108: | ||
Badness: 0.0466 | Badness: 0.0466 | ||
= Cohemiripple = | == Cohemiripple == | ||
{{see also| Sensamagic clan #Cohemiripple }} | {{see also| Sensamagic clan #Cohemiripple }} | ||
| Line 125: | Line 125: | ||
[[Badness]]: 0.1902 | [[Badness]]: 0.1902 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 141: | Line 141: | ||
</div></div> | </div></div> | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
Revision as of 15:11, 31 May 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
- diamond monotone range: [92.308, 109.091] (1\13 to 1\11)
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]]
⟨⟨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]]
⟨⟨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]]
⟨⟨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