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|12EDO]] is about as accurate as it can be. | ||
== Ripple == | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
| Line 12: | Line 11: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* [[ | * [[Diamond monotone]] range: [92.308, 109.091] (1\13 to 1\11) | ||
{{Val list|legend=1| 11c, 12, 71b, 83b, 95b, 107bc, 119bc }} | {{Val list|legend=1| 11c, 12, 71b, 83b, 95b, 107bc, 119bc }} | ||
| Line 18: | Line 17: | ||
[[Badness]]: 0.1389 | [[Badness]]: 0.1389 | ||
== 7-limit | === 7-limit === | ||
{{see also| Mint temperaments #Ripple }} | {{see also| Mint temperaments #Ripple }} | ||
| Line 33: | Line 32: | ||
{{Val list|legend=1| 12 }} | {{Val list|legend=1| 12 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.059735 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 45: | Line 43: | ||
POTE generator: ~21/20 = 99.385 | POTE generator: ~21/20 = 99.385 | ||
{{Val list | Vals: {{Val list| 12 }} | ||
Badness: 0. | Badness: 0.038811 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 59: | Line 56: | ||
POTE generator: ~21/20 = 98.572 | POTE generator: ~21/20 = 98.572 | ||
{{Val list | Vals: {{Val list| 12f }} | ||
Badness: 0. | Badness: 0.031639 | ||
== Hemiripple | == Hemiripple == | ||
{{see also| Slendro clan #Hemiripple }} | {{see also| Slendro clan #Hemiripple }} | ||
| Line 76: | Line 73: | ||
[[POTE generator]]: ~36/35 = 50.826 | [[POTE generator]]: ~36/35 = 50.826 | ||
{{Val list|legend=1| 23d, 24, 47d, | {{Val list|legend=1| 23d, 24, 47d, 71bdd }} | ||
[[Badness]]: 0.175113 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 90: | Line 86: | ||
POTE generator: ~36/35 = 50.826 | POTE generator: ~36/35 = 50.826 | ||
{{Val list | Vals: {{Val list| 23de, 24, 47de, 71bdde }} | ||
Badness: 0.066834 | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 104: | Line 99: | ||
POTE generator: ~36/35 = 50.635 | POTE generator: ~36/35 = 50.635 | ||
{{Val list | Vals: {{Val list| 23de, 24, 47de, 71bdde }} | ||
Badness: 0. | Badness: 0.046588 | ||
== Cohemiripple | == Cohemiripple == | ||
{{see also| Sensamagic clan #Cohemiripple }} | {{see also| Sensamagic clan #Cohemiripple }} | ||
| Line 123: | Line 118: | ||
{{Val list|legend=1| 11cd, 13cd, 24 }} | {{Val list|legend=1| 11cd, 13cd, 24 }} | ||
[[Badness]]: 0. | [[Badness]]: 0.190208 | ||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 135: | Line 129: | ||
POTE generator: ~7/5 = 549.945 | POTE generator: ~7/5 = 549.945 | ||
{{Val list | Vals: {{Val list| 11cdee, 13cdee, 24 }} | ||
Badness: 0. | Badness: 0.082716 | ||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
| Line 151: | Line 142: | ||
POTE generator: ~7/5 = 549.958 | POTE generator: ~7/5 = 549.958 | ||
{{Val list | Vals: {{Val list| 11cdeef, 13cdeef, 24 }} | ||
Badness: 0.049933 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 12:05, 8 June 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]]
Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]
POTE generator: ~21/20 = 99.483
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.031639
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: 0.175113
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.046588
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: 0.190208
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
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.049933