User:VIxen/Sandbox: Difference between revisions
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These are rank-3 temperaments | = Wizmic family = | ||
These are rank-3 temperaments where the wizma [[420175/419904]] is tempered out. For the clan of rank-2 temperaments with this comma, see [[Wizmic microtemperaments]]. | |||
== Wizmic == | == Wizmic == | ||
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[[Badness]]: 0.867 × 10<sup>-3</sup> | [[Badness]]: 0.867 × 10<sup>-3</sup> | ||
=== 13-limit ( | === 13-limit (ibnsinmic) === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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[[Badness]]: 1.56 × 10<sup>-3</sup> | [[Badness]]: 1.56 × 10<sup>-3</sup> | ||
= Skeetsmic family = | |||
These are rank-3 temperaments where the [[skeetsma]] is tempered out. | |||
== Skeetsmic == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 14348907/14336000 | |||
[[Mapping]]: [{{val| 1 0 0 -14 }}, {{val| 0 1 0 15 }}, {{val| 0 0 1 -3 }}] | |||
Mapping generators: ~2, ~3, ~5 | |||
{{Val list|legend=1| 5, 7d, 12d, 39ddd, 44cdd, 46d, 48, 53, 111, 118, 171, 742, 795, 913, 966, 1137, 1308, 2050, 2221, 2392, 3358, 3529, 7229b, 10758bbd }} | |||
[[Badness]]: 0.333 × 10<sup>-3</sup> | |||
== 58 & 224 & 460 == | |||
{{see also| Kalismic temperaments }} | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 9801/9800, 1240029/1239040 | |||
[[Mapping]]: [{{val| 2 0 1 -28 -25 }}, {{val| 0 1 0 15 13 }}, {{val| 0 0 1 -3 -2 }}] | |||
Mapping generators: ~99/70, ~3, ~5 | |||
{{Val list|legend=1| 10c, 12de, 44cddeee, 46de, 48, 58, 106, 118, 224, 342, 742, 966, 1084, 1308, 1650, 2392, 2734, 5126bdb, 6776bd }} | |||
[[Badness]]: 3.2 × 10<sup>-3</sup> | |||
=== 13-limit === | |||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 9801/9800, 10648/10647, 59535/59488 | |||
[[Mapping]]: [{{val| 2 0 1 -31 -27 -22 }}, {{val| 0 1 0 15 13 11 }}, {{val| 0 0 2 -6 -4 -3 }}] | |||
Mapping generators: ~99/70, ~3, ~220/117 | |||
{{Val list|legend=1| 12de, 46def, 58, 166, 224, 460, 684, 1426, 2334, 3076 }} | |||
[[Badness]]: 1.31 × 10<sup>-3</sup> | |||
Revision as of 04:13, 21 June 2022
Wizmic family
These are rank-3 temperaments where the wizma 420175/419904 is tempered out. For the clan of rank-2 temperaments with this comma, see Wizmic microtemperaments.
Wizmic
Subgroup: 2.3.5.7
Comma list: 420175/419904
Mapping: [⟨1 0 3 0], ⟨0 1 4 0], ⟨0 0 -5 2]]
Mapping generators: ~2, ~3, ~648/245
Badness: 0.0864 × 10-3
Gersemi
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 41503/41472
Mapping: [⟨2 0 1 2 6], ⟨0 1 4 0 2], ⟨0 0 -5 2 -3]]
Mapping generators: ~99/70, ~3, ~144/77
Badness: 0.368 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 4096/4095, 9801/9800, 41503/41472
Mapping: [⟨2 0 1 2 6 21], ⟨0 1 4 0 2 -6], ⟨0 0 -5 2 -3 3]]
Mapping generators: ~99/70, ~3, ~144/77
Badness: 0.867 × 10-3
13-limit (ibnsinmic)
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 17303/17280
Mapping: [⟨2 0 1 2 6 -3], ⟨0 1 4 0 2 1], ⟨0 0 -5 2 -3 4]]
Mapping generators: ~99/70, ~3, ~144/77
Badness: 1.56 × 10-3
Skeetsmic family
These are rank-3 temperaments where the skeetsma is tempered out.
Skeetsmic
Subgroup: 2.3.5.7
Comma list: 14348907/14336000
Mapping: [⟨1 0 0 -14], ⟨0 1 0 15], ⟨0 0 1 -3]]
Mapping generators: ~2, ~3, ~5
Badness: 0.333 × 10-3
58 & 224 & 460
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 1240029/1239040
Mapping: [⟨2 0 1 -28 -25], ⟨0 1 0 15 13], ⟨0 0 1 -3 -2]]
Mapping generators: ~99/70, ~3, ~5
Badness: 3.2 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 9801/9800, 10648/10647, 59535/59488
Mapping: [⟨2 0 1 -31 -27 -22], ⟨0 1 0 15 13 11], ⟨0 0 2 -6 -4 -3]]
Mapping generators: ~99/70, ~3, ~220/117
Badness: 1.31 × 10-3