User:VIxen/Sandbox: Difference between revisions
m →Gersemi: confused the badnesses of the 13-limit extensions |
→Gersemi: +intro, +leprechaunish 13-23 limits |
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== Gersemi == | == Gersemi == | ||
To the wizma [-6 -8 2 5⟩ = 420175/419904, the kalisma is a natural complement, as their product is the [[tinge]]. | |||
18/7 is a possible [[equave]]. [[Fokker block]]s of 128 notes are available for it, corresponding to 94edo. 18/7 is split into 4 parts that become ~19/15 in 19-limit. Also, (18/7)<sup>3</sup> ~ 17/1 via the [[5832/5831|chlorisma]]. However, the tones 9/8 and (19/15)/(9/8) = 152/135 have distinct mappings. | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
[[Comma list]]: 4225/4224, 9801/9800, 41503/41472 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 9 }}, {{val| 0 1 9 -2 5 -6 }}, {{val| 0 0 -10 4 -6 7 }}] | |||
Mapping generators: ~99/70, ~3, ~154/65 | |||
{{Val list|legend=1| 44, 50, 94, 144, 176, 220, 270, 590, 684, 954 }} | |||
[[Badness]]: 1.06 × 10<sup>-3</sup> | |||
=== 17-limit === | |||
Subgroup: 2.3.5.7.11.13.17 | |||
[[Comma list]]: 1089/1088, 1225/1224, 2025/2023, 4225/4224 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 9 0 }}, {{val| 0 1 9 -2 5 -6 12 }}, {{val| 0 0 -10 4 -6 7 -12 }}] | |||
Mapping generators: ~99/70, ~3, ~154/65 | |||
{{Val list|legend=1| 44, 50, 94, 144g, 176g, 220g, 270, 364, 414, 634g, 684 }} | |||
[[Badness]]: 1.46 × 10<sup>-3</sup> | |||
=== 19-limit === | |||
Subgroup: 2.3.5.7.11.13.19 | |||
[[Comma list]]: 1089/1088, 1225/1224, 1729/1728, 2926/2925, 3762/3757 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 9 0 1 }}, {{val| 0 1 9 -2 5 -6 12 11 }}, {{val| 0 0 -10 4 -6 7 -12 -11 }}] | |||
Mapping generators: ~99/70, ~3, ~45/19 | |||
{{Val list|legend=1| 44, 50, 94, 144gh, 176g, 220g, 270, 414h, 590, 634g, 684h }} | |||
[[Badness]]: 1.11 × 10<sup>-3</sup> | |||
=== 23-limit === | |||
Subgroup: 2.3.5.7.11.13.19.23 | |||
[[Comma list]]: 897/896, 1089/1088, 1225/1224, 1729/1728, 2737/2736, 2926/2925 | |||
[[Mapping]]: [{{val| 2 0 1 2 6 9 0 1 7 }}, {{val| 0 1 9 -2 5 -6 12 11 3 }}, {{val| 0 0 -10 4 -6 7 -12 -11 -3 }}] | |||
Mapping generators: ~99/70, ~3, ~45/19 | |||
{{Val list|legend=1| 44, 50, 94, 144gh, 176g, 220g, 226, 270, 320i, 364i, 414hi }} | |||
[[Badness]]: 1.23 × 10<sup>-3</sup> | |||
=== 13-limit (ibnsinmic) === | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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[[Badness]]: 0.867 × 10<sup>-3</sup> | [[Badness]]: 0.867 × 10<sup>-3</sup> | ||
=== 13-limit (schisminic | === 13-limit (schisminic) === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||