Kalismic temperaments: Difference between revisions
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These are rank | These are rank-3 temperaments tempering out [[9801/9800]], but we can begin by looking at the rank-4 temperament. | ||
= Kalismic = | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 9801/9800 | |||
[[Mapping]]: [{{val| 2 0 0 0 3 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 0 1 }}, {{val| 0 0 0 1 1 }}] | |||
Mapping generators: ~99/70, ~3, ~5, ~7 | |||
{{Val list|legend=1| 4, 12, 22, 46, 58, 72, 118, 130, 152, 270, 342, 512, 836, 1084, 1236, 1406, 1578, 1848, 2684, 4038, 4190, 4532, 11254 }} | |||
= Odin = | = Odin = | ||
{{see also| Landscape family }} | {{see also| Landscape family }} | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 9801/9800, 151263/151250 | |||
[[Mapping]]: [{{val| 6 0 0 8 17 }}, {{val| 0 1 0 -2 -4 }}, {{val| 0 0 1 2 3 }}] | |||
Mapping generators: ~55/49, ~3, ~5 | |||
{{Val list|legend=1| 12, 42, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464 }} | |||
Badness: 0. | [[Badness]]: 0.116 × 10<sup>-3</sup> | ||
= Loki = | = Loki = | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 5632/5625, 9801/9800 | |||
[[Mapping]]: [{{val| 2 0 0 -21 -18 }}, {{val| 0 1 0 4 2 }}, {{val| 0 0 1 3 4 }}] | |||
Badness: 0. | Mapping generators: ~99/70, ~3, ~5 | ||
{{Val list|legend=1| 12, 22, 86, 108, 118, 130, 248, 270, 670, 822, 940, 1092 }} | |||
[[Badness]]: 0.493 × 10<sup>-3</sup> | |||
= Van Gogh = | = Van Gogh = | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 9801/9800, 199297406/199290375 | |||
[[Mapping]]: [{{val| 2, 0, 8, 0, 11 }}, {{val| 0, 1, 1, 2, 1 }}, {{val| 0, 0, -9, -1, -10 }}] | |||
Mapping generators: ~99/70, ~3, ~9/7 | |||
{{Val list|legend=1| 22, 58, 80, 284, 320, 342, 742, 764, 1084, 1106, 1448, 1506, 1848, 4038, 4802, 5144, 6992 }} | |||
Badness: 0. | [[Badness]]: 0.297 × 10<sup>-3</sup> | ||
[[Category: | [[Category:Regular temperament theory]] | ||
[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Kalismic]] | [[Category:Kalismic]] | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Revision as of 07:14, 24 May 2021
These are rank-3 temperaments tempering out 9801/9800, but we can begin by looking at the rank-4 temperament.
Kalismic
Subgroup: 2.3.5.7.11
Comma list: 9801/9800
Mapping: [⟨2 0 0 0 3], ⟨0 1 0 0 -2], ⟨0 0 1 0 1], ⟨0 0 0 1 1]]
Mapping generators: ~99/70, ~3, ~5, ~7
Odin
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 151263/151250
Mapping: [⟨6 0 0 8 17], ⟨0 1 0 -2 -4], ⟨0 0 1 2 3]]
Mapping generators: ~55/49, ~3, ~5
Badness: 0.116 × 10-3
Loki
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800
Mapping: [⟨2 0 0 -21 -18], ⟨0 1 0 4 2], ⟨0 0 1 3 4]]
Mapping generators: ~99/70, ~3, ~5
Badness: 0.493 × 10-3
Van Gogh
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 199297406/199290375
Mapping: [⟨2, 0, 8, 0, 11], ⟨0, 1, 1, 2, 1], ⟨0, 0, -9, -1, -10]]
Mapping generators: ~99/70, ~3, ~9/7
Badness: 0.297 × 10-3