Swetismic temperaments: Difference between revisions
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== Swetismic == | == Swetismic == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 540/539 | [[Comma list]]: 540/539 | ||
[[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 0 1 -2 }}] | [[Mapping]]: [{{val| 1 0 0 0 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 0 1 -2 }}] | ||
Mapping generators: ~2, ~3, ~5, ~7 | |||
{{Val list|legend=1| 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578 }} | {{Val list|legend=1| 9, 10, 19, 22, 31, 41, 53, 58, 72, 130, 152, 224, 354, 537, 578 }} | ||
== Hades == | == Hades == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 540/539, 4000/3993 | [[Comma list]]: 540/539, 4000/3993 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 540/539, 729/728, 1575/1573 | Comma list: 540/539, 729/728, 1575/1573 | ||
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=== Cerberus === | === Cerberus === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 364/363, 540/539 | Comma list: 351/350, 364/363, 540/539 | ||
Mapping: [{{val| 2 1 0 2 3 1 }}, {{val| 0 3 0 5 -1 -4 }}, {{val| 0 0 1 0 1 2 }}] | Mapping: [{{val| 2 1 0 2 3 1 }}, {{val| 0 3 0 5 -1 -4 }}, {{val| 0 0 1 0 1 2 }}] | ||
Vals: {{val list| 22, 50, 58, 72, 130 }} | Vals: {{val list| 22, 50, 58, 72, 130 }} | ||
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== Minos == | == Minos == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 540/539, 12005/11979 | [[Comma list]]: 540/539, 12005/11979 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 364/363, 540/539, 676/675 | Comma list: 364/363, 540/539, 676/675 | ||
Mapping: [{{val| 1 0 2 1 2 1 }}, {{val| 0 2 4 3 4 7 }}, {{val| 0 0 -5 -1 -3 -5 }}] | Mapping: [{{val| 1 0 2 1 2 1 }}, {{val| 0 2 4 3 4 7 }}, {{val| 0 0 -5 -1 -3 -5 }}] | ||
Vals: {{val list| 9, 54, 58, 72, 121, 130, 193 }} | Vals: {{val list| 9, 54, 58, 72, 121, 130, 193 }} | ||
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== Persephone == | == Persephone == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 540/539, 88209/87500 | [[Comma list]]: 540/539, 88209/87500 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 540/539, 847/845 | Comma list: 351/350, 540/539, 847/845 | ||
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== Hypnos == | == Hypnos == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 540/539, 72171/71680 | [[Comma list]]: 540/539, 72171/71680 | ||
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=== 13-limit === | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 169/168, 540/539, 729/728 | Comma list: 169/168, 540/539, 729/728 | ||
Revision as of 11:28, 3 October 2021
These are rank-3 temperaments tempering out 540/539, but we can begin by looking at the rank-4 temperament.
Swetismic
Subgroup: 2.3.5.7.11
Comma list: 540/539
Mapping: [⟨1 0 0 0 2], ⟨0 1 0 0 3], ⟨0 0 0 1 -2]]
Mapping generators: ~2, ~3, ~5, ~7
Hades
Subgroup: 2.3.5.7.11
Comma list: 540/539, 4000/3993
Mapping: [⟨2 1 0 2 3], ⟨0 3 0 5 -1], ⟨0 0 1 0 1]]
Mapping generators: ~99/70, ~9/7, ~5
Badness: 0.361 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1575/1573
Mapping: [⟨2 1 0 2 3 -2], ⟨0 3 0 5 -1 13], ⟨0 0 1 0 1 0]]
Mapping generators: ~99/70, ~9/7, ~5
Vals: Template:Val list
Badness: 0.535 × 10-3
Cerberus
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 540/539
Mapping: [⟨2 1 0 2 3 1], ⟨0 3 0 5 -1 -4], ⟨0 0 1 0 1 2]]
Vals: Template:Val list
Badness: 0.766 × 10-3
Minos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 12005/11979
Mapping: [⟨1 0 2 1 2], ⟨0 2 4 3 4], ⟨0 0 -5 -1 -3]]
Mapping generators: ~2, ~121/70, ~49/33
Badness: 0.886 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675
Mapping: [⟨1 0 2 1 2 1], ⟨0 2 4 3 4 7], ⟨0 0 -5 -1 -3 -5]]
Vals: Template:Val list
Badness: 0.724 × 10-3
Persephone
Subgroup: 2.3.5.7.11
Comma list: 540/539, 88209/87500
Mapping: [⟨1 0 4 -2 10], ⟨0 1 4 0 7], ⟨0 0 -5 3 -11]]
Badness: 2.015 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 540/539, 847/845
Mapping: [⟨1 0 4 -2 10 7], ⟨0 1 4 0 7 5], ⟨0 0 -5 3 -11 -7]]
Vals: Template:Val list
Badness: 0.997 × 10-3
Hypnos
Subgroup: 2.3.5.7.11
Comma list: 540/539, 72171/71680
Mapping: [⟨1 0 0 -3 8], ⟨0 3 0 11 -13], ⟨0 0 1 0 1]]
Badness: 1.629 × 10-3
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 540/539, 729/728
Mapping: [⟨1 0 0 -3 8 0], ⟨0 3 0 11 -13 7], ⟨0 0 1 0 1 0]]
Vals: Template:Val list
Badness: 1.439 × 10-3