Porcupine rank three family: Difference between revisions
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These are the rank-3 temperaments tempering out the porcupine comma or maximal diesis, [[250/243]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. | These are the rank-3 temperaments tempering out the porcupine comma or maximal diesis, [[250/243]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth. | ||
== Rank-3 porcupine == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: [[250/243]] | |||
[[Mapping]]: [{{val| 1 2 3 0 }}, {{val| 0 -3 -5 0 }}, {{val| 0 0 0 1 }}] | |||
Mapping generators: ~2, ~10/9, ~7 | |||
[[POTE generator]]s: ~10/9 = 163.9504, ~7/4 = 970.0552 | |||
{{Val list|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }} | |||
[[Badness]]: 0.535 × 10<sup>-3</sup> | |||
== Sonic == | == Sonic == | ||
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[[Mapping]]: [{{val| 1 2 3 0 4 }}, {{val| 0 -3 -5 0 -4 }}, {{val| 0 0 0 1 0 }}] | [[Mapping]]: [{{val| 1 2 3 0 4 }}, {{val| 0 -3 -5 0 -4 }}, {{val| 0 0 0 1 0 }}] | ||
[[POTE generator]]s: ~10 | [[POTE generator]]s: ~11/10 = 164.0777, ~7/4 = 967.8413 | ||
{{Val list|legend=1| | {{Val list|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }} | ||
[[Badness]]: 0.523 × 10<sup>-3</sup> | [[Badness]]: 0.523 × 10<sup>-3</sup> | ||
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[[Mapping]]: [{{val| 1 2 3 0 0 }}, {{val| 0 -3 -5 0 5 }}, {{val| 0 0 0 1 1 }}] | [[Mapping]]: [{{val| 1 2 3 0 0 }}, {{val| 0 -3 -5 0 5 }}, {{val| 0 0 0 1 1 }}] | ||
[[POTE generator]]s: ~10/9 = 161. | [[POTE generator]]s: ~10/9 = 161.5193, ~7/4 = 971.0457 | ||
{{Val list|legend=1| 15, | {{Val list|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }} | ||
[[Badness]]: 1.973 × 10<sup>-3</sup> | [[Badness]]: 1.973 × 10<sup>-3</sup> | ||
Revision as of 18:35, 24 November 2021
These are the rank-3 temperaments tempering out the porcupine comma or maximal diesis, 250/243. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.
Rank-3 porcupine
Subgroup: 2.3.5.7
Mapping: [⟨1 2 3 0], ⟨0 -3 -5 0], ⟨0 0 0 1]]
Mapping generators: ~2, ~10/9, ~7
POTE generators: ~10/9 = 163.9504, ~7/4 = 970.0552
Badness: 0.535 × 10-3
Sonic
Subgroup: 2.3.5.7.11
Comma list: 55/54, 100/99
Mapping: [⟨1 2 3 0 4], ⟨0 -3 -5 0 -4], ⟨0 0 0 1 0]]
POTE generators: ~11/10 = 164.0777, ~7/4 = 967.8413
Badness: 0.523 × 10-3
Tikal
Subgroup: 2.3.5.7.11
Comma list: 56/55, 250/243
Mapping: [⟨1 2 3 0 0], ⟨0 -3 -5 0 5], ⟨0 0 0 1 1]]
POTE generators: ~10/9 = 161.5193, ~7/4 = 971.0457
Badness: 1.973 × 10-3