Porcupine rank-3 family: Difference between revisions
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These are the rank | 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. | ||
==Sonic== | == Sonic == | ||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 55/54, 100/99 | |||
[[Mapping]]: [{{val| 1 2 3 0 4 }}, {{val| 0 -3 -5 0 -4 }}, {{val| 0 0 0 1 0 }}] | |||
[[POTE generator]]s: ~10/9 = 164.078, ~7/4 = 967.841 | |||
{{Val list|legend=1| 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce }} | |||
[[Badness]]: 0.523 × 10<sup>-3</sup> | |||
== Tikal == | |||
Subgroup: 2.3.5.7.11 | |||
[[Comma list]]: 56/55, 250/243 | |||
[[Mapping]]: [{{val| 1 2 3 0 0 }}, {{val| 0 -3 -5 0 5 }}, {{val| 0 0 0 1 1 }}] | |||
Badness: | [[POTE generator]]s: ~10/9 = 161.519, ~7/4 = 971.046 | ||
{{Val list|legend=1| 15, 37e, 52be }} | |||
[[Badness]]: 1.973 × 10<sup>-3</sup> | |||
[[Category:Regular temperament theory]] | |||
[[Category:Temperament family]] | |||
[[Category:Porcupine rank-3 family| ]] <!-- main article --> | |||
[[Category:Rank 3]] | |||
Revision as of 13:08, 19 June 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.
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: ~10/9 = 164.078, ~7/4 = 967.841
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 = 161.519, ~7/4 = 971.046
Badness: 1.973 × 10-3