Porcupine rank three family: Difference between revisions

m Cleanup
+rank-3 porcupine
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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: ~10/9 = 164.078, ~7/4 = 967.841
[[POTE generator]]s: ~11/10 = 164.0777, ~7/4 = 967.8413


{{Val list|legend=1| 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce }}
{{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 = 161.519, ~7/4 = 971.046
[[POTE generator]]s: ~10/9 = 161.5193, ~7/4 = 971.0457


{{Val list|legend=1| 15, 37e, 52be }}
{{Val list|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}


[[Badness]]: 1.973 × 10<sup>-3</sup>
[[Badness]]: 1.973 × 10<sup>-3</sup>