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Porcupine rank three family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
 
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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.  
{{Technical data page}}
The '''porcupine rank-3 family''' of [[temperament]]s [[tempering out|tempers 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 ==
== Rank-3 porcupine ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: [[250/243]]
[[Comma list]]: [[250/243]]


[[Mapping]]: [{{val| 1 2 3 0 }}, {{val| 0 -3 -5 0 }}, {{val| 0 0 0 1 }}]
{{Mapping|legend=1| 1 2 3 0 | 0 -3 -5 0 | 0 0 0 1 }}


Mapping generators: ~2, ~10/9, ~7
: mapping generators: ~2, ~10/9, ~7


[[POTE generator]]s: ~10/9 = 163.9504, ~7/4 = 970.0552
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552


{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
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== Sonic ==
== Sonic ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 55/54, 100/99
[[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 }}]
{{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }}


[[POTE generator]]s: ~11/10 = 164.0777, ~7/4 = 967.8413
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/10 = 164.0777, ~7/4 = 967.8413


{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
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== Tikal ==
== Tikal ==
Subgroup: 2.3.5.7.11
[[Subgroup]]: 2.3.5.7.11


[[Comma list]]: 56/55, 250/243
[[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 }}]
{{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }}


[[POTE generator]]s: ~10/9 = 161.5193, ~7/4 = 971.0457
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 161.5193, ~7/4 = 971.0457


{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}
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[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Pages with mostly numerical content]]
[[Category:Porcupine rank-3 family| ]] <!-- main article -->
[[Category:Porcupine rank-3 family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Rank 3]]
Retrieved from "https://en.xen.wiki/w/Porcupine_rank_three_family"