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Porcupine rank-3 family: Difference between revisions

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{{Technical data page}}<br><br>
{{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.  
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.  


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


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.5444{{c}}, ~10/9 = 163.8881{{c}}, ~7/4 = 969.6868{{c}}
: [[error map]]: {{val| -0.456 +5.469 -7.121 -0.050 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 164.0621{{c}}, ~7/4 = 969.4180{{c}}
: error map: {{val| 0.000 +5.859 -6.624 +0.592 }}


{{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 }}


[[Badness]]: 0.535 × 10<sup>-3</sup>
[[Badness]] (Sintel): 2.36


== Sonic ==
== Sonic ==
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{{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }}
{{Mapping|legend=1| 1 2 3 0 4 | 0 -3 -5 0 -4 | 0 0 0 1 0 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/10 = 164.0777, ~7/4 = 967.8413
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3290{{c}}, ~11/10 = 164.1227{{c}}, ~7/4 = 968.1067{{c}}
: [[error map]]: {{val| +0.329 +6.335 -5.940 -0.061 -6.492 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 163.9951{{c}}, ~7/4 = 968.2673{{c}}
: error map: {{val| 0.000 +6.060 -6.289 -0.559 -7.298 }}


{{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 }}


[[Badness]]: 0.523 × 10<sup>-3</sup>
[[Badness]] (Sintel): 0.629


== Tikal ==
== Tikal ==
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{{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }}
{{Mapping|legend=1| 1 2 3 0 0 | 0 -3 -5 0 5 | 0 0 0 1 1 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 161.5193, ~7/4 = 971.0457
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1195.9857{{c}}, ~11/10 = 160.9790{{c}}, ~7/4 = 967.7973{{c}}
: [[error map]]: {{val| -4.014 +7.079 -3.252 -9.057 +13.346 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/10 = 162.1977{{c}}, ~7/4 = 964.6202{{c}}
: error map: {{val| 0.000 +11.452 +2.698 -4.206 +24.291 }}


{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}
{{Optimal ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}


[[Badness]]: 1.973 × 10<sup>-3</sup>
[[Badness]] (Sintel): 2.37


[[Category:Temperament families]]
[[Category:Porcupine rank-3 family| ]] <!-- main article -->
[[Category:Porcupine rank-3 family| ]] <!-- main article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Porcupine| ]] <!-- key article -->
[[Category:Rank 3]]
[[Category:Temperament families]]
[[Category:Catalogs of rank-3 temperaments]]
Retrieved from "https://en.xen.wiki/w/Porcupine_rank-3_family"