Porcupine rank three family: Difference between revisions

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-These are the rank three 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.
-==Sonic==
+== Rank-3 porcupine ==
-Commas: 55/54, 100/99
+[[Subgroup]]: 2.3.5.7
-Map: [&lt;1 2 3 0 4|, &lt;0 -3 -5 0 -4|, &lt;0 0 0 1 0|]
+[[Comma list]]: [[250/243]]
-Generators: ~10/9 = 164.078, ~7 = 3367.841
+{{Mapping|legend=1| 1 2 3 0 | 0 -3 -5 0 | 0 0 0 1 }}
-EDOs: 7, 14c, 15, 22, 37, 44d, 51, 66, 73ce, 139bce, 212bce
+: mapping generators: ~2, ~10/9, ~7
-Badness: 0.000523
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 163.9504, ~7/4 = 970.0552
-==Tikal==
+{{Optimal ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 73c }}
-Commas: 56/55, 250/243
-Map: [&lt;1 2 3 0 0], &lt;0 -3 -5 0 5|, &lt;0 0 0 1 1|]
+[[Badness]]: 0.535 × 10<sup>-3</sup>
-POTE generators: ~10/9 = 161.519, ~7 = 3371.046
+== Sonic ==
+[[Subgroup]]: 2.3.5.7.11
-EDOs: 15, 37e, 52be
+[[Comma list]]: 55/54, 100/99
-Badness: 0.001973
+{{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 ET sequence|legend=1| 7d, 8d, 14c, 15, 22, 37, 51, 88b }}
+[[Badness]]: 0.523 × 10<sup>-3</sup>
+== Tikal ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 56/55, 250/243
+{{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 ET sequence|legend=1| 7d, 8d, 15, 30dee, 37ee, 52bee }}
+[[Badness]]: 1.973 × 10<sup>-3</sup>
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Porcupine rank-3 family| ]] <!-- main article -->
+[[Category:Porcupine| ]] <!-- key article -->
+[[Category:Rank 3]]