Porcupine rank three family: Difference between revisions

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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.

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 ==

Subgroup: 2.3.5.7

[[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

: 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 }}

[[Badness]]: 0.535 × 10-3

== Sonic ==

Subgroup: 2.3.5.7.11

[[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: ~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 }}

[[Badness]]: 0.523 × 10-3

== Tikal ==

Subgroup: 2.3.5.7.11

[[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 }}]

[[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 }}

[[Badness]]: 1.973 × 10-3

~~[[Category:Regular temperament theory]]~~

[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Porcupine rank-3 family| ]]

[[Category:Porcupine| ]]

[[Category:Rank 3]]

@@ Line 1: / Line 1: @@
-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 ==
-Subgroup: 2.3.5.7
+[[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|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
-{{Val list|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>
 == Sonic ==
-Subgroup: 2.3.5.7.11
+[[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 }}]
+{{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
-{{Val list|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>
 == Tikal ==
-Subgroup: 2.3.5.7.11
+[[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 }}]
+{{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
-{{Val list|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>
-[[Category:Regular temperament theory]]
 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Porcupine rank-3 family| ]] <!-- main article -->
+[[Category:Porcupine| ]] <!-- key article -->
 [[Category:Rank 3]]