Porcupine family: Difference between revisions

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 * [[49/48]], the slendro diesis, for [[#Nautilus|nautilus]].
-All these 7-limit extensions notably share the same 2.3.5.11 subgroup, ''porkypine''.
+All these 7-limit extensions notably share the same 2.3.5.11 subgroup, known as ''porkypine''.
-Temperaments discussed elsewhere include [[opossum]], [[Septisemi temperaments #Oxygen|oxygen]], and [[Dicot family #Jamesbond|jamesbond]].
+Temperaments discussed elsewhere include [[Dicot family #Jamesbond|jamesbond]].
 == Porcupine ==
@@ Line 208: / Line 208: @@
 Badness: 0.026043
-== Hystrix ==
+== Opossum ==
-Hystrix provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: 36/35, 160/147
+[[Comma list]]: 28/27, 126/125
-[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -1 }}]
+[[Mapping]]: [{{val| 1 2 3 4 }}, {{val| 0 -3 -5 -9 }}]
-{{Multival|legend=1| 3 5 1 1 -7 -12 }}
+{{Multival|legend=1| 3 5 9 1 6 7 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 165.1845
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 161.3063
 [[Minimax tuning]]:
-* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
+* [[7-odd-limit|7-]] and [[9-odd-limit]] [[eigenmonzo basis]]: 2.7
-: [[Eigenmonzo basis]]: 2.5
-{{Val list|legend=1| 7, 8d, 15d }}
+{{Val list|legend=1| 7d, 8d, 15 }}
-[[Badness]]: 0.044944
+[[Badness]]: 0.040650
 === 11-limit ===
 Subgroup: 2.3.5.7.11
-Comma list: 22/21, 36/35, 80/77
+Comma list: 28/27, 55/54, 77/75
+Mapping: [{{val| 1 2 3 4 4 }}, {{val| 0 -3 -5 -9 -4 }}]
+Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.3646
+Minimax tuning:
+* 11-odd-limit eigenmonzo basis: 2.7
+Optimal GPV sequence: {{Val list| 7d, 8d, 15 }}
+Badness: 0.022325
+=== 13-limit  ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 28/27, 40/39, 55/54, 66/65
+Mapping: [{{val| 1 2 3 4 4 4 }}, {{val| 0 -3 -5 -9 -4 -2 }}]
-Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -3 -5 -1 -4 }}]
+Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 161.6312
-Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.7684
+Minimax tuning:
+* 13- and 15-odd-limit eigenmonzo basis: 2.7
-Optimal GPV sequence: {{val list| 7, 8d, 15d }}
+Optimal GPV sequence: {{Val list| 7d, 8d, 15, 38bceff }}
-Badness: 0.026790
+Badness: 0.019389
 == Porky ==
@@ Line 343: / Line 359: @@
 Badness: 0.030233
+== Hystrix ==
+Hystrix provides a less complex avenue to the 7-limit. Unfortunately in temperaments as in life you get what you pay for, and hystrix, for which a generator of 2\15 or 9\68 can be used, is a temperament for the adventurous souls who have probably already tried [[15edo]]. They can try the even sharper fifth of hystrix in [[68edo]] and see how that suits.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 36/35, 160/147
+[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -1 }}]
+{{Multival|legend=1| 3 5 1 1 -7 -12 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 165.1845
+[[Minimax tuning]]:
+* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~10/9 = {{monzo| 3/5 0 -1/5 }}
+: [[Eigenmonzo basis]]: 2.5
+{{Val list|legend=1| 7, 8d, 15d }}
+[[Badness]]: 0.044944
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 22/21, 36/35, 80/77
+Mapping: [{{val| 1 2 3 3 4 }}, {{val| 0 -3 -5 -1 -4 }}]
+Optimal tuning (CTE): ~2 = 1\1, ~11/10 = 164.7684
+Optimal GPV sequence: {{val list| 7, 8d, 15d }}
+Badness: 0.026790
+== Oxygen ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 21/20, 175/162
+[[Mapping]]: [{{val| 1 2 3 3 }}, {{val| 0 -3 -5 -2 }}]
+{{Multival|legend=1| 3 5 2 1 -5 -9 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 161.3408
+{{Val list|legend=1| 7d }}
+[[Badness]]: 0.059866
 == Hedgehog ==