Porcupine family: Difference between revisions

← Older edit

VisualWikitext

@@ Line 1: / Line 1: @@
-{{interwiki
-| de = Porcupine
-| en = Porcupine family
-| es =
-| ja =
-}}
 {{Technical data page}}
 The '''porcupine family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[porcupine comma]], [[250/243]], also called the maximal diesis.
@@ Line 70: / Line 64: @@
 Badness (Sintel): 0.303
-==== Undecimation ====
-Subgroup: 2.3.5.11.13
-Comma list: 55/54, 100/99, 512/507
-Subgroup-val mapping: {{mapping| 1 -1 -2 0 5 | 0 6 10 8 -3 }}
-: mapping generators: ~2, ~88/65
-Optimal tunings:
-* WE: ~2 = 1199.4791{{c}}, ~88/65 = 517.9845{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~88/65 = 518.1740{{c}}
-{{Optimal ET sequence|legend=0| 7, 23bc, 30, 37, 44 }}
-Badness (Sintel): 1.21
-===== Full 13-limit =====
-This temperament is used by most edos that have porcupine and tune 13 well.
-Subgroup: 2.3.5.7.11.13
-Comma list: 55/54, 64/63, 100/99, 512/507
-Mapping: {{mapping| 1 5 8 -4 8 2| 0 -6 -10 12 -8 3 }}
-mapping generators: ~2, ~52/35
-Optimal tunings:
-*WE: ~2 = 1198.457{{c}}, ~52/35 = 680.519{{c}}
-* CWE: ~2 = 1200.000{{c}}, ~52/35 = 681.418{{c}}
-{{Optimal ET sequence|legend=0|7, 30, 37, 44}}
-Badness (Sintel): 1.679
 == Septimal porcupine ==
@@ Line 252: / Line 209: @@
 Badness (Sintel): 1.08
+==== Undecimation ====
+This weak extension is used by most patent vals that support porcupine and tune 13 well.
+Subgroup: 2.3.5.7.11.13
+Comma list: 55/54, 64/63, 100/99, 169/168
+Mapping: {{mapping| 1 -1 -2 8 0 5 | 0 6 10 -12 8 -3 }}
+: mapping generators: ~2, ~35/26
+Optimal tunings:
+* WE: ~2 = 1198.4569{{c}}, ~35/26 = 517.9375{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/26 = 518.5822{{c}}
+{{Optimal ET sequence|legend=0| 7, 30, 37, 81bd }}
+Badness (Sintel): 1.68
 == Opossum ==
@@ Line 732: / Line 707: @@
 Badness (Sintel): 1.85
+[[Category:Porcupine family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Porcupine family| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Porcupine| ]] <!-- key article -->
-[[Category:Rank 2]]