Blackwood family: Difference between revisions

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-{{Interwiki
-| en = Blackwood family
-| de = Blackwood-Limmisch
-| es =
-| ja =
-}}
 {{Technical data page}}
 The '''blackwood family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] 256/243, the [[Pythagorean limma]]. As a consequence, [[3/2]] is always represented by 3\5, 720 [[cent]]s assuming pure octaves. While quite sharp, this is close enough to a just fifth to serve as a fifth, and some people are fond of it. All temperaments shown here are pentaploid acot.
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 == Septimal blackwood ==
+{{Main| Blackwood }}
 [[Subgroup]]: 2.3.5.7
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 [[Badness]] (Sintel): 0.649
-==== Undecimal blackwood ====
+=== Undecimal blackwood ===
 Subgroup: 2.3.5.7.11
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 Badness (Sintel): 0.815
-===== 13-limit =====
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
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 Badness (Sintel): 0.847
-==== Farrier ====
+=== Farrier ===
 Subgroup: 2.3.5.7.11
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 Badness (Sintel): 0.965
-===== 13-limit =====
+==== 13-limit ====
 Subgroup: 2.3.5.7.11.13
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 Badness (Sintel): 0.922
-==== Ferrum ====
+=== Ferrum ===
 Subgroup: 2.3.5.7.11
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 Badness (Sintel): 1.02
+== Quindecic ==
+Quindecic preserves the [[11-limit]] structure of [[15edo]], with an independent generator for [[13/1|harmonic 13]].
+[[Subgroup]]: 2.3.5.7.11.13
+[[Comma list]]: 28/27, 49/48, 55/54, 77/75
+[[Mapping]]: {{mapping| 15 24 35 42 52 0 | 0 0 0 0 0 1 }}
+: mapping generators: ~22/21, ~13
+[[Optimal tuning]]s:
+* [[WE]]: ~22/21 = 79.770{{c}}, ~13/8 = 850.476{{c}} (~40/39 = 26.999{{c}})
+* [[CWE]]: ~22/21 = 80.000{{c}}, ~13/8 = 850.793{{c}} (~40/39 = 29.207{{c}})
+{{Optimal ET sequence|legend=1| 15, 30 }}
+[[Badness]] (Sintel): 1.20
 [[Category:Blackwood family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Rank 2]]
+[[Category:Catalogs of rank-2 temperaments]]