Landscape family: Difference between revisions

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 The '''landscape family''' of [[rank-3 temperament]]s [[tempering out|tempers out]] the [[landscape comma]], 250047/250000.
-Considered below are landy and house, besides the 7-limit temperament.
 == Landscape ==
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 [[Badness]] (Sintel): 0.0940
+=== Overview to extensions ===
+Extensions of landscape include landy, odin, tyr and house, all considered below.
 == Landy ==
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 Comma list: 364/363, 441/440, 625/624
-Mapping: {{mapping| 3 0 0 4 -1 -12 | 0 1 0 -2 -2 -1 | 0 0 1 2 3 4 }}
+{{Mapping|legend=0| 3 0 0 4 -1 -12 | 0 1 0 -2 -2 -1 | 0 0 1 2 3 4 }}
 Optimal tunings:
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 Comma list: 676/675, 1001/1000, 3025/3024
-Mapping: {{mapping| 3 0 0 4 8 -3 | 0 2 0 -4 1 3 | 0 0 1 2 0 1 }}
+{{Mapping|legend=0| 3 0 0 4 8 -3 | 0 2 0 -4 1 3 | 0 0 1 2 0 1 }}
 Optimal tunings:
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 Badness (Sintel): 0.514
-Complexity spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7
 == House ==
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 [[Badness]] (Sintel): 2.31
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 6656/6655, 105644/105625, 123201/123200
+{{Mapping|legend=0| 3 0 -13 -22 10 -10 | 0 1 4 6 0 4 | 0 0 5 10 -2 11 }}
+Optimal tunings:
+* WE: ~63/50 = 399.9957{{c}}, ~3/2 = 701.9629{{c}}, ~224/117 = 75.6993{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~3/2 = 701.9689{{c}}, ~224/117 = 75.6997{{c}}
+{{Optimal ET sequence|legend=0| 111, 159, 270, 855, 966, 1125, 1236, 1506, 2901, 4137, 4407, 12951cef }}
+Badness (Sintel): 0.851
+[[Category:Landscape family| ]] <!-- main article -->
 [[Category:Temperament families]]
-[[Category:Landscape family| ]] <!-- main article -->
+[[Category:Catalogs of rank-3 temperaments]]
-[[Category:Rank 3]]

Landscape family: Difference between revisions

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