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.
-Discussed elsewhere are:
-* ''[[Odin]]'' (+9801/9800 or +151263/151250) → [[Kalismic temperaments #Odin|Kalismic temperaments]]
-* ''[[Tyr]]'' (+3025/3024 or +102487/102400) → [[Lehmerismic temperaments #Tyr|Lehmerismic temperaments]]
-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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 Badness (Sintel): 0.923
+== Odin ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 9801/9800, 151263/151250
+{{Mapping|legend=1| 6 0 0 8 17 | 0 1 0 -2 -4 | 0 0 1 2 3 }}
+: mapping generators: ~55/49, ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~55/49 = 200.0008{{c}}, ~3/2 = 701.9318{{c}}, ~5/4 = 386.3342{{c}}
+: [[error map]]: {{val| +0.005 -0.018 +0.031 -0.004 -0.018 }}
+* [[CWE]]: ~55/49 = 200.0000{{c}}, ~3/2 = 701.9320{{c}}, ~5/4 = 386.3393{{c}}
+: error map: {{val| 0.000 -0.023 +0.026 -0.011 -0.028 }}
+{{Optimal ET sequence|legend=1| 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e }}
+[[Badness]] (Sintel): 0.140
+== Tyr ==
+[[Subgroup]]: 2.3.5.7.11
+[[Comma list]]: 3025/3024, 102487/102400
+{{Mapping|legend=1| 3 0 0 4 8 | 0 2 0 -4 1 | 0 0 1 2 0 }}
+: mapping generators: ~63/50, ~400/231, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.0162{{c}}, ~400/231 = 950.9828{{c}}, ~5/4 = 386.2400{{c}}
+: [[error map]]: {{val| +0.049 +0.011 +0.024 -0.017 -0.205 }}
+* [[CWE]]: ~63/50 = 400.0000{{c}}, ~400/231 = 950.9591{{c}}, ~5/4 = 386.2764{{c}}
+: error map: {{val| 0.000 -0.037 -0.037 -0.109 -0.359 }}
+{{Optimal ET sequence|legend=1| 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee }}
+[[Badness]] (Sintel): 0.311
+=== Borneo ===
+Subgroup: 2.3.5.7.11.13
+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 }}
+Optimal tunings:
+* WE: ~63/50 = 400.0002{{c}}, ~26/15 = 951.0850{{c}}, ~5/4 = 386.5817{{c}}
+* CWE: ~63/50 = 400.0000{{c}}, ~26/15 = 951.0846{{c}}, ~5/4 = 386.5821{{c}}
+{{Optimal ET sequence|legend=0| 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270 }}
+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: {{mapping| 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:Temperament families]]
 [[Category:Landscape family| ]] <!-- main article -->
 [[Category:Rank 3]]