Landscape family: Difference between revisions

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+{{Technical data page}}
 __FORCETOC__
-The landscape family of rank three temperaments tempers out the landscape comma, 250047/250000.
+The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.
-=Landscape=
+== Landscape  ==
-Comma: 250047/250000
--limit minimax tuning
+[[Subgroup]]: 2.3.5.7
-[|9 0 0 0&gt;, |4 3 6 -3&gt;, |0 0 9 0&gt;, |4 -6 6 6&gt;]/9
+[[Comma list]]: 250047/250000
-Eigenmonzos: 7/6, 5/4
+{{Mapping|legend=1| 3 0 0 4 | 0 1 0 -2 | 0 0 1 2 }}
--limit minimax tuning
+: mapping generators: ~63/50, ~3, ~5
-[|12 0 0 0&gt;, |4 6 6 -3&gt;, |0 0 12 0&gt;, |8 -12 12 6&gt;]/12
+[[Minimax tuning]]:
+* [[7-odd-limit]]
+: {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
+* [[9-odd-limit]]
+: {{monzo list| 12 0 0 0 | 4 6 6 -3 | 0 0 12 0 | 8 -12 12 6 }}/12
+:  [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7
-Eigenmonzos: 5/4, 9/7
+{{Optimal ET sequence|legend=1| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}
-Map: [&lt;3 0 0 4|, &lt;0 1 0 -2|, &lt;0 0 1 2|]
+[[Badness]]: 0.02130 × 10<sup>-3</sup>
+== House ==
+House tempers out the [[quartisma]] alongside the landscape comma.
-Generators: 63/50, 3, 5
+[[Subgroup]]: 2.3.5.7.11
-EDOs: 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555
+[[Comma list]]: 250047/250000, 117440512/117406179
-^5*Badness: 2.130
+{{Mapping|legend=1| 3 0 2 8 16 | 0 1 4 6 0 | 0 0 -5 -10 2 }}
-=[[Kalismic_temperaments#Odin|Odin]]=
+: mapping generators: ~63/50, ~3, ~9801/5120
-=[[Lehmerismic_temperaments#Tyr|Tyr]]=
+[[Optimal tuning]] ([[CTE]]) ~63/50 = 1\3, ~3/2 = 701.9592, ~9801/5120 = 1124.2969
-[[Category:family]]
-[[Category:landscape]]
+{{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}
-[[Category:temperament_family]]
+[[Badness]]: 1.92 × 10<sup>-3</sup>
+== Odin  ==
+{{See also| Kalismic temperaments #Odin }}
+== Tyr  ==
+{{See also| Lehmerismic temperaments #Tyr }}
+[[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Landscape family| ]] <!-- main article -->
+[[Category:Landscape| ]] <!-- key article -->
+[[Category:Rank 3]]