Revision as of 07:08, 24 May 2021

The landscape family of rank-3 temperaments tempers out the landscape comma, 250047/250000.

Landscape

Subgroup: 2.3.5.7

Comma list: 250047/250000

Mapping: [<3 0 0 4|, <0 1 0 -2|, <0 0 1 2|]

Mapping generators: ~63/50, ~3, ~5

[[9 0 0 0⟩, [4 3 6 -3⟩, [0 0 9 0⟩, [4 -6 6 6⟩]/9

Eigenmonzos: 7/6, 5/4

[[12 0 0 0⟩, [4 6 6 -3⟩, [0 0 12 0⟩, [8 -12 12 6⟩]/12

Eigenmonzos: 5/4, 9/7

Badness: 0.02130 × 10^-3

See also: Kalismic temperaments § Odin

See also: Lehmerismic temperaments § Tyr

@@ Line 1: / Line 1: @@
 __FORCETOC__
-The '''landscape family''' of rank three temperaments tempers out the [[landscape comma]], 250047/250000.
+The '''landscape family''' of rank-3 temperaments tempers out the [[landscape comma]], 250047/250000.
 = 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]]: [&lt;3 0 0 4|, &lt;0 1 0 -2|, &lt;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]]
-Eigenmonzos: 5/4, 9/7
+: [{{monzo| 9 0 0 0 }}, {{monzo| 4 3 6 -3 }}, {{monzo| 0 0 9 0 }}, {{monzo| 4 -6 6 6 }}]/9
+: Eigenmonzos: 7/6, 5/4
-Map: [&lt;3 0 0 4|, &lt;0 1 0 -2|, &lt;0 0 1 2|]
+* [[9-odd-limit]]
+: [{{monzo| 12 0 0 0 }}, {{monzo| 4 6 6 -3 }}, {{monzo| 0 0 12 0 }}, {{monzo| 8 -12 12 6 }}]/12
-Generators: 63/50, 3, 5
+: Eigenmonzos: 5/4, 9/7
 {{EDOs|legend=1| 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555 }}
-<sup>5</sup> × badness: 2.130
+[[Badness]]: 0.02130 × 10<sup>-3</sup>
 = Odin =
@@ Line 31: / Line 30: @@
 {{see also| Lehmerismic temperaments #Tyr }}
-[[Category:Theory]]
+[[Category:Regular temperament theory]]
 [[Category:Temperament family]]
 [[Category:Landscape]]
 [[Category:Rank 3]]