Landscape family: Difference between revisions

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__FORCETOC__

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

The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.

== Landscape ==

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* [[7-odd-limit]]

: {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9

: [[Eigenmonzo basis|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.7/3

: [[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|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.9/7

: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

{{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 }}

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House tempers out the [[quartisma]] alongside the landscape comma.

Subgroup: 2.3.5.7.11

[[Subgroup]]: 2.3.5.7.11

Comma list: 250047/250000, ~~2517630976~~/~~2516421875~~

[[Comma list]]: 250047/250000, 117440512/117406179

: mapping generators: ~63/50 = 1\3, ~3, ~9801/5120

: mapping generators: ~63/50, ~3, ~9801/5120

[[Optimal tuning]] ([[CTE]]) ~63/50 = 1\3, ~3/2 = 701.9592, ~9801/5120 = 1124.2969

{{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}

[[Badness]]: 1.92 × 10<sup>-3</sup>

~~[[Support]]ing [[ET]]s: {{EDOs|45, 111, 159, 270, 381, 429, 537, 966, 1236, 1506, 1395, 1665, 1776, 2901}}~~

== Odin ==

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[[Category:Temperament families]]

[[Category:Pages with mostly numerical content]]

[[Category:Landscape family| ]]

[[Category:Landscape| ]]

[[Category:Rank 3]]

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+{{Technical data page}}
 __FORCETOC__
-The '''landscape family''' of rank-3 temperaments tempers out the [[landscape comma]], 250047/250000.
+The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000.
 == Landscape  ==
@@ Line 15: / Line 16: @@
 * [[7-odd-limit]]
 : {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9
-: [[Eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5.7/3
+: [[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|eigenmonzo (unchanged-interval) basis]]: 2.5.9/7
+:  [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7
 {{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 }}
@@ Line 26: / Line 27: @@
 House tempers out the [[quartisma]] alongside the landscape comma.
-Subgroup: 2.3.5.7.11
+[[Subgroup]]: 2.3.5.7.11
-Comma list: 250047/250000, 2517630976/2516421875
+[[Comma list]]: 250047/250000, 117440512/117406179
 {{Mapping|legend=1| 3 0 2 8 16 | 0 1 4 6 0 | 0 0 -5 -10 2 }}
-: mapping generators: ~63/50 = 1\3, ~3, ~9801/5120
+: mapping generators: ~63/50, ~3, ~9801/5120
+[[Optimal tuning]] ([[CTE]]) ~63/50 = 1\3, ~3/2 = 701.9592, ~9801/5120 = 1124.2969
+{{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }}
+[[Badness]]: 1.92 × 10<sup>-3</sup>
-[[Support]]ing [[ET]]s: {{EDOs|45, 111, 159, 270, 381, 429, 537, 966, 1236, 1506, 1395, 1665, 1776, 2901}}
 == Odin  ==
 {{See also| Kalismic temperaments #Odin }}
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 [[Category:Temperament families]]
+[[Category:Pages with mostly numerical content]]
 [[Category:Landscape family| ]] <!-- main article -->
 [[Category:Landscape| ]] <!-- key article -->
 [[Category:Rank 3]]