Landscape family: Difference between revisions
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{{Technical data page}} | |||
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The '''landscape family''' of rank-3 | The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000. | ||
== Landscape == | == Landscape == | ||
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* [[7-odd-limit]] | * [[7-odd-limit]] | ||
: {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9 | : {{monzo list| 9 0 0 0 | 4 3 6 -3 | 0 0 9 0 | 4 -6 6 6 }}/9 | ||
: [[Eigenmonzo basis| | : [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3 | ||
* [[9-odd-limit]] | * [[9-odd-limit]] | ||
: {{monzo list| 12 0 0 0 | 4 6 6 -3 | 0 0 12 0 | 8 -12 12 6 }}/12 | : {{monzo list| 12 0 0 0 | 4 6 6 -3 | 0 0 12 0 | 8 -12 12 6 }}/12 | ||
: [[Eigenmonzo basis| | : [[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 }} | {{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 }} | ||
[[Badness]]: 0.02130 × 10<sup>-3</sup> | [[Badness]]: 0.02130 × 10<sup>-3</sup> | ||
== House == | |||
House tempers out the [[quartisma]] alongside the landscape comma. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[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, ~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> | |||
== Odin == | == Odin == | ||
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[[Category:Temperament families]] | [[Category:Temperament families]] | ||
[[Category:Pages with mostly numerical content]] | |||
[[Category:Landscape family| ]] <!-- main article --> | [[Category:Landscape family| ]] <!-- main article --> | ||
[[Category:Landscape| ]] <!-- key article --> | [[Category:Landscape| ]] <!-- key article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
Latest revision as of 00:37, 24 June 2025
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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
- unchanged-interval (eigenmonzo) basis: 2.5.7/3
- [[12 0 0 0⟩, [4 6 6 -3⟩, [0 0 12 0⟩, [8 -12 12 6⟩]/12
- unchanged-interval (eigenmonzo) basis: 2.5.9/7
Optimal ET sequence: 3, 12, 27, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555
Badness: 0.02130 × 10-3
House
House tempers out the quartisma alongside the landscape comma.
Subgroup: 2.3.5.7.11
Comma list: 250047/250000, 117440512/117406179
Mapping: [⟨3 0 2 8 16], ⟨0 1 4 6 0], ⟨0 0 -5 -10 2]]
- 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: 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee
Badness: 1.92 × 10-3