Landscape family: Difference between revisions
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{{Technical data page}} | {{Technical data page}} | ||
The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000. | The '''landscape family''' of [[rank-3 temperament]]s tempers out the [[landscape comma]], 250047/250000. | ||
Considered below is house, besides the 7-limit temperament. Discussed elsewhere are [[Kalismic temperaments #Odin|odin]] and [[Lehmerismic temperaments #Tyr|tyr]]. | |||
== Landscape == | == Landscape == | ||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
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: mapping generators: ~63/50, ~3, ~5 | : mapping generators: ~63/50, ~3, ~5 | ||
[[Optimal tuning]]s: | |||
* [[WE]]: ~63/50 = 400.001{{c}}, ~3/2 = 701.938{{c}}, ~5/4 = 386.335{{c}} | |||
* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.939{{c}}, ~5/4 = 386.339{{c}} | |||
[[Minimax tuning]]: | [[Minimax tuning]]: | ||
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{{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]] (Sintel): 0.094<!-- 0.02130 × 10<sup>-3</sup> by Smith's --> | ||
== House == | == House == | ||
House tempers out the [[quartisma]] alongside the landscape comma. | House tempers out the [[quartisma]] alongside the landscape comma. | ||
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: mapping generators: ~63/50, ~3, ~9801/5120 | : mapping generators: ~63/50, ~3, ~9801/5120 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~63/50 = 399.996{{c}}, ~3/2 = 701.960{{c}}, ~9801/5120 = 1124.286{{c}} | |||
* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.965{{c}}, ~9801/5120 = 1124.298{{c}} | |||
{{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }} | {{Optimal ET sequence|legend=1| 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee }} | ||
[[Badness]]: | [[Badness]] (Sintel): 2.305 | ||
[[Category:Temperament families]] | [[Category:Temperament families]] | ||
Revision as of 04:27, 21 February 2026
- 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.
Considered below is house, besides the 7-limit temperament. Discussed elsewhere are odin and tyr.
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
- WE: ~63/50 = 400.001 ¢, ~3/2 = 701.938 ¢, ~5/4 = 386.335 ¢
- CWE: ~63/50 = 400.000 ¢, ~3/2 = 701.939 ¢, ~5/4 = 386.339 ¢
- [[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 (Sintel): 0.094
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
- WE: ~63/50 = 399.996 ¢, ~3/2 = 701.960 ¢, ~9801/5120 = 1124.286 ¢
- CWE: ~63/50 = 400.000 ¢, ~3/2 = 701.965 ¢, ~9801/5120 = 1124.298 ¢
Optimal ET sequence: 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee
Badness (Sintel): 2.305