Landscape family: Difference between revisions
No edit summary Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 3: | Line 3: | ||
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. | ||
Discussed elsewhere are: | |||
* ''[[Odin]]'' (+9801/9800 or +151263/151250) → [[Kalismic temperaments #Odin|Kalismic temperaments]] | |||
* ''[[Tyr]]'' (+3025/3024 or +102487/102400) → [[Lehmerismic temperaments #Tyr|Lehmerismic temperaments]] | |||
== Landscape | Considered below are landy and house, besides the 7-limit temperament. | ||
== Landscape == | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||
| Line 29: | Line 33: | ||
[[Badness]] (Sintel): 0.094<!-- 0.02130 × 10<sup>-3</sup> by Smith's --> | [[Badness]] (Sintel): 0.094<!-- 0.02130 × 10<sup>-3</sup> by Smith's --> | ||
== Landy == | |||
Landy tempers out the [[441/440|werckisma]] and [[4375/4356|fantaresma]], alongside the landscape comma. | |||
[[Subgroup]]: 2.3.5.7.11 | |||
[[Comma list]]: 441/440, 4375/4356 | |||
{{Mapping|legend=1| 3 0 0 4 -1 | 0 1 0 -2 -2 | 0 0 1 2 3 }} | |||
: mapping generators: ~63/50, ~3, ~5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~63/50 = 400.078{{c}}, ~3/2 = 701.696{{c}}, ~5/4 = 385.162{{c}} | |||
* [[CWE]]: ~63/50 = 400.000{{c}}, ~3/2 = 701.709{{c}}, ~5/4 = 385.341{{c}} | |||
{{Optimal ET sequence|legend=1| 12, 15, 27e, 45e, 57, 60e, 72, 159 }} | |||
[[Badness]] (Sintel): 0.792 | |||
== House == | == House == | ||
Revision as of 04:49, 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.
Discussed elsewhere are:
- Odin (+9801/9800 or +151263/151250) → Kalismic temperaments
- Tyr (+3025/3024 or +102487/102400) → Lehmerismic temperaments
Considered below are landy and house, besides the 7-limit temperament.
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
Landy
Landy tempers out the werckisma and fantaresma, alongside the landscape comma.
Subgroup: 2.3.5.7.11
Comma list: 441/440, 4375/4356
Mapping: [⟨3 0 0 4 -1], ⟨0 1 0 -2 -2], ⟨0 0 1 2 3]]
- mapping generators: ~63/50, ~3, ~5
- WE: ~63/50 = 400.078 ¢, ~3/2 = 701.696 ¢, ~5/4 = 385.162 ¢
- CWE: ~63/50 = 400.000 ¢, ~3/2 = 701.709 ¢, ~5/4 = 385.341 ¢
Optimal ET sequence: 12, 15, 27e, 45e, 57, 60e, 72, 159
Badness (Sintel): 0.792
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