Landscape family: Difference between revisions
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Comma list: 364/363, 441/440, 625/624 | Comma list: 364/363, 441/440, 625/624 | ||
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Comma list: 676/675, 1001/1000, 3025/3024 | Comma list: 676/675, 1001/1000, 3025/3024 | ||
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Comma list: 6656/6655, 105644/105625, 123201/123200 | Comma list: 6656/6655, 105644/105625, 123201/123200 | ||
{{Mapping|legend=0| 3 0 -13 -22 10 -10 | 0 1 4 6 0 4 | 0 0 5 10 -2 11 }} | |||
Optimal tunings: | Optimal tunings: | ||
Revision as of 12:32, 24 September 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.
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 = 400.0012 ¢, ~3/2 = 701.9383 ¢, ~5/4 = 386.3350 ¢
- error map: ⟨+0.004 -0.013 +0.028 -0.021]
- CWE: ~63/50 = 400.0000 ¢, ~3/2 = 701.9387 ¢, ~5/4 = 386.3385 ¢
- error map: ⟨0.000 -0.016 +0.025 -0.026]
- [[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: 12, 27, 39d, 45, 57, 60, 72, 99, 171, 441, 612, 1236, 1407, 1578, 1848, 2019, 6498, 8346, 8517, 10536, 12555, 22920d
Badness (Sintel): 0.0940
Overview to extensions
Extensions of landscape include landy, odin, tyr and house, all considered below.
Landy
Named by Xenllium in 2026, 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]]
- WE: ~63/50 = 400.078 ¢, ~3/2 = 701.696 ¢, ~5/4 = 385.162 ¢
- error map: ⟨+0.234 -0.025 -0.684 -1.116 +1.632]
- CWE: ~63/50 = 400.000 ¢, ~3/2 = 701.709 ¢, ~5/4 = 385.341 ¢
- error map: ⟨0.000 -0.246 -0.972 -1.562 +1.287]
Optimal ET sequence: 12, 15, 27e, 45e, 57, 60e, 72, 159, 231, 330, 402d
Badness (Sintel): 0.792
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 625/624
Mapping: [⟨3 0 0 4 -1 -12], ⟨0 1 0 -2 -2 -1], ⟨0 0 1 2 3 4]]
Optimal tunings:
- WE: ~63/50 = 400.0548 ¢, ~3/2 = 701.8141 ¢, ~5/4 = 385.3981 ¢
- CWE: ~63/50 = 400.0000 ¢, ~3/2 = 701.7720 ¢, ~5/4 = 385.4420 ¢
Optimal ET sequence: 12f, 15, 27eff, 45efff, 57f, 60eff, 72, 87, 159, 243, 330
Badness (Sintel): 0.923
Odin
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 151263/151250
Mapping: [⟨6 0 0 8 17], ⟨0 1 0 -2 -4], ⟨0 0 1 2 3]]
- mapping generators: ~55/49, ~3, ~5
- WE: ~55/49 = 200.0008 ¢, ~3/2 = 701.9318 ¢, ~5/4 = 386.3342 ¢
- error map: ⟨+0.005 -0.018 +0.031 -0.004 -0.018]
- CWE: ~55/49 = 200.0000 ¢, ~3/2 = 701.9320 ¢, ~5/4 = 386.3393 ¢
- error map: ⟨0.000 -0.023 +0.026 -0.011 -0.028]
Optimal ET sequence: 12, 42, 48dee, 54c, 60e, 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 7464, 17118e, 18966e
Badness (Sintel): 0.140
Tyr
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 102487/102400
Mapping: [⟨3 0 0 4 8], ⟨0 2 0 -4 1], ⟨0 0 1 2 0]]
- mapping generators: ~63/50, ~400/231, ~5
- WE: ~63/50 = 400.0162 ¢, ~400/231 = 950.9828 ¢, ~5/4 = 386.2400 ¢
- error map: ⟨+0.049 +0.011 +0.024 -0.017 -0.205]
- CWE: ~63/50 = 400.0000 ¢, ~400/231 = 950.9591 ¢, ~5/4 = 386.2764 ¢
- error map: ⟨0.000 -0.037 -0.037 -0.109 -0.359]
Optimal ET sequence: 15, 24d, 33cd, 39d, 54c, 57, 72, 159, 183, 198, 255, 270, 342, 612, 954, 1566, 2091e, 2361e, 2433e, 2703e, 3045e, 3315ee, 3657ee
Badness (Sintel): 0.311
Borneo
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1001/1000, 3025/3024
Mapping: [⟨3 0 0 4 8 -3], ⟨0 2 0 -4 1 3], ⟨0 0 1 2 0 1]]
Optimal tunings:
- WE: ~63/50 = 400.0002 ¢, ~26/15 = 951.0850 ¢, ~5/4 = 386.5817 ¢
- CWE: ~63/50 = 400.0000 ¢, ~26/15 = 951.0846 ¢, ~5/4 = 386.5821 ¢
Optimal ET sequence: 15, 24d, 33cdff, 39df, 57f, 72, 111, 159, 183, 198, 270
Badness (Sintel): 0.514
Complexity spectrum: 12/11, 15/13, 11/8, 4/3, 11/10, 18/13, 6/5, 5/4, 13/12, 15/11, 11/9, 13/10, 10/9, 7/5, 16/15, 13/11, 9/8, 16/13, 8/7, 14/11, 15/14, 7/6, 14/13, 9/7
House
Named by Eliora in 2024, house tempers out the quartisma alongside the landscape comma.
Subgroup: 2.3.5.7.11
Comma list: 250047/250000, 117440512/117406179
Mapping: [⟨3 0 -13 -22 10], ⟨0 1 4 6 0], ⟨0 0 5 10 -2]]
- mapping generators: ~63/50, ~3, ~10240/9801
- WE: ~63/50 = 399.9958 ¢, ~3/2 = 701.9604 ¢, ~10240/9801 = 75.7013 ¢
- error map: ⟨-0.012 -0.007 +0.039 -0.034 +0.043]
- CWE: ~63/50 = 400.0000 ¢, ~3/2 = 701.9652 ¢, ~10240/9801 = 75.7024 ¢
- error map: ⟨0.000 +0.010 +0.059 -0.011 +0.087]
Optimal ET sequence: 111, 159, 270, 696, 966, 1236, 1506, 2631, 2901, 4137, 4407, 8544e, 12951ce, 14187cee
Badness (Sintel): 2.31
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 6656/6655, 105644/105625, 123201/123200
Mapping: [⟨3 0 -13 -22 10 -10], ⟨0 1 4 6 0 4], ⟨0 0 5 10 -2 11]]
Optimal tunings:
- WE: ~63/50 = 399.9957 ¢, ~3/2 = 701.9629 ¢, ~224/117 = 75.6993 ¢
- CWE: ~63/50 = 400.0000 ¢, ~3/2 = 701.9689 ¢, ~224/117 = 75.6997 ¢
Optimal ET sequence: 111, 159, 270, 855, 966, 1125, 1236, 1506, 2901, 4137, 4407, 12951cef
Badness (Sintel): 0.851