Maquila family: Difference between revisions
Switch to Sintel's badness, WE & CWE tunings |
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Comma list: 99/98, 176/175, 73728/73205 | Comma list: 99/98, 176/175, 73728/73205 | ||
{{Mapping|legend=0| 1 -6 5 -7 -1 | 0 17 -6 22 10 }} | |||
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Comma list: 99/98, 144/143, 176/175, 847/845 | Comma list: 99/98, 144/143, 176/175, 847/845 | ||
{{Mapping|legend=0| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 245/242, 385/384, 686/675 | Comma list: 245/242, 385/384, 686/675 | ||
{{Mapping|legend=0| 1 -6 5 -3 -1 | 0 17 -6 13 10 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 91/90, 169/168, 245/242, 385/384 | Comma list: 91/90, 169/168, 245/242, 385/384 | ||
{{Mapping|legend=0| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 540/539, 5632/5625, 12005/11979 | Comma list: 540/539, 5632/5625, 12005/11979 | ||
{{Mapping|legend=0| 1 -6 5 -5 -1 | 0 34 -12 35 20 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 364/363, 540/539, 676/675, 3584/3575 | Comma list: 364/363, 540/539, 676/675, 3584/3575 | ||
{{Mapping|legend=0| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }} | |||
Optimal tunings: | Optimal tunings: | ||
Latest 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 maquila family of temperaments tempers out the maquila comma (monzo: [49 -6 -17⟩, ratio: 562 949 953 421 312 / 556 182 861 328 125).
Maquila
Subgroup: 2.3.5
Comma list: [49 -6 -17⟩
Mapping: [⟨1 -6 5], ⟨0 17 -6]]
- mapping generators: ~2, ~512/375
- WE: ~2 = 1199.7466 ¢, ~512/375 = 535.3242 ¢
- error map: ⟨-0.253 +0.078 +0.474]
- CWE: ~2 = 1200.0000 ¢, ~512/375 = 535.4324 ¢
- error map: ⟨0.000 +0.396 +1.092]
Optimal ET sequence: 9, 47b, 56, 65, 186, 251, 316, 381, 697c
Badness (Sintel): 11.1
Septimal maquila
Subgroup: 2.3.5.7
Comma list: 225/224, 30233088/28824005
Mapping: [⟨1 -6 5 -7], ⟨0 17 -6 22]]
- WE: ~2 = 1199.3017 ¢, ~48/35 = 535.0104 ¢
- error map: ⟨-0.698 -2.589 +0.133 +6.290]
- CWE: ~2 = 1200.0000 ¢, ~48/35 = 535.3050 ¢
- error map: ⟨0.000 -1.770 +1.856 +7.884]
Optimal ET sequence: 9, 56d, 65d *
Badness (Sintel): 5.88
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 176/175, 73728/73205
Mapping: [⟨1 -6 5 -7 -1], ⟨0 17 -6 22 10]]
Optimal tunings:
- WE: ~2 = 1199.3341 ¢, ~15/11 = 535.0238 ¢
- CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.3050 ¢
Optimal ET sequence: 9, 56d, 65d *
* optimal patent val: 74
Badness (Sintel): 2.40
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 144/143, 176/175, 847/845
Mapping: [⟨1 -6 5 -7 -1 -7], ⟨0 17 -6 22 10 24]]
Optimal tunings:
- WE: ~2 = 1199.2163 ¢, ~15/11 = 534.9484 ¢
- CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.2780 ¢
Optimal ET sequence: 9, 56df, 65d, 139df *
* optimal patent val: 74
Badness (Sintel): 1.74
Maquiloid
Subgroup: 2.3.5.7
Comma list: 686/675, 65625/65536
Mapping: [⟨1 -6 5 -3], ⟨0 17 -6 13]]
- WE: ~2 = 1200.3854 ¢, ~175/128 = 535.6538 ¢
- error map: ⟨+0.385 +1.847 +1.691 -6.483]
- CWE: ~2 = 1200.0000 ¢, ~175/128 = 535.4907 ¢
- error map: ⟨0.000 +1.387 +0.742 -7.447]
Optimal ET sequence: 9, 47b, 56, 65, 121d
Badness (Sintel): 4.78
11-limit
Subgroup: 2.3.5.7.11
Comma list: 245/242, 385/384, 686/675
Mapping: [⟨1 -6 5 -3 -1], ⟨0 17 -6 13 10]]
Optimal tunings:
- WE: ~2 = 1200.0926 ¢, ~15/11 = 535.5265 ¢
- CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.4873 ¢
Optimal ET sequence: 9, 47b, 56, 65
Badness (Sintel): 2.19
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 169/168, 245/242, 385/384
Mapping: [⟨1 -6 5 -3 -1 -3], ⟨0 17 -6 13 10 15]]
Optimal tunings:
- WE: ~2 = 1200.3916 ¢, ~15/11 = 535.6758 ¢
- CWE: ~2 = 1200.0000 ¢, ~15/11 = 535.5109 ¢
Optimal ET sequence: 9, 47b, 56, 65f
Badness (Sintel): 1.73
Hemimaquila
Subgroup: 2.3.5.7
Comma list: 6144/6125, 184528125/184473632
Mapping: [⟨1 -6 5 -5], ⟨0 34 -12 35]]
- WE: ~2 = 1199.7108 ¢, ~7/6 = 267.6515 ¢
- error map: ⟨-0.289 -0.069 +0.422 +0.422]
- CWE: ~2 = 1200.0000 ¢, ~7/6 = 267.7125 ¢
- error map: ⟨0.000 +0.271 +1.136 +1.112]
Optimal ET sequence: 121, 130, 251, 381
Badness (Sintel): 2.82
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 5632/5625, 12005/11979
Mapping: [⟨1 -6 5 -5 -1], ⟨0 34 -12 35 20]]
Optimal tunings:
- WE: ~2 = 1199.5846 ¢, ~7/6 = 267.6248 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/6 = 267.7125 ¢
Optimal ET sequence: 121, 130, 251e, 381e
Badness (Sintel): 1.57
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 540/539, 676/675, 3584/3575
Mapping: [⟨1 -6 5 -5 -1 -5], ⟨0 34 -12 35 20 39]]
Optimal tunings:
- WE: ~2 = 1199.6184 ¢, ~7/6 = 267.6343 ¢
- CWE: ~2 = 1200.0000 ¢, ~7/6 = 267.7145 ¢
Optimal ET sequence: 121, 130, 251e, 381e
Badness (Sintel): 1.01