Maquila family

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

Optimal tunings:

• 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]]

Optimal tunings:

• 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 *

* optimal patent val: 74

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]]

Optimal tunings:

• 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]]

Optimal tunings:

• 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