Maquila family: Difference between revisions

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{{Technical data page}}
{{Technical data page}}
The '''maquila family''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the [[maquila comma]], 562949953421312/556182861328125 = {{monzo| 49 -6 -17 }}.
The '''maquila family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[maquila comma]] ({{monzo|legend=1| 49 -6 -17 }}, [[ratio]]: 562 949 953 421 312 / 556 182 861 328 125).  


== Maquila ==
== Maquila ==
Line 9: Line 9:
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~512/375 = 535.437
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~512/375 = 535.437{{c}}


{{Optimal ET sequence|legend=1| 9, 38b, 47b, 56, 65, 186, 251, 316, 381, 697c }}
{{Optimal ET sequence|legend=1| 9, 38b, 47b, 56, 65, 186, 251, 316, 381, 697c }}


[[Badness]]: 0.472510
[[Badness]] (Smith): 0.472510


== Septimal maquila ==
== Septimal maquila ==
Line 22: Line 22:
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 535.322
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~48/35 = 535.322{{c}}


{{Optimal ET sequence|legend=1| 9, 56d, 65d }}
{{Optimal ET sequence|legend=1| 9, 56d, 65d }}


[[Badness]]: 0.232430
[[Badness]] (Smith): 0.232430


=== 11-limit ===
=== 11-limit ===
Line 35: Line 35:
Mapping: {{mapping| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}
Mapping: {{mapping| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.321
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.321{{c}}


{{Optimal ET sequence|legend=1| 9, 56d, 65d }}
{{Optimal ET sequence|legend=0| 9, 56d, 65d }}


Badness: 0.072550
Badness (Smith): 0.072550


=== 13-limit ===
=== 13-limit ===
Line 48: Line 48:
Mapping: {{mapping| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}
Mapping: {{mapping| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.298
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.298{{c}}


{{Optimal ET sequence|legend=1| 9, 56df, 65d, 139df, 204ddff }}
{{Optimal ET sequence|legend=0| 9, 56df, 65d, 139df, 204ddff }}


Badness: 0.042198
Badness (Smith): 0.042198


== Maquiloid ==
== Maquiloid ==
Line 61: Line 61:
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 535.482
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~175/128 = 535.482{{c}}


{{Optimal ET sequence|legend=1| 9, 38b, 47b, 56, 65, 121d, 186dd }}
{{Optimal ET sequence|legend=1| 9, 38b, 47b, 56, 65, 121d, 186dd }}


[[Badness]]: 0.188977
[[Badness]] (Smith): 0.188977


=== 11-limit ===
=== 11-limit ===
Line 74: Line 74:
Mapping: {{mapping| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}
Mapping: {{mapping| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.485
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.485{{c}}


{{Optimal ET sequence|legend=1| 9, 38be, 47b, 56, 65, 121d, 186dde }}
{{Optimal ET sequence|legend=0| 9, 38be, 47b, 56, 65, 121d, 186dde }}


Badness: 0.066234
Badness (Smith): 0.066234


=== 13-limit ===
=== 13-limit ===
Line 87: Line 87:
Mapping: {{mapping| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}
Mapping: {{mapping| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}


Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.501
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/11 = 535.501{{c}}


{{Optimal ET sequence|legend=1| 9, 38be, 47b, 56, 65f, 121df, 186ddeff }}
{{Optimal ET sequence|legend=0| 9, 38be, 47b, 56, 65f, 121df, 186ddeff }}


Badness: 0.041850
Badness (Smith): 0.041850


== Hemimaquila ==
== Hemimaquila ==
Line 100: Line 100:
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}


[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 267.716
[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/6 = 267.716{{c}}


{{Optimal ET sequence|legend=1| 9, 121, 130, 251, 381 }}
{{Optimal ET sequence|legend=1| 9, 121, 130, 251, 381 }}


[[Badness]]: 0.111465
[[Badness]] (Smith): 0.111465


=== 11-limit ===
=== 11-limit ===
Line 113: Line 113:
Mapping: {{mapping| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}
Mapping: {{mapping| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.717
Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/6 = 267.717{{c}}


{{Optimal ET sequence|legend=1| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=0| 9, 121, 130, 251e, 381e }}


Badness: 0.047440
Badness (Smith): 0.047440


=== 13-limit ===
=== 13-limit ===
Line 126: Line 126:
Mapping: {{mapping| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}
Mapping: {{mapping| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}


Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.719
Optimal tuning (POTE): ~2 = 1200.000, ~7/6 = 267.719{{c}}


{{Optimal ET sequence|legend=1| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=0| 9, 121, 130, 251e, 381e }}


Badness: 0.024445
Badness (Smith): 0.024445


[[Category:Maquila family| ]] <!-- main article -->
[[Category:Maquila family| ]] <!-- main article -->

Revision as of 08:42, 21 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]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~512/375 = 535.437 ¢

Optimal ET sequence: 9, 38b, 47b, 56, 65, 186, 251, 316, 381, 697c

Badness (Smith): 0.472510

Septimal maquila

Subgroup: 2.3.5.7

Comma list: 225/224, 30233088/28824005

Mapping: [⟨1 -6 5 -7], ⟨0 17 -6 22]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~48/35 = 535.322 ¢

Optimal ET sequence: 9, 56d, 65d

Badness (Smith): 0.232430

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 tuning (POTE): ~2 = 1200.000 ¢, ~15/11 = 535.321 ¢

Optimal ET sequence: 9, 56d, 65d

Badness (Smith): 0.072550

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 tuning (POTE): ~2 = 1200.000 ¢, ~15/11 = 535.298 ¢

Optimal ET sequence: 9, 56df, 65d, 139df, 204ddff

Badness (Smith): 0.042198

Maquiloid

Subgroup: 2.3.5.7

Comma list: 686/675, 65625/65536

Mapping: [⟨1 -6 5 -3], ⟨0 17 -6 13]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~175/128 = 535.482 ¢

Optimal ET sequence: 9, 38b, 47b, 56, 65, 121d, 186dd

Badness (Smith): 0.188977

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 tuning (POTE): ~2 = 1200.000 ¢, ~15/11 = 535.485 ¢

Optimal ET sequence: 9, 38be, 47b, 56, 65, 121d, 186dde

Badness (Smith): 0.066234

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 tuning (POTE): ~2 = 1200.000 ¢, ~15/11 = 535.501 ¢

Optimal ET sequence: 9, 38be, 47b, 56, 65f, 121df, 186ddeff

Badness (Smith): 0.041850

Hemimaquila

Subgroup: 2.3.5.7

Comma list: 6144/6125, 184528125/184473632

Mapping: [⟨1 -6 5 -5], ⟨0 34 -12 35]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 267.716 ¢

Optimal ET sequence: 9, 121, 130, 251, 381

Badness (Smith): 0.111465

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 tuning (POTE): ~2 = 1200.000 ¢, ~7/6 = 267.717 ¢

Optimal ET sequence: 9, 121, 130, 251e, 381e

Badness (Smith): 0.047440

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 tuning (POTE): ~2 = 1200.000, ~7/6 = 267.719 ¢

Optimal ET sequence: 9, 121, 130, 251e, 381e

Badness (Smith): 0.024445

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