Maquila family: Difference between revisions

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The maquila family tempers out the [[maquila comma]], 562949953421312/556182861328125 = {{monzo|49 -6 -17}}.
{{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 }}.


== Maquila ==
== Maquila ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


[[Comma]]: 562949953421312/556182861328125
[[Comma list]]: {{monzo| 49 -6 -17 }}


[[Mapping]]: [{{val|1 -6 5}}, {{val|0 17 -6}}]
{{Mapping|legend=1| 1 -6 5 | 0 17 -6 }}


[[POTE generator]]: ~512/375 = 535.437
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~512/375 = 535.437


{{Val list|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]]: 0.472510


=== 7-limit ===
== Septimal maquila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 225/224, 30233088/28824005
[[Comma list]]: 225/224, 30233088/28824005


[[Mapping]]: [{{val|1 -6 5 -7}}, {{val|0 17 -6 22}}]
{{Mapping|legend=1| 1 -6 5 -7 | 0 17 -6 22 }}


{{Multival|legend=1|17 -6 22 -49 -13 68}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~48/35 = 535.322


[[POTE generator]]: ~48/35 = 535.322
{{Optimal ET sequence|legend=1| 9, 56d, 65d }}
 
{{Val list|legend=1| 9, 56d, 65d }}


[[Badness]]: 0.232430
[[Badness]]: 0.232430
Line 34: Line 33:
Comma list: 99/98, 176/175, 73728/73205
Comma list: 99/98, 176/175, 73728/73205


Mapping: [{{val|1 -6 5 -7 -1}}, {{val|0 17 -6 22 10}}]
Mapping: {{mapping| 1 -6 5 -7 -1 | 0 17 -6 22 10 }}


POTE generator: ~15/11 = 535.321
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.321


Optimal GPV sequence: {{Val list| 9, 56d, 65d }}
{{Optimal ET sequence|legend=1| 9, 56d, 65d }}


Badness: 0.072550
Badness: 0.072550
Line 47: Line 46:
Comma list: 99/98, 144/143, 176/175, 847/845
Comma list: 99/98, 144/143, 176/175, 847/845


Mapping: [{{val|1 -6 5 -7 -1 -7}}, {{val|0 17 -6 22 10 24}}]
Mapping: {{mapping| 1 -6 5 -7 -1 -7 | 0 17 -6 22 10 24 }}


POTE generator: ~15/11 = 535.298
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.298


Optimal GPV sequence: {{Val list| 9, 56df, 65d, 139df, 204ddff }}
{{Optimal ET sequence|legend=1| 9, 56df, 65d, 139df, 204ddff }}


Badness: 0.042198
Badness: 0.042198


== Maquiloid ==
== Maquiloid ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 686/675, 65625/65536
[[Comma list]]: 686/675, 65625/65536


[[Mapping]]: [{{val|1 -6 5 -3}}, {{val|0 17 -6 13}}]
{{Mapping|legend=1| 1 -6 5 -3 | 0 17 -6 13 }}


{{Multival|legend=1|17 -6 13 -49 -27 47}}
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~175/128 = 535.482


[[POTE generator]]: ~175/128 = 535.482
{{Optimal ET sequence|legend=1| 9, 38b, 47b, 56, 65, 121d, 186dd }}
 
{{Val list|legend=1| 9, 38b, 47b, 56, 65, 121d, 186dd }}


[[Badness]]: 0.188977
[[Badness]]: 0.188977
Line 75: Line 72:
Comma list: 245/242, 385/384, 686/675
Comma list: 245/242, 385/384, 686/675


Mapping: [{{val|1 -6 5 -3 -1}}, {{val|0 17 -6 13 10}}]
Mapping: {{mapping| 1 -6 5 -3 -1 | 0 17 -6 13 10 }}


POTE generator: ~15/11 = 535.485
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.485


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


Badness: 0.066234
Badness: 0.066234
Line 88: Line 85:
Comma list: 91/90, 169/168, 245/242, 385/384
Comma list: 91/90, 169/168, 245/242, 385/384


Mapping: [{{val|1 -6 5 -3 -1 -3}}, {{val|0 17 -6 13 10 15}}]
Mapping: {{mapping| 1 -6 5 -3 -1 -3 | 0 17 -6 13 10 15 }}


POTE generator: ~15/11 = 535.501
Optimal tuning (POTE): ~2 = 1\1, ~15/11 = 535.501


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


Badness: 0.041850
Badness: 0.041850


== Hemimaquila ==
== Hemimaquila ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 184528125/184473632
[[Comma list]]: 6144/6125, 184528125/184473632


[[Mapping]]: [{{val|1 -6 5 -5}}, {{val|0 34 -12 35}}]
{{Mapping|legend=1| 1 -6 5 -5 | 0 34 -12 35 }}
 
{{Multival|legend=1|34 -12 35 -98 -40 115}}


[[POTE generator]]: ~7/6 = 267.716
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/6 = 267.716


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


[[Badness]]: 0.111465
[[Badness]]: 0.111465
Line 116: Line 111:
Comma list: 540/539, 5632/5625, 12005/11979
Comma list: 540/539, 5632/5625, 12005/11979


Mapping: [{{val|1 -6 5 -5 -1}}, {{val|0 34 -12 35 20}}]
Mapping: {{mapping| 1 -6 5 -5 -1 | 0 34 -12 35 20 }}


POTE generator: ~7/6 = 267.717
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.717


Optimal GPV sequence: {{Val list| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=1| 9, 121, 130, 251e, 381e }}


Badness: 0.047440
Badness: 0.047440
Line 129: Line 124:
Comma list: 364/363, 540/539, 676/675, 3584/3575
Comma list: 364/363, 540/539, 676/675, 3584/3575


Mapping: [{{val|1 -6 5 -5 -1 -5}}, {{val|0 34 -12 35 20 39}}]
Mapping: {{mapping| 1 -6 5 -5 -1 -5 | 0 34 -12 35 20 39 }}


POTE generator: ~7/6 = 267.719
Optimal tuning (POTE): ~2 = 1\1, ~7/6 = 267.719


Optimal GPV sequence: {{Val list| 9, 121, 130, 251e, 381e }}
{{Optimal ET sequence|legend=1| 9, 121, 130, 251e, 381e }}


Badness: 0.024445
Badness: 0.024445


[[Category:Theory]]
[[Category:Temperament families]]
[[Category:Temperament families]]
[[Category:Maquila]]
[[Category:Pages with mostly numerical content]]
[[Category:Maquila family| ]] <!-- main article -->
[[Category:Maquila| ]] <!-- key article -->
[[Category:Rank 2]]
[[Category:Rank 2]]

Latest revision as of 00:34, 24 June 2025

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 rank-2 temperaments tempers out the maquila comma, 562949953421312/556182861328125 = [49 -6 -17⟩.

Maquila

Subgroup: 2.3.5

Comma list: [49 -6 -17⟩

Mapping: [⟨1 -6 5], ⟨0 17 -6]]

Optimal tuning (POTE): ~2 = 1\1, ~512/375 = 535.437

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

Badness: 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 = 1\1, ~48/35 = 535.322

Optimal ET sequence: 9, 56d, 65d

Badness: 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 = 1\1, ~15/11 = 535.321

Optimal ET sequence: 9, 56d, 65d

Badness: 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 = 1\1, ~15/11 = 535.298

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

Badness: 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 = 1\1, ~175/128 = 535.482

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

Badness: 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 = 1\1, ~15/11 = 535.485

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

Badness: 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 = 1\1, ~15/11 = 535.501

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

Badness: 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 = 1\1, ~7/6 = 267.716

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

Badness: 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 = 1\1, ~7/6 = 267.717

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

Badness: 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 = 1\1, ~7/6 = 267.719

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

Badness: 0.024445

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