Escapade family: Difference between revisions

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Move alphaquarter here as a strong extension; also move arch here as its 5-limit part seems simpler
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The '''escapade family''' tempers out the [[escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s.
The '''escapade family''' tempers out the [[escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s.
Extensions of escapade include (septimal) escapade, alphaquarter, escaped, septisuperfourth (aka biscapade) and arch, all considered below.


== Escapade ==
== Escapade ==
Line 13: Line 15:


[[Badness]]: 0.083778
[[Badness]]: 0.083778
=== Extensions ===
Extensions of escapade include (septimal) escapade, escaped and biscapade (septisuperfourth), considered below, as well as these temperaments discussed elsewhere:
* ''[[Arch]]'', {3136/3125, 5250987/5242880} → [[Hemimean clan #Arch]]
* ''[[Alphaquarter]]'', {5120/5103, 29360128/29296875} → [[Hemifamity temperaments #Alphaquarter]]


== Septimal escapade ==
== Septimal escapade ==
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Badness: 0.035261
Badness: 0.035261
== Alphaquarter ==
Subgroup: 2.3.5.7
[[Comma list]]: 5120/5103, 29360128/29296875
[[Mapping]]: [{{val| 1 2 2 0 }}, {{val| 0 -9 7 61 }}]
{{Multival|legend=1| 9 -7 -61 -32 -122 -122 }}
[[POTE generator]]: ~16128/15625 = 55.243
{{Val list|legend=1| 87, 152, 239, 391 }}
[[Badness]]: 0.116594
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 5120/5103
Mapping: [{{val| 1 2 2 0 3 }}, {{val| 0 -9 7 61 10 }}]
POTE generator: ~33/32 = 55.243
Vals: {{Val list| 87, 152, 239, 391 }}
Badness: 0.029638


== Escaped ==
== Escaped ==
{{See also|Sensamagic clan #Escaped}}
{{See also| Sensamagic clan #Escaped }}


This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with 19e&27 temperament (sensi extension).''
This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. ''Not to be confused with 19e&27 temperament (sensi extension).''
Line 160: Line 185:


Badness: 0.033038
Badness: 0.033038
== Arch ==
Subgroup: 2.3.5.7
[[Comma list]]: 3136/3125, 5250987/5242880
[[Mapping]]: [{{val| 1 2 2 2 }}, {{val| 0 -18 14 35 }}]
{{Multival|legend=1| 18 -14 -35 -64 -106 -42 }}
[[POTE generator]]: ~64/63 = 27.668
{{Val list|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}
[[Badness]]: 0.094345
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3136/3125, 4000/3993
Mapping: [{{val| 1 2 2 2 3 }}, {{val| 0 -18 14 35 20 }}]
POTE generator: ~64/63 = 27.663
Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 911cde }}
Badness: 0.036541
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 364/363, 441/440, 676/675, 3136/3125
Mapping: [{{val| 1 2 2 2 3 4 }}, {{val| 0 -18 14 35 20 -13 }}]
POTE generator: ~64/63 = 27.660
Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 564e }}
Badness: 0.019504


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]

Revision as of 21:42, 1 January 2022

The escapade family tempers out the escapade comma, [32 -7 -9⟩, of size 9.492 cents.

Extensions of escapade include (septimal) escapade, alphaquarter, escaped, septisuperfourth (aka biscapade) and arch, all considered below.

Escapade

Subgroup: 2.3.5

Comma list: 4294967296/4271484375

Mapping: [⟨1 2 2], ⟨0 -9 7]]

POTE generator: ~16875/16384 = 55.293

Template:Val list

Badness: 0.083778

Septimal escapade

Subgroup: 2.3.5.7

Comma list: 225/224, 12288/12005

Mapping: [⟨1 2 2 3], ⟨0 -9 7 -4]]

⟨⟨9 -7 4 -32 -19 29]]

POTE generator: ~49/48 = 55.327

Template:Val list

Badness: 0.077950

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 2560/2541

Mapping: [⟨1 2 2 3 3], ⟨0 -9 7 -4 10]]

POTE generator: ~33/32 = 55.354

Optimal GPV sequence: Template:Val list

Badness: 0.036700

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 99/98, 176/175, 507/500

Mapping: [⟨1 2 2 3 3 3], ⟨0 -9 7 -4 10 15]]

POTE generator: ~26/25 = 55.550

Optimal GPV sequence: Template:Val list

Badness: 0.035261

Alphaquarter

Subgroup: 2.3.5.7

Comma list: 5120/5103, 29360128/29296875

Mapping: [⟨1 2 2 0], ⟨0 -9 7 61]]

⟨⟨9 -7 -61 -32 -122 -122]]

POTE generator: ~16128/15625 = 55.243

Template:Val list

Badness: 0.116594

11-limit

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 4000/3993, 5120/5103

Mapping: [⟨1 2 2 0 3], ⟨0 -9 7 61 10]]

POTE generator: ~33/32 = 55.243

Vals: Template:Val list

Badness: 0.029638

Escaped

See also: Sensamagic clan § Escaped

This temperament is also called as "sensa" because it tempers out 245/243, 352/351, and 385/384 as a sensamagic temperament. Not to be confused with 19e&27 temperament (sensi extension).

Subgroup: 2.3.5.7

Comma list: 245/243, 65625/65536

Mapping: [⟨1 2 2 4], ⟨0 -9 7 -26]]

⟨⟨9 -7 26 -32 16 80]]

POTE generator: ~28/27 = 55.122

Template:Val list

Badness: 0.088746

11-limit

Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 4000/3993

Mapping: [⟨1 2 2 4 3], ⟨0 -9 7 -26 10]]

POTE generator: ~28/27 = 55.126

Optimal GPV sequence: Template:Val list

Badness: 0.035844

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 245/243, 352/351, 385/384, 625/624

Mapping: [⟨1 2 2 4 3 2], ⟨0 -9 7 -26 10 37]]

POTE generator: ~28/27 = 55.138

Optimal GPV sequence: Template:Val list

Badness: 0.031366

Septisuperfourth

Subgroup: 2.3.5.7

Comma list: 6144/6125, 118098/117649

Mapping: [⟨2 4 4 7], ⟨0 -9 7 -15]]

⟨⟨18 -14 30 -64 -3 109]]

POTE generator: ~16875/16384 = 55.320

Template:Val list

Badness: 0.059241

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 5632/5625

Mapping: [⟨2 4 4 7 6], ⟨0 -9 7 -15 10]]

POTE generator: ~33/32 = 55.304

Optimal GPV sequence: Template:Val list

Badness: 0.024619

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 3584/3575

Mapping: [⟨2 4 4 7 6 11], ⟨0 -9 7 -15 10 -39]]

POTE generator: ~33/32 = 55.325

Optimal GPV sequence: Template:Val list

Badness: 0.022887

Septisuperquad

This temperament is also called as "biscapade".

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 540/539, 4096/4095

Mapping: [⟨2 4 4 7 6 5], ⟨0 -9 7 -15 10 26]]

POTE generator: ~33/32 = 55.359

Optimal GPV sequence: Template:Val list

Badness: 0.033038

Arch

Subgroup: 2.3.5.7

Comma list: 3136/3125, 5250987/5242880

Mapping: [⟨1 2 2 2], ⟨0 -18 14 35]]

⟨⟨18 -14 -35 -64 -106 -42]]

POTE generator: ~64/63 = 27.668

Template:Val list

Badness: 0.094345

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 3136/3125, 4000/3993

Mapping: [⟨1 2 2 2 3], ⟨0 -18 14 35 20]]

POTE generator: ~64/63 = 27.663

Optimal GPV sequence: Template:Val list

Badness: 0.036541

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 364/363, 441/440, 676/675, 3136/3125

Mapping: [⟨1 2 2 2 3 4], ⟨0 -18 14 35 20 -13]]

POTE generator: ~64/63 = 27.660

Optimal GPV sequence: Template:Val list

Badness: 0.019504

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