Escapade family: Difference between revisions

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The '''escapade family''' tempers out the [[escapade_comma|escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s. It includes the [[Hemifamity temperaments|alphaquarter temperament]] and the [[Hemimean clan|arch temperament]].
The '''escapade family''' tempers out the [[escapade_comma|escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s. It includes the [[Hemifamity temperaments|alphaquarter temperament]] and the [[Hemimean clan|arch temperament]].


== Escapade ==
== Escapade ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Comma: 4294967296/4271484375
[[Comma]]: 4294967296/4271484375


Mapping: [<1 2 2|, <0 -9 7|]
[[Mapping]]: [{{Val|1 2 2}}, {{Val|0 -9 7}}]


[[POTE generator]]: ~16875/16384 = 55.293
[[POTE generator]]: ~16875/16384 = 55.293


EDOs: [[21edo|21]], [[22edo|22]], [[43edo|43]], [[65edo|65]], 152, 217, 586, 803
{{Val list|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}


Badness: 0.083778
Badness: 0.083778


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 225/224, 12288/12005
[[Comma list]]: 225/224, 12288/12005


Mapping: [<1 2 2 3|, <0 -9 7 -4|]
[[Mapping]]: [{{val|1 2 2 3}}, {{val|0 -9 7 -4}}]


Wedgie: <<9 -7 4 -32 -19 29||
{{Multival|legend=1|9 -7 4 -32 -19 29}}


POTE generator: ~49/48 = 55.327
[[POTE generator]]: ~49/48 = 55.327


Vals: 21, 22, 43, 65d
{{Val list|legend=1| 21, 22, 43, 65d }}


Badness: 0.077950
[[Badness]]: 0.077950


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


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


Mapping: [<1 2 2 3 3|, <0 -9 7 -4 10|]
Mapping: [{{val|1 2 2 3 3}}, {{val|0 -9 7 -4 10}}]


POTE generator: ~49/48 = 55.354
POTE generator: ~49/48 = 55.354


Vals: 21, 22, 43, 65d
Vals: {{Val list| 21, 22, 43, 65d }}


Badness: 0.036700
Badness: 0.036700


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


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


Mapping: [<1 2 2 3 3 3|, <0 -9 7 -4 10 15|]
Mapping: [{{val|1 2 2 3 3 3}}, {{val|0 -9 7 -4 10 15}}]


POTE generator: ~26/25 = 55.550
POTE generator: ~26/25 = 55.550


Vals: 21, 22, 43
Vals: {{Val list| 21, 22, 43 }}


Badness: 0.035261
Badness: 0.035261


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


Line 74: Line 74:
[[Badness]]: 0.088746
[[Badness]]: 0.088746


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 87: Line 87:
Badness: 0.035844
Badness: 0.035844


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 100: Line 100:
Badness: 0.031366
Badness: 0.031366


== Biscapade ==
== Biscapade ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 115: Line 115:
[[Badness]]: 0.059241
[[Badness]]: 0.059241


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 128: Line 128:
Badness: 0.024619
Badness: 0.024619


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Revision as of 03:41, 10 June 2021

The escapade family tempers out the escapade comma, [32 -7 -9⟩, of size 9.492 cents. It includes the alphaquarter temperament and the arch temperament.

Escapade

Subgroup: 2.3.5

Comma: 4294967296/4271484375

Mapping: [⟨1 2 2], ⟨0 -9 7]]

POTE generator: ~16875/16384 = 55.293

Template:Val list

Badness: 0.083778

7-limit

Subgroup: 2.3.5.7

Comma list: 225/224, 12288/12005

Mapping: [⟨1 2 2 3], ⟨0 -9 7 -4]]

Wedgie: ⟨⟨ 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: ~49/48 = 55.354

Vals: 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

Vals: Template:Val list

Badness: 0.035261

Escaped

See also: Sensamagic clan § Escaped

This temperament is also known 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]]

Wedgie: ⟨⟨ 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

Vals: 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

Vals: Template:Val list

Badness: 0.031366

Biscapade

Subgroup: 2.3.5.7

Comma list: 6144/6125, 118098/117649

Mapping: [⟨2 4 4 7], ⟨0 -9 7 -15]]

Wedgie: ⟨⟨ 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

Vals: Template:Val list

Badness: 0.024619

13-limit

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

Vals: Template:Val list

Badness: 0.033038

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