Escapade family

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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

Optimal GPV sequence21, 22, 43, 65, 152, 217, 586, 803

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]]

Wedgie⟨⟨9 -7 4 -32 -19 29]]

POTE generator: ~49/48 = 55.327

Optimal GPV sequence21, 22, 43, 65d

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: 21, 22, 43, 65d

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: 21, 22, 43

Badness: 0.035261

Alphaquarter

Subgroup: 2.3.5.7

Comma list: 5120/5103, 29360128/29296875

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

Wedgie⟨⟨9 -7 -61 -32 -122 -122]]

POTE generator: ~16128/15625 = 55.243

Optimal GPV sequence65d, 87, 152, 239, 391

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

Optimal GPV sequence: 65d, 87, 152, 239, 391

Badness: 0.029638

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 625/624, 847/845, 1575/1573

Mapping: [1 2 2 0 3 2], 0 -9 7 61 10 37]]

POTE generator: ~33/32 = 55.236

Optimal GPV sequence: 65d, 87, 152f, 239f

Badness: 0.025344

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]]

Wedgie⟨⟨9 -7 26 -32 16 80]]

POTE generator: ~28/27 = 55.122

Optimal GPV sequence22, 65, 87, 196, 283

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: 22, 65, 87, 196, 283

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: 22, 65, 87, 283

Badness: 0.031366

Septisuperfourth

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

Optimal GPV sequence22, 86, 108, 130, 152, 282

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: 22, 86, 108, 130, 152, 282

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: 22f, 108f, 130, 282

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: 22, 108, 130

Badness: 0.033038

Arch

Subgroup: 2.3.5.7

Comma list: 3136/3125, 5250987/5242880

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

Wedgie⟨⟨18 -14 -35 -64 -106 -42]]

POTE generator: ~64/63 = 27.668

Optimal GPV sequence43, 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: [1 2 2 2 3], 0 -18 14 35 20]]

POTE generator: ~64/63 = 27.663

Optimal GPV sequence: 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: [1 2 2 2 3 4], 0 -18 14 35 20 -13]]

POTE generator: ~64/63 = 27.660

Optimal GPV sequence: 43, 87, 130, 217, 347e, 564e

Badness: 0.019504