Escapade family
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
For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of 16ed5/3#Intervals.
Subgroup: 2.3.5
Comma list: 4294967296/4271484375
Mapping: [⟨1 2 2], ⟨0 -9 7]]
- mapping generators: ~2, ~16875/16384
Optimal ET sequence: 21, 22, 43, 65, 152, 217, 586, 803
Badness: 0.083778
2.3.5.11 subgroup
Subgroup: 2.3.5.11
Comma list: 4000/3993, 5632/5625
Mapping: [⟨1 2 2 3], ⟨0 -9 7 10]]
Optimal tuning (CTE): ~2 = 1\1, ~33/32 = 55.2760
Optimal ET sequence: 21, 22, 43, 65, 87, 152, 369, 521e, 1194bcee, 1715bceeee
Badness: 0.0107
2.3.5.11.31 subgroup
Subgroup: 2.3.5.11.31
Comma list: 496/495, 961/960, 4000/3993
Mapping: [⟨1 2 2 3 5], ⟨0 -9 7 10 -1]]
Optimal tuning (CTE): ~2 = 1\1, ~33/32 = 55.276
Optimal ET sequence: 21, 22, 43, 65, 87, 152, 369, 521e, 673e, 1194bcee, 1867bceeee
Badness (Dirichlet): 0.251
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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~49/48 = 55.327
Optimal ET sequence: 21, 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]]
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.354
Optimal ET 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]]
Optimal tuning (POTE): ~2 = 1\1, ~26/25 = 55.550
Optimal ET 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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~16128/15625 = 55.243
Optimal ET sequence: 65d, 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]]
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.243
Optimal ET 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]]
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.236
Optimal ET sequence: 65d, 87, 152f, 239f
Badness: 0.025344
Escaped
This temperament was also known as "sensa" in earlier materials 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 ]]
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.122
Optimal ET sequence: 22, 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]]
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.126
Optimal ET 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]]
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.138
Optimal ET 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]]
- mapping generators: ~343/243, ~16875/16384
Wedgie: ⟨⟨ 18 -14 30 -64 -3 109 ]]
Optimal tuning (POTE): ~343/243 = 1\2, ~16875/16384 = 55.320
Optimal ET sequence: 22, 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]]
Optimal tuning (POTE): ~99/70 = 1\2, ~33/32 = 55.304
Optimal ET 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]]
Optimal tuning (POTE): ~99/70 = 1\2, ~33/32 = 55.325
Optimal ET sequence: 22f, 108f, 130, 282
Badness: 0.022887
Septisuperquad
This temperament is also known 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]]
Optimal tuning (POTE): ~55/39 = 1\2, ~33/32 = 55.359
Optimal ET 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]]
- mapping generators: ~2, ~64/63
Wedgie: ⟨⟨ 18 -14 -35 -64 -106 -42 ]]
Optimal tuning (POTE): ~2 = 1\1, ~64/63 = 27.668
Optimal ET sequence: 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: [⟨1 2 2 2 3], ⟨0 -18 14 35 20]]
Optimal tuning (POTE): ~2 = 1\1, ~64/63 = 27.663
Optimal ET 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]]
Optimal tuning (POTE): ~2 = 1\1, ~64/63 = 27.660
Optimal ET sequence: 43, 87, 130, 217, 347e, 564e
Badness: 0.019504