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
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
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