Escapade family: Difference between revisions

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"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence
Line 12: Line 12:
[[POTE generator]]: ~16875/16384 = 55.293
[[POTE generator]]: ~16875/16384 = 55.293


{{Val list|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}


[[Badness]]: 0.083778
[[Badness]]: 0.083778
Line 27: Line 27:
[[POTE generator]]: ~49/48 = 55.327
[[POTE generator]]: ~49/48 = 55.327


{{Val list|legend=1| 21, 22, 43, 65d }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}


[[Badness]]: 0.077950
[[Badness]]: 0.077950
Line 40: Line 40:
POTE generator: ~33/32 = 55.354
POTE generator: ~33/32 = 55.354


Optimal GPV sequence: {{Val list| 21, 22, 43, 65d }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}


Badness: 0.036700
Badness: 0.036700
Line 53: Line 53:
POTE generator: ~26/25 = 55.550
POTE generator: ~26/25 = 55.550


Optimal GPV sequence: {{Val list| 21, 22, 43 }}
{{Optimal ET sequence|legend=1| 21, 22, 43 }}


Badness: 0.035261
Badness: 0.035261
Line 68: Line 68:
[[POTE generator]]: ~16128/15625 = 55.243
[[POTE generator]]: ~16128/15625 = 55.243


{{Val list|legend=1| 65d, 87, 152, 239, 391 }}
{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}


[[Badness]]: 0.116594
[[Badness]]: 0.116594
Line 81: Line 81:
POTE generator: ~33/32 = 55.243
POTE generator: ~33/32 = 55.243


Optimal GPV sequence: {{Val list| 65d, 87, 152, 239, 391 }}
{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}


Badness: 0.029638
Badness: 0.029638
Line 94: Line 94:
POTE generator: ~33/32 = 55.236
POTE generator: ~33/32 = 55.236


Optimal GPV sequence: {{Val list| 65d, 87, 152f, 239f }}
{{Optimal ET sequence|legend=1| 65d, 87, 152f, 239f }}


Badness: 0.025344
Badness: 0.025344
Line 111: Line 111:
[[POTE generator]]: ~28/27 = 55.122
[[POTE generator]]: ~28/27 = 55.122


{{Val list|legend=1| 22, 65, 87, 196, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}


[[Badness]]: 0.088746
[[Badness]]: 0.088746
Line 124: Line 124:
POTE generator: ~28/27 = 55.126
POTE generator: ~28/27 = 55.126


Optimal GPV sequence: {{Val list| 22, 65, 87, 196, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}


Badness: 0.035844
Badness: 0.035844
Line 137: Line 137:
POTE generator: ~28/27 = 55.138
POTE generator: ~28/27 = 55.138


Optimal GPV sequence: {{Val list| 22, 65, 87, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 283 }}


Badness: 0.031366
Badness: 0.031366
Line 152: Line 152:
[[POTE generator]]: ~16875/16384 = 55.320
[[POTE generator]]: ~16875/16384 = 55.320


{{Val list|legend=1| 22, 86, 108, 130, 152, 282 }}
{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}


[[Badness]]: 0.059241
[[Badness]]: 0.059241
Line 165: Line 165:
POTE generator: ~33/32 = 55.304
POTE generator: ~33/32 = 55.304


Optimal GPV sequence: {{Val list| 22, 86, 108, 130, 152, 282 }}
{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}


Badness: 0.024619
Badness: 0.024619
Line 178: Line 178:
POTE generator: ~33/32 = 55.325
POTE generator: ~33/32 = 55.325


Optimal GPV sequence: {{Val list| 22f, 108f, 130, 282 }}
{{Optimal ET sequence|legend=1| 22f, 108f, 130, 282 }}


Badness: 0.022887
Badness: 0.022887
Line 193: Line 193:
POTE generator: ~33/32 = 55.359
POTE generator: ~33/32 = 55.359


Optimal GPV sequence: {{Val list| 22, 108, 130 }}
{{Optimal ET sequence|legend=1| 22, 108, 130 }}


Badness: 0.033038
Badness: 0.033038
Line 208: Line 208:
[[POTE generator]]: ~64/63 = 27.668
[[POTE generator]]: ~64/63 = 27.668


{{Val list|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}


[[Badness]]: 0.094345
[[Badness]]: 0.094345
Line 221: Line 221:
POTE generator: ~64/63 = 27.663
POTE generator: ~64/63 = 27.663


Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 911cde }}
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347e, 911cde }}


Badness: 0.036541
Badness: 0.036541
Line 234: Line 234:
POTE generator: ~64/63 = 27.660
POTE generator: ~64/63 = 27.660


Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 564e }}
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347e, 564e }}


Badness: 0.019504
Badness: 0.019504

Revision as of 16:18, 7 May 2023

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 ET sequence: 21, 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 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]]

POTE generator: ~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]]

POTE generator: ~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 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~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]]

Wedgie: ⟨⟨ 18 -14 30 -64 -3 109 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~33/32 = 55.325

Optimal ET 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 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]]

Wedgie: ⟨⟨ 18 -14 -35 -64 -106 -42 ]]

POTE generator: ~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]]

POTE generator: ~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]]

POTE generator: ~64/63 = 27.660

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

Badness: 0.019504

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