Escapade family: Difference between revisions

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== Escapade ==
== Escapade ==
Subgroup: 2.3.5
[[Subgroup]]: 2.3.5


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


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -9 7 }}]
{{Mapping|legend=1| 1 2 2 | 0 -9 7 }}


[[POTE generator]]: ~16875/16384 = 55.293
: mapping generators: ~2, ~16875/16384
 
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16875/16384 = 55.293


{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65, 152, 217, 586, 803 }}
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== Septimal escapade ==
== Septimal escapade ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


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


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


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


[[POTE generator]]: ~49/48 = 55.327
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/48 = 55.327


{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}
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Comma list: 99/98, 176/175, 2560/2541
Comma list: 99/98, 176/175, 2560/2541


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


POTE generator: ~33/32 = 55.354
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.354


{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}
{{Optimal ET sequence|legend=1| 21, 22, 43, 65d }}
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Comma list: 78/77, 99/98, 176/175, 507/500
Comma list: 78/77, 99/98, 176/175, 507/500


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


POTE generator: ~26/25 = 55.550
Optimal tuning (POTE): ~2 = 1\1, ~26/25 = 55.550


{{Optimal ET sequence|legend=1| 21, 22, 43 }}
{{Optimal ET sequence|legend=1| 21, 22, 43 }}
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== Alphaquarter ==
== Alphaquarter ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 5120/5103, 29360128/29296875
[[Comma list]]: 5120/5103, 29360128/29296875


[[Mapping]]: [{{val| 1 2 2 0 }}, {{val| 0 -9 7 61 }}]
{{Mapping|legend=1| 1 2 2 0 | 0 -9 7 61 }}


{{Multival|legend=1| 9 -7 -61 -32 -122 -122 }}
{{Multival|legend=1| 9 -7 -61 -32 -122 -122 }}


[[POTE generator]]: ~16128/15625 = 55.243
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~16128/15625 = 55.243


{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}
{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}
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Comma list: 3025/3024, 4000/3993, 5120/5103
Comma list: 3025/3024, 4000/3993, 5120/5103


Mapping: [{{val| 1 2 2 0 3 }}, {{val| 0 -9 7 61 10 }}]
Mapping: {{mapping| 1 2 2 0 3 | 0 -9 7 61 10 }}


POTE generator: ~33/32 = 55.243
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.243


{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}
{{Optimal ET sequence|legend=1| 65d, 87, 152, 239, 391 }}
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Comma list: 352/351, 625/624, 847/845, 1575/1573
Comma list: 352/351, 625/624, 847/845, 1575/1573


Mapping: [{{val| 1 2 2 0 3 2 }}, {{val| 0 -9 7 61 10 37 }}]
Mapping: {{mapping| 1 2 2 0 3 2 | 0 -9 7 61 10 37 }}


POTE generator: ~33/32 = 55.236
Optimal tuning (POTE): ~2 = 1\1, ~33/32 = 55.236


{{Optimal ET sequence|legend=1| 65d, 87, 152f, 239f }}
{{Optimal ET sequence|legend=1| 65d, 87, 152f, 239f }}
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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).''
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
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 245/243, 65625/65536
[[Comma list]]: 245/243, 65625/65536


[[Mapping]]: [{{val| 1 2 2 4 }}, {{val| 0 -9 7 -26 }}]
{{Mapping|legend=1| 1 2 2 4 | 0 -9 7 -26 }}


{{Multival|legend=1| 9 -7 26 -32 16 80 }}
{{Multival|legend=1| 9 -7 26 -32 16 80 }}


[[POTE generator]]: ~28/27 = 55.122
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 55.122


{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}
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Comma list: 245/243, 385/384, 4000/3993
Comma list: 245/243, 385/384, 4000/3993


Mapping: [{{val| 1 2 2 4 3 }}, {{val| 0 -9 7 -26 10 }}]
Mapping: {{mapping| 1 2 2 4 3 | 0 -9 7 -26 10 }}


POTE generator: ~28/27 = 55.126
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.126


{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 196, 283 }}
Line 133: Line 135:
Comma list: 245/243, 352/351, 385/384, 625/624
Comma list: 245/243, 352/351, 385/384, 625/624


Mapping: [{{val| 1 2 2 4 3 2 }}, {{val| 0 -9 7 -26 10 37 }}]
Mapping: {{mapping| 1 2 2 4 3 2 | 0 -9 7 -26 10 37 }}


POTE generator: ~28/27 = 55.138
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 55.138


{{Optimal ET sequence|legend=1| 22, 65, 87, 283 }}
{{Optimal ET sequence|legend=1| 22, 65, 87, 283 }}
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== Septisuperfourth ==
== Septisuperfourth ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 6144/6125, 118098/117649
[[Comma list]]: 6144/6125, 118098/117649


[[Mapping]]: [{{val| 2 4 4 7 }}, {{val| 0 -9 7 -15 }}]
{{Mapping|legend=1| 2 4 4 7 | 0 -9 7 -15 }}
 
: mapping generators: ~343/243, ~16875/16384


{{Multival|legend=1| 18 -14 30 -64 -3 109 }}
{{Multival|legend=1| 18 -14 30 -64 -3 109 }}


[[POTE generator]]: ~16875/16384 = 55.320
[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~16875/16384 = 55.320


{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}
{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}
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Comma list: 540/539, 4000/3993, 5632/5625
Comma list: 540/539, 4000/3993, 5632/5625


Mapping: [{{val| 2 4 4 7 6 }}, {{val| 0 -9 7 -15 10 }}]
Mapping: {{mapping| 2 4 4 7 6 | 0 -9 7 -15 10 }}


POTE generator: ~33/32 = 55.304
Optimal tuning (POTE): ~99/70 = 1\2, ~33/32 = 55.304


{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}
{{Optimal ET sequence|legend=1| 22, 86, 108, 130, 152, 282 }}
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Comma list: 540/539, 729/728, 1575/1573, 3584/3575
Comma list: 540/539, 729/728, 1575/1573, 3584/3575


Mapping: [{{val| 2 4 4 7 6 11 }}, {{val| 0 -9 7 -15 10 -39 }}]
Mapping: {{mapping| 2 4 4 7 6 11 | 0 -9 7 -15 10 -39 }}


POTE generator: ~33/32 = 55.325
Optimal tuning (POTE): ~99/70 = 1\2, ~33/32 = 55.325


{{Optimal ET sequence|legend=1| 22f, 108f, 130, 282 }}
{{Optimal ET sequence|legend=1| 22f, 108f, 130, 282 }}
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==== Septisuperquad ====
==== Septisuperquad ====
This temperament is also called as "biscapade".
This temperament is also known as "biscapade".


Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13
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Comma list: 351/350, 364/363, 540/539, 4096/4095
Comma list: 351/350, 364/363, 540/539, 4096/4095


Mapping: [{{val| 2 4 4 7 6 5 }}, {{val| 0 -9 7 -15 10 26 }}]
Mapping: {{mapping| 2 4 4 7 6 5 | 0 -9 7 -15 10 26 }}


POTE generator: ~33/32 = 55.359
Optimal tuning (POTE): ~55/39 = 1\2, ~33/32 = 55.359


{{Optimal ET sequence|legend=1| 22, 108, 130 }}
{{Optimal ET sequence|legend=1| 22, 108, 130 }}
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== Arch ==
== Arch ==
Subgroup: 2.3.5.7
[[Subgroup]]: 2.3.5.7


[[Comma list]]: 3136/3125, 5250987/5242880
[[Comma list]]: 3136/3125, 5250987/5242880


[[Mapping]]: [{{val| 1 2 2 2 }}, {{val| 0 -18 14 35 }}]
{{Mapping|legend=1| 1 2 2 2 | 0 -18 14 35 }}
 
: mapping generators: ~2, ~64/63


{{Multival|legend=1| 18 -14 -35 -64 -106 -42 }}
{{Multival|legend=1| 18 -14 -35 -64 -106 -42 }}


[[POTE generator]]: ~64/63 = 27.668
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~64/63 = 27.668


{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347, 824c, 1171c, 1518cd }}
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Comma list: 441/440, 3136/3125, 4000/3993
Comma list: 441/440, 3136/3125, 4000/3993


Mapping: [{{val| 1 2 2 2 3 }}, {{val| 0 -18 14 35 20 }}]
Mapping: {{mapping| 1 2 2 2 3 | 0 -18 14 35 20 }}


POTE generator: ~64/63 = 27.663
Optimal tuning (POTE): ~2 = 1\1, ~64/63 = 27.663


{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347e, 911cde }}
{{Optimal ET sequence|legend=1| 43, 87, 130, 217, 347e, 911cde }}
Line 230: Line 236:
Comma list: 364/363, 441/440, 676/675, 3136/3125
Comma list: 364/363, 441/440, 676/675, 3136/3125


Mapping: [{{val| 1 2 2 2 3 4 }}, {{val| 0 -18 14 35 20 -13 }}]
Mapping: {{mapping| 1 2 2 2 3 4 | 0 -18 14 35 20 -13 }}


POTE generator: ~64/63 = 27.660
Optimal tuning (POTE): ~2 = 1\1, ~64/63 = 27.660


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

Revision as of 06:37, 17 July 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]]

mapping generators: ~2, ~16875/16384

Optimal tuning (POTE): ~2 = 1\1, ~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 ]]

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

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