Escapade family: Difference between revisions
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=== Extensions === | === Extensions === | ||
Extensions of escapade include (septimal) escapade, escaped and biscapade, considered below, as well as these temperaments discussed elsewhere: | Extensions of escapade include (septimal) escapade, escaped and biscapade (septisuperfourth), considered below, as well as these temperaments discussed elsewhere: | ||
* ''[[ | * ''[[Arch]]'', {3136/3125, 5250987/5242880} → [[Hemimean clan #Arch]] | ||
* ''[[ | * ''[[Alphaquarter]]'', {5120/5103, 29360128/29296875} → [[Hemifamity temperaments #Alphaquarter]] | ||
== Septimal escapade == | == Septimal escapade == | ||
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POTE generator: ~33/32 = 55.354 | POTE generator: ~33/32 = 55.354 | ||
Optimal GPV sequence: {{Val list| 21, 22, 43, 65d }} | |||
Badness: 0.036700 | Badness: 0.036700 | ||
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POTE generator: ~26/25 = 55.550 | POTE generator: ~26/25 = 55.550 | ||
Optimal GPV sequence: {{Val list| 21, 22, 43 }} | |||
Badness: 0.035261 | Badness: 0.035261 | ||
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POTE generator: ~28/27 = 55.126 | POTE generator: ~28/27 = 55.126 | ||
Optimal GPV sequence: {{Val list| 22, 65, 87, 196, 283 }} | |||
Badness: 0.035844 | Badness: 0.035844 | ||
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POTE generator: ~28/27 = 55.138 | POTE generator: ~28/27 = 55.138 | ||
Optimal GPV sequence: {{Val list| 22, 65, 87, 283 }} | |||
Badness: 0.031366 | Badness: 0.031366 | ||
== Septisuperfourth | == Septisuperfourth == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
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POTE generator: ~33/32 = 55.304 | POTE generator: ~33/32 = 55.304 | ||
Optimal GPV sequence: {{Val list| 22, 86, 108, 130, 152, 282 }} | |||
Badness: 0.024619 | Badness: 0.024619 | ||
==== 13-limit | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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POTE generator: ~33/32 = 55.325 | POTE generator: ~33/32 = 55.325 | ||
Optimal GPV sequence: {{Val list| 22f, 108f, 130, 282 }} | |||
Badness: 0.022887 | Badness: 0.022887 | ||
==== | ==== Septisuperquad ==== | ||
This temperament is also called as "biscapade". | |||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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: [{{val| 2 4 4 7 6 5 }}, {{val| 0 -9 7 -15 10 26 }}] | ||
POTE generator: ~33/32 = 55.359 | POTE generator: ~33/32 = 55.359 | ||
Optimal GPV sequence: {{Val list| 22, 108, 130 }} | |||
Badness: 0.033038 | Badness: 0.033038 | ||
Revision as of 12:45, 29 December 2021
The escapade family tempers out the escapade comma, [32 -7 -9⟩, of size 9.492 cents.
Escapade
Subgroup: 2.3.5
Comma list: 4294967296/4271484375
Mapping: [⟨1 2 2], ⟨0 -9 7]]
POTE generator: ~16875/16384 = 55.293
Badness: 0.083778
Extensions
Extensions of escapade include (septimal) escapade, escaped and biscapade (septisuperfourth), considered below, as well as these temperaments discussed elsewhere:
- Arch, {3136/3125, 5250987/5242880} → Hemimean clan #Arch
- Alphaquarter, {5120/5103, 29360128/29296875} → Hemifamity temperaments #Alphaquarter
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
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: Template:Val list
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: Template:Val list
Badness: 0.035261
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
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: Template:Val list
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: Template:Val list
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
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: Template:Val list
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: Template:Val list
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: Template:Val list
Badness: 0.033038