Escapade family: Difference between revisions

m Septisuperfourth aka biscapade: normalize the generator
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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]]
* ''[[Arch]]'', {3136/3125, 5250987/5242880} → [[Hemimean clan #Arch]]
* ''[[alphaquarter]]'', {5120/5103, 29360128/29296875} → [[Hemifamity temperaments #Alphaquarter]]
* ''[[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


Vals: {{Val list| 21, 22, 43, 65d }}
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


Vals: {{Val list| 21, 22, 43 }}
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


Vals: {{Val list| 22, 65, 87, 196, 283 }}
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


Vals: {{Val list| 22, 65, 87, 283 }}
Optimal GPV sequence: {{Val list| 22, 65, 87, 283 }}


Badness: 0.031366
Badness: 0.031366


== Septisuperfourth aka biscapade ==
== 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


Vals: {{Val list| 22, 86, 108, 130, 152, 282 }}
Optimal GPV sequence: {{Val list| 22, 86, 108, 130, 152, 282 }}


Badness: 0.024619
Badness: 0.024619


==== 13-limit (septisuperfourth) ====
==== 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


Vals: {{Val list| 22f, 108f, 130, 282 }}
Optimal GPV sequence: {{Val list| 22f, 108f, 130, 282 }}


Badness: 0.022887
Badness: 0.022887


==== 13-limit (biscapade aka septisuperquad) ====
==== 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


Vals: {{Val list| 22, 108, 130 }}
Optimal GPV sequence: {{Val list| 22, 108, 130 }}


Badness: 0.033038
Badness: 0.033038