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 |