Escapade family: Difference between revisions
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Move alphaquarter here as a strong extension; also move arch here as its 5-limit part seems simpler |
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The '''escapade family''' tempers out the [[escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s. | The '''escapade family''' tempers out the [[escapade comma]], {{monzo|32 -7 -9}}, of size 9.492 [[cent]]s. | ||
Extensions of escapade include (septimal) escapade, alphaquarter, escaped, septisuperfourth (aka biscapade) and arch, all considered below. | |||
== Escapade == | == Escapade == | ||
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[[Badness]]: 0.083778 | [[Badness]]: 0.083778 | ||
== Septimal escapade == | == Septimal escapade == | ||
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Badness: 0.035261 | Badness: 0.035261 | ||
== Alphaquarter == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 5120/5103, 29360128/29296875 | |||
[[Mapping]]: [{{val| 1 2 2 0 }}, {{val| 0 -9 7 61 }}] | |||
{{Multival|legend=1| 9 -7 -61 -32 -122 -122 }} | |||
[[POTE generator]]: ~16128/15625 = 55.243 | |||
{{Val list|legend=1| 87, 152, 239, 391 }} | |||
[[Badness]]: 0.116594 | |||
=== 11-limit === | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 3025/3024, 4000/3993, 5120/5103 | |||
Mapping: [{{val| 1 2 2 0 3 }}, {{val| 0 -9 7 61 10 }}] | |||
POTE generator: ~33/32 = 55.243 | |||
Vals: {{Val list| 87, 152, 239, 391 }} | |||
Badness: 0.029638 | |||
== Escaped == | == Escaped == | ||
{{See also|Sensamagic clan #Escaped}} | {{See also| Sensamagic clan #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).'' | 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).'' | ||
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Badness: 0.033038 | Badness: 0.033038 | ||
== Arch == | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 3136/3125, 5250987/5242880 | |||
[[Mapping]]: [{{val| 1 2 2 2 }}, {{val| 0 -18 14 35 }}] | |||
{{Multival|legend=1| 18 -14 -35 -64 -106 -42 }} | |||
[[POTE generator]]: ~64/63 = 27.668 | |||
{{Val list|legend=1| 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: [{{val| 1 2 2 2 3 }}, {{val| 0 -18 14 35 20 }}] | |||
POTE generator: ~64/63 = 27.663 | |||
Optimal GPV sequence: {{Val list| 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: [{{val| 1 2 2 2 3 4 }}, {{val| 0 -18 14 35 20 -13 }}] | |||
POTE generator: ~64/63 = 27.660 | |||
Optimal GPV sequence: {{Val list| 43, 87, 130, 217, 347e, 564e }} | |||
Badness: 0.019504 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||