Amity family: Difference between revisions
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The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It can also be described as the 46&53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you. | The '''amity family''' tempers out the 5-limit [[amity comma]], 1600000/1594323. The generator for the [[amity]] temperament is the acute minor third, which means the 6/5 just minor third raised by an 81/80 comma to 243/200, and from this it derives its name. It can also be described as the 46&53 temperament, which tempers out [[4375/4374]] and [[5120/5103]] in the 7-limit. [[99edo|99EDO]] is a good tuning for amity, with generator 28\99, and MOS of 11, 18, 25, 32, 39, 46 or 53 notes are available. If you are looking for a different kind of neutral third this could be the temperament for you. | ||
= Amity = | = Amity = | ||
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== Extensions == | == Extensions == | ||
The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, and 16875/16807 for familia. | The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, and 16875/16807 for familia. | ||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
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Badness: 0.031331 | Badness: 0.031331 | ||
= Paramity = | |||
The ''paramity'' temperament (53&311, named by [[User:Xenllium|Xenllium]]) tempers out the horwell comma (65625/65536) and [[garischisma]] (33554432/33480783). | |||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 65625/65536, 1600000/1594323 | |||
[[Mapping]]: [{{val|1 3 6 -17}}, {{val|0 -5 -13 70}}] | |||
[[POTE generator]]: ~243/200 = 339.553 | |||
{{Val list|legend=1| 53, 205d, 258, 311, 675, 986, 1297c, 2283bc }} | |||
[[Badness]]: 0.113655 | |||
== 11-limit == | |||
Subgroup: 2.3.5.7.11 | |||
Comma list: 6250/6237, 19712/19683, 41503/41472 | |||
Mapping: [{{val|1 3 6 -17 36}}, {{val|0 -5 -13 70 -115}}] | |||
POTE generator: ~243/200 = 339.554 | |||
Vals: {{Val list| 53, 205de, 258, 311, 675, 986 }} | |||
Badness: 0.064853 | |||
== 13-limit == | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683 | |||
Mapping: [{{val|1 3 6 -17 36 17}}, {{val|0 -5 -13 70 -115 -47}}] | |||
POTE generator: ~243/200 = 339.554 | |||
Vals: {{Val list| 53, 205de, 258, 311, 675, 986, 1661cf }} | |||
Badness: 0.030347 | |||
== 17-limit == | |||
Subgroup: 2.3.5.7.11.13.17 | |||
Comma list: 625/624, 1225/1224, 2080/2079, 2200/2197, 2431/2430 | |||
Mapping: [{{val|1 3 6 -17 36 17 -31}}, {{val|0 -5 -13 70 -115 -47 124}}] | |||
POTE generator: ~243/200 = 339.555 | |||
Vals: {{Val list| 53, 205deg, 258g, 311, 675, 1661cf, 2336bccf, 3011bccf }} | |||
Badness: 0.024118 | |||
== 19-limit == | |||
Subgroup: 2.3.5.7.11.13.17.19 | |||
Comma list: 625/624, 1225/1224, 1540/1539, 1729/1728, 2080/2079, 2200/2197 | |||
Mapping: [{{val|1 3 6 -17 36 17 -31 15}}, {{val|0 -5 -13 70 -115 -47 124 -38}}] | |||
POTE generator: ~208/171 = 339.555 | |||
Vals: {{Val list| 53, 205deg, 258g, 311, 675, 986, 1661cfh }} | |||
Badness: 0.017420 | |||
= Accord = | = Accord = | ||