Amity family: Difference between revisions
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The generator for [[amity]] temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, [[5120/5103]] and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. [[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 generator for [[amity]] temperament is the acute minor third, which means an ordinary 6/5 minor third raised by an 81/80 comma to 243/200, and from this it derives its name. Aside from the ragisma it tempers out the 5-limit amity comma, 1600000/1594323, [[5120/5103]] and 6144/6125. It can also be described as the 46&53 temperament, or by its wedgie, <<5 13 -17 9 -41 -76||. [[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. | ||
Temperaments not discussed here include [[amicable]] and [[chromat]]. | Temperaments not discussed here include [[Breedsmic temperament|amicable]] and [[Hemimean clan|chromat]]. | ||
= Amity = | = Amity = | ||
{{see also|Ragismic microtemperaments #Amity}} | {{see also|Ragismic microtemperaments #Amity}} | ||
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== Hitchcock == | == Hitchcock == | ||
Comma list: 121/120, 176/175, 2200/2187 | Comma list: 121/120, 176/175, 2200/2187 | ||
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Badness: 0.031307 | Badness: 0.031307 | ||
=Accord= | = Accord = | ||
[[Comma list]]: 126/125, 100352/98415 | |||
[[Mapping]]: [<1 3 6 11|, <0 -5 -13 -29|] | |||
[[Wedgie]]: <<5 13 29 9 32 31|| | |||
[[POTE tuning|POTE generator]]: ~243/200 = 338.993 | |||
[[EDO|Vals]]: {{Val list| 7d, 46, 131c, 177c }} | |||
[[Badness]]: 0.095612 | |||
== 11-limit == | |||
Comma list: 121/120, 126/125, 896/891 | |||
Mapping: [<1 3 6 11 6|, <0 -5 -13 -29 -9|] | |||
POTE generator: ~11/9 = 339.047 | POTE generator: ~11/9 = 339.047 | ||
Vals: {{Val list| 7d, 46, 177c, 223bc, 269bce }} | |||
Badness: 0.042468 | |||
= Bamity = | |||
[[Comma list]]: 245/243, 64827/64000 | |||
[[Mapping]]: [<2 1 -1 3|, <0 5 13 6|] | |||
[[Wedgie]]: <<10 26 12 18 -9 -45|| | |||
[[POTE tuning|POTE generator]]: ~7/6 = 260.402 | |||
[[EDO|Vals]]: {{Val list| 46, 60, 106d }} | |||
[[Badness]]: 0.083601 | |||
== 11-limit == | |||
Comma list: 121/120, 245/243, 441/440 | |||
Mapping: [<2 1 -1 3 3|, <0 5 13 6 9|] | |||
POTE generator: ~7/6 = 260.393 | POTE generator: ~7/6 = 260.393 | ||
Vals: {{Val list| 14c, 46, 60e, 106de }} | |||
Badness: 0.035504 | |||
== 13-limit == | |||
Comma list: 91/90, 121/120, 245/243, 441/440 | |||
Mapping: [<2 1 -1 3 3 0|, <0 5 13 6 9 17|] | |||
POTE generator: ~7/6 = 260.618 | POTE generator: ~7/6 = 260.618 | ||
Vals: {{Val list| 46, 106def, 152def }} | |||
Badness: 0.030885 | |||
= Hamity = | |||
[[Comma list]]: 2430/2401, 4000/3969 | |||
[[Mapping]]: [<1 8 19 15|, <0 -10 -26 -19|] | |||
[[Wedgie]]: <<10 26 19 18 2 -29|| | |||
[[POTE tuning|POTE generator]]: ~9/7 = 430.219 | |||
[[EDO|Vals]]: {{Val list| 14c, 39d, 53 }} | |||
[[Badness]]: 0.073956 | |||
== 11-limit == | |||
Comma list: 99/98, 121/120, 4000/3969 | |||
Mapping: [<1 8 19 15 15|, <0 -10 -26 -19 -18|] | |||
POTE generator: ~9/7 = 430.192 | POTE generator: ~9/7 = 430.192 | ||
Vals: {{Val list| 14c, 39d, 53 }} | |||
Badness: 0.042947 | |||
== 13-limit == | |||
Comma list: 99/98, 121/120, 275/273, 572/567 | |||
Mapping: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|] | |||
POTE generator: ~9/7 = 430.216 | POTE generator: ~9/7 = 430.216 | ||
Vals: {{Val list| 14cf, 53 }} | |||
Badness: 0. | Badness: 0.029753 | ||
[[Category:Theory]] | [[Category:Theory]] | ||