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|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|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 [[Breedsmic temperaments|amicable]] and [[ | Temperaments not discussed here include [[Breedsmic temperaments|amicable]] and [[Hemimage temperaments|chromat]]. | ||
= Amity = | = Amity = | ||
Revision as of 10:49, 18 April 2021
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.
Amity
Comma: 1600000/1594323
Mapping: [<1 3 6|, <0 -5 -13|]
POTE generator: ~243/200 = 339.519
Badness: 0.021960
7-limit
Comma list: 4375/4374, 5120/5103
Mapping: [<1 3 6 -2|, <0 -5 -13 17|]
Wedgie: <<5 13 -17 9 -41 -76||
POTE generator: ~128/105 = 339.432
Badness: 0.023649
11-limit
Comma list: 540/539, 4375/4374, 5120/5103
Mapping: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]
POTE generator: ~128/105 = 339.464
Vals: Template:Val list
Badness: 0.031506
13-limit
Comma list: 352/351, 540/539, 625/624, 847/845
Mapping: [<1 3 6 -2 21 17|, <0 -5 -13 17 -62 -47|]
POTE generator: ~128/105 = 339.481
Vals: Template:Val list
Badness: 0.028008
Hitchcock
Comma list: 121/120, 176/175, 2200/2187
Mapping: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
POTE generator: ~11/9 = 339.390
Vals: Template:Val list
Badness: 0.035187
13-limit
Comma list: 121/120, 169/168, 176/175, 325/324
Mapping: [<1 3 6 -2 6 2|, <0 -5 -13 17 -9 6|]
POTE generator: ~11/9 = 339.419
Vals: Template:Val list
Badness: 0.022448
Hemiamity
Comma list: 3025/3024, 4375/4374, 5120/5103
Mapping: [<2 1 -1 13 13|, <0 5 13 -17 -14|]
POTE generator: ~64/55 = 339.439
Vals: Template:Val list
Badness: 0.031307
Accord
Comma list: 126/125, 100352/98415
Mapping: [<1 3 6 11|, <0 -5 -13 -29|]
Wedgie: <<5 13 29 9 32 31||
POTE generator: ~243/200 = 338.993
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
Vals: Template:Val list
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 generator: ~7/6 = 260.402
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
Vals: Template:Val list
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
Vals: Template:Val list
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 generator: ~9/7 = 430.219
Badness: 0.073956
11-limit
Comma list: 99/98, 121/120, 2200/2187
Mapping: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]
POTE generator: ~9/7 = 430.192
Vals: Template:Val list
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
Vals: Template:Val list
Badness: 0.029753