Amity family
Amity[edit]
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.
In the 5-limit amity is a genuine microtemperament, with 58/205 being a possible tuning. Another good choice is (64/5)^(1/13), which gives pure major thirds.
Comma: 1600000/1594323
POTE generator: ~243/200 = 339.519
Map: [<1 3 6|, <0 -5 -13|]
EDOs: 7, 39, 46, 53, 152, 205, 463, 668, 873
Badness: 0.0220
7-limit[edit]
Commas: 4375/4374, 5120/5103
POTE generator: ~243/200 = 339.432
Map: [<1 3 6 -2|, <0 -5 -13 17|]
Wedgie: <<5 13 -17 9 -41 -76||
EDOs: 7, 39, 46, 53, 99, 251, 350
Badness: 0.0236
11-limit[edit]
Commas: 540/539, 4375/4374, 5120/5103
POTE generator: ~243/200 = 339.464
Map: [<1 3 6 -2 21|, <0 -5 -13 17 -62|]
EDOs: 53, 99e, 152, 555de, 707de, 859bde
Badness: 0.0315
Hitchcock[edit]
Commas: 121/120, 176/175, 2200/2187
POTE generator: ~11/9 = 339.340
Map: [<1 3 6 -2 6|, <0 -5 -13 17 -9|]
EDOs: 7, 39, 46, 53, 99
Badness: 0.0352
Hemiamity[edit]
Commas: 4375/4374, 5120/5103, 3025/3024
POTE generator: ~ 243/200 = 339.493
Map: [<2 1 -1 13 13|, <0 5 13 -17 -14|]
EDOs: 14, 46, 106, 152, 350
Bamity[edit]
Commas: 245/243, 64827/64000
POTE generator: ~7/6 = 260.402
Map: [<2 1 -1 3|, <0 5 13 6|]
Wedgie: <<10 26 12 18 -9 -45||
EDOs: 46, 60, 106d
Badness: 0.0836
11-limit[edit]
Commas: 121/120, 245/243, 441/440
POTE generator: ~7/6 = 260.393
Map: [<2 1 -1 3 3|, <0 5 13 6 9|]
EDOs: 14c, 46, 60e, 106de
Badness: 0.0355
13-limit[edit]
Commas: 91/90, 121/120, 245/243, 441/440
POTE generator: ~7/6 = 260.618
Map: [<2 1 -1 3 3 0|, <0 5 13 6 9 17|]
EDOs: 46, 106def, 152def
Badness: 0.0309
Hamity[edit]
Commas: 2430/2401, 4000/3969
POTE generator: ~9/7 = 430.219
Map: [<1 8 19 15|, <0 -10 -26 -19|]
Wedgie: <<10 26 19 18 2 -29||
EDOs: 14c, 39d, 53
Badness: 0.0740
11-limit[edit]
Commas: 99/98, 121/120, 4000/3969
POTE generator: ~9/7 = 430.192
Map: [<1 8 19 15 15|, <0 -10 -26 -19 -18|]
EDOs: 14c, 39d, 53
Badness: 0.0429
13-limit[edit]
Commas: 99/98, 121/120, 275/273, 572/567
POTE generator: ~9/7 = 430.216
Map: [<1 8 19 15 15 30|, <0 -10 -26 -19 -18 -41|]
EDOs: 53
Badness: 0.0298