Amity family
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 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
Subgroup: 2.3.5
Comma list: 1600000/1594323
Mapping: [⟨1 3 6], ⟨0 -5 -13]]
Mapping generators: ~2, ~243/200
POTE generator: ~243/200 = 339.519
Badness: 0.021960
Extensions
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:
- amicable, {2401/2400, 1600000/1594323} → Breedsmic temperaments #Amicable
- chromat, {10976/10935, 235298/234375} → Hemimage temperaments #Chromat
- witch, {420175/419904, 1600000/1594323} → Wizmic microtemperaments #Witch
Septimal amity
Subgroup: 2.3.5.7
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
Subgroup: 2.3.5.7.11
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
Optimal GPV sequence: Template:Val list
Badness: 0.031506
13-limit
Subgroup: 2.3.5.7.11.13
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
Optimal GPV sequence: Template:Val list *
* optimal patent val: 205
Badness: 0.028008
Hitchcock
Subgroup: 2.3.5.7.11
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
Optimal GPV sequence: Template:Val list
Badness: 0.035187
13-limit
Subgroup: 2.3.5.7.11.13
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
Optimal GPV sequence: Template:Val list
Badness: 0.022448
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 121/120, 154/153, 169/168, 176/175, 273/272
Mapping: [⟨1 3 6 -2 6 2 -1], ⟨0 -5 -13 17 -9 6 18]]
POTE generator: ~11/9 = 339.366
Optimal GPV sequence: Template:Val list
Badness: 0.019395
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 121/120, 154/153, 169/168, 171/170, 176/175, 190/189
Mapping: [⟨1 3 6 -2 6 2 -1 0], ⟨0 -5 -13 17 -9 6 18 15]]
POTE generator: ~11/9 = 339.407
Optimal GPV sequence: Template:Val list
Badness: 0.017513
Catamite
The catamite temperament (46&99e) tempers out 441/440 (werckisma) and 896/891 (pentacircle) in the 11-limit; 196/195, 352/351 and 364/363 in the 13-limit. The word "catamite" itself is a term for male homosexual, but also a play on the words "cata-" (down) and "amity."
Subgroup: 2.3.5.7.11
Comma list: 441/440, 896/891, 4375/4374
Mapping: [⟨1 3 6 -2 -7], ⟨0 -5 -13 17 37]]
POTE generator: ~128/105 = 339.340
Optimal GPV sequence: Template:Val list
Badness: 0.040976
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 196/195, 352/351, 364/363, 4375/4374
Mapping: [⟨1 3 6 -2 -7 -11], ⟨0 -5 -13 17 37 52]]
POTE generator: ~128/105 = 339.313
Optimal GPV sequence: Template:Val list
Badness: 0.034215
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 196/195, 256/255, 352/351, 364/363, 1156/1155
Mapping: [⟨1 3 6 -2 -7 -11 -1], ⟨0 -5 -13 17 37 52 18]]
POTE generator: ~17/14 = 339.313
Optimal GPV sequence: Template:Val list
Badness: 0.021193
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 196/195, 256/255, 343/342, 352/351, 364/363, 476/475
Mapping: [⟨1 3 6 -2 -7 -11 -1 -13], ⟨0 -5 -13 17 37 52 18 61]]
POTE generator: ~17/14 = 339.325
Optimal GPV sequence: Template:Val list
Badness: 0.018864
Hemiamity
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4375/4374, 5120/5103
Mapping: [⟨2 1 -1 13 13], ⟨0 5 13 -17 -14]]
Mapping generators: ~99/70, ~64/55
POTE generator: ~64/55 = 260.561
Optimal GPV sequence: Template:Val list
Badness: 0.031307
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 352/351, 847/845, 1716/1715, 3025/3024
Mapping: [⟨2 1 -1 13 13 20], ⟨0 5 13 -17 -14 -29]]
POTE generator: ~64/55 = 260.583
Optimal GPV sequence: Template:Val list
Badness: 0.025784
Accord
Subgroup: 2.3.5.7
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
Subgroup: 2.3.5.7.11
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
Optimal GPV sequence: Template:Val list
Badness: 0.042468
Houborizic
The houborizic temperament (53&113) tempers out the marvel comma, 225/224. It is so named because it is closely related to the houboriz tuning (generator: 339.774971 cents).
Subgroup: 2.3.5.7
Comma list: 225/224, 1250000/1240029
Mapping: [⟨1 3 6 13], ⟨0 -5 -13 -36]]
Wedgie: ⟨⟨ 5 13 36 9 43 47 ]]
POTE generator: ~243/200 = 339.763
Badness: 0.066638
11-limit
Subgroup: 2.3.5.7.11
Comma list: 225/224, 385/384, 1250000/1240029
Mapping: [⟨1 3 6 13 -9], ⟨0 -5 -13 -36 44]]
POTE generator: ~243/200 = 339.763
Optimal GPV sequence: Template:Val list
Badness: 0.067891
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 225/224, 325/324, 385/384, 2200/2197
Mapping: [⟨1 3 6 13 -9 2], ⟨0 -5 -13 -36 44 6]]
POTE generator: ~39/32 = 339.764
Optimal GPV sequence: Template:Val list
Badness: 0.032996
Houbor
Subgroup: 2.3.5.7.11
Comma list: 121/120, 225/224, 2200/2187
Mapping: [⟨1 3 6 13 6], ⟨0 -5 -13 -36 -9]]
POTE generator: ~11/9 = 339.814
Optimal GPV sequence: Template:Val list
Badness: 0.045232
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 121/120, 225/224, 275/273, 325/324
Mapping: [⟨1 3 6 13 6 2], ⟨0 -5 -13 -36 -9 6]]
POTE generator: ~11/9 = 339.784
Optimal GPV sequence: Template:Val list
Badness: 0.031331
Paramity
The paramity temperament (53&311) tempers out the horwell comma (65625/65536) and garischisma (33554432/33480783).
Subgroup: 2.3.5.7
Comma list: 65625/65536, 1600000/1594323
Mapping: [⟨1 3 6 -17], ⟨0 -5 -13 70]]
POTE generator: ~243/200 = 339.553
Badness: 0.113655
11-limit
Subgroup: 2.3.5.7.11
Comma list: 6250/6237, 19712/19683, 41503/41472
Mapping: [⟨1 3 6 -17 36], ⟨0 -5 -13 70 -115]]
POTE generator: ~243/200 = 339.554
Optimal GPV sequence: Template:Val list
Badness: 0.064853
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 2080/2079, 2200/2197, 19712/19683
Mapping: [⟨1 3 6 -17 36 17], ⟨0 -5 -13 70 -115 -47]]
POTE generator: ~243/200 = 339.554
Optimal GPV sequence: Template:Val list
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: [⟨1 3 6 -17 36 17 -31], ⟨0 -5 -13 70 -115 -47 124]]
POTE generator: ~243/200 = 339.555
Optimal GPV sequence: Template:Val list
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: [⟨1 3 6 -17 36 17 -31 15], ⟨0 -5 -13 70 -115 -47 124 -38]]
POTE generator: ~208/171 = 339.555
Optimal GPV sequence: Template:Val list
Badness: 0.017420
Bamity
Bamity has a period of half octave and tempers out the sensamagic comma, 245/243. The name "bamity" is a play on the words "bi-" and "amity".
Subgroup: 2.3.5.7
Comma list: 245/243, 64827/64000
Mapping: [⟨2 1 -1 3], ⟨0 5 13 6]]
Mapping generators: ~343/240, ~7/6
Wedgie: ⟨⟨ 10 26 12 18 -9 -45 ]]
POTE generator: ~7/6 = 260.402
Badness: 0.083601
11-limit
Subgroup: 2.3.5.7.11
Comma list: 121/120, 245/243, 441/440
Mapping: [⟨2 1 -1 3 3], ⟨0 5 13 6 9]]
Mapping generators: ~99/70, ~7/6
POTE generator: ~7/6 = 260.393
Optimal GPV sequence: Template:Val list
Badness: 0.035504
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 91/90, 121/120, 245/243, 441/440
Mapping: [⟨2 1 -1 3 3 0], ⟨0 5 13 6 9 17]]
Mapping generators: ~55/39, ~7/6
POTE generator: ~7/6 = 260.618
Optimal GPV sequence: Template:Val list
Badness: 0.030885
Hamity
Hamity has a generator of about 430 cents which represents 9/7. It is also generated by half of acute minor "tenth" (acute minor third of 243/200 plus an octave), and its name is a play on the words "half" and "acute minor tenth".
Subgroup: 2.3.5.7
Comma list: 2430/2401, 4000/3969
Mapping: [⟨1 -2 -7 -4], ⟨0 10 26 19]]
Wedgie: ⟨⟨ 10 26 19 18 2 -29 ]]
POTE generator: ~9/7 = 430.219
Badness: 0.073956
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 121/120, 2200/2187
Mapping: [⟨1 -2 -7 -4 -3], ⟨0 10 26 19 18]]
POTE generator: ~9/7 = 430.192
Optimal GPV sequence: Template:Val list
Badness: 0.042947
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 99/98, 121/120, 275/273, 572/567
Mapping: [⟨1 -2 -7 -4 -3 -11], ⟨0 10 26 19 18 41]]
POTE generator: ~9/7 = 430.216
Optimal GPV sequence: Template:Val list
Badness: 0.029753
Gamity
The gamity temperament (46&113) tempers out the gamelisma, 1029/1024. It splits the interval of grave major sixth (~400/243, an octave minus acute minor third) in three.
Subgroup: 2.3.5.7
Comma list: 1029/1024, 1071875/1062882
Mapping: [⟨1 -2 -7 4], ⟨0 15 39 -5]]
Wedgie: ⟨⟨ 15 39 -5 27 -50 -121 ]]
POTE generator: ~189/160 = 286.787
Badness: 0.125733
11-limit
Subgroup: 2.3.5.7.11
Comma list: 385/384, 441/440, 1071875/1062882
Mapping: [⟨1 -2 -7 4 8], ⟨0 15 39 -5 -19]]
POTE generator: ~33/28 = 286.797
Optimal GPV sequence: Template:Val list
Badness: 0.051111
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 325/324, 364/363, 385/384, 10985/10976
Mapping: [⟨1 -2 -7 4 8 8], ⟨0 15 39 -5 -19 -18]]
POTE generator: ~13/11 = 286.789
Optimal GPV sequence: Template:Val list
Badness: 0.030297
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 273/272, 325/324, 364/363, 385/384, 3773/3757
Mapping: [⟨1 -2 -7 4 8 8 6], ⟨0 15 39 -5 -19 -18 -8]]
POTE generator: ~13/11 = 286.795
Optimal GPV sequence: Template:Val list
Badness: 0.022036
Trinity
The trinity temperament (152&159) tempers out the meter comma, 703125/702464. It splits the interval of acute minor tenth (~243/100, an octave plus acute minor third) in three. It was so named for the following reason - 133\311 (133 steps of 311edo) is a possible generator, which is placed around 3\7 (1.1¢ flat), three of which makes acute minor third of ~243/200 with octave reduction.
Subgroup: 2.3.5.7
Comma list: 703125/702464, 1600000/1594323
Mapping: [⟨1 8 19 46], ⟨0 -15 -39 -101]]
Wedgie: ⟨⟨ 15 39 101 27 118 125 ]]
POTE generator: ~168/125 = 513.178
Badness: 0.119453
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 4000/3993, 19712/19683
Mapping: [⟨1 8 19 46 18], ⟨0 -15 -39 -101 -34]]
POTE generator: ~121/90 = 513.177
Optimal GPV sequence: Template:Val list
Badness: 0.031296
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 625/624, 1575/1573, 2080/2079, 13720/13689
Mapping: [⟨1 8 19 46 18 64], ⟨0 -15 -39 -101 -34 -141]]
POTE generator: ~35/26 = 513.182
Optimal GPV sequence: Template:Val list
Badness: 0.026418
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 595/594, 625/624, 833/832, 1575/1573, 8624/8619
Mapping: [⟨1 8 19 46 18 64 -22], ⟨0 -15 -39 -101 -34 -141 61]]
POTE generator: ~35/26 = 513.186
Optimal GPV sequence: Template:Val list
Badness: 0.025588
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 595/594, 625/624, 833/832, 969/968, 1216/1215, 1575/1573
Mapping: [⟨1 8 19 46 18 64 -22 53], ⟨0 -15 -39 -101 -34 -141 61 -114]]
POTE generator: ~35/26 = 513.185
Optimal GPV sequence: Template:Val list
Badness: 0.018412
23-limit
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 595/594, 625/624, 760/759, 833/832, 875/874, 969/968, 1105/1104
Mapping: [⟨1 8 19 46 18 64 -22 53 49], ⟨0 -15 -39 -101 -34 -141 61 -114 -104]]
POTE generator: ~35/26 = 513.185
Optimal GPV sequence: Template:Val list
Badness: 0.014343
29-limit
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 595/594, 625/624, 760/759, 784/783, 833/832, 875/874, 969/968, 1045/1044
Mapping: [⟨1 8 19 46 18 64 -22 53 49 72], ⟨0 -15 -39 -101 -34 -141 61 -114 -104 -157]]
POTE generator: ~35/26 = 513.186
Optimal GPV sequence: Template:Val list
Badness: 0.012038
Familia
The familia temperament (113&152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.
Subgroup: 2.3.5.7
Comma list: 16875/16807, 1600000/1594323
Mapping: [⟨1 8 19 20], ⟨0 -25 -65 -67]]
Wedgie: ⟨⟨ 25 65 67 45 36 -27 ]]
POTE generator: ~11907/10000 = 307.941
Badness: 0.144551
11-limit
Subgroup: 2.3.5.7.11
Comma list: 540/539, 1375/1372, 1600000/1594323
Mapping: [⟨1 8 19 20 5], ⟨0 -25 -65 -67 -6]]
POTE generator: ~3200/2673 = 307.906
Optimal GPV sequence: Template:Val list
Badness: 0.051740
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 540/539, 729/728, 1375/1372, 2205/2197
Mapping: [⟨1 8 19 20 5 25], ⟨0 -25 -65 -67 -6 -83]]
POTE generator: ~143/120 = 307.913
Optimal GPV sequence: Template:Val list
Badness: 0.038473