Amity family

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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 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

Main article: Amity
See also: Ragismic microtemperaments #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

Optimal GPV sequence7, 39, 46, 53, 152, 205, 463, 668, 873

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:

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

Optimal GPV sequence7, 32c, 39, 46, 53, 99, 251, 350, 601cd, 951bcdd

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: 46e, 53, 99e, 152, 555dee, 707ddee, 859bddee

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: 46ef, 53, 99ef, 152f *

* 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: 7, 39, 46, 53, 99

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: 7, 39, 46, 53, 99

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: 7, 39, 46, 53, 99

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: 7, 39h, 46, 53, 99h

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: 46, 99e, 145, 244e

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: 46, 99ef, 145

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: 46, 99ef, 145

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: 46, 99ef, 145

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: 14cde, 46, 106, 152, 350, 502d

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: 46, 106f, 152f, 198, 350f, 548cdff

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

Optimal GPV sequence7d, 39d, 46, 131c, 177c

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: 7d, 39d, 46, 177c, 223bc, 269bce

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

Optimal GPV sequence7d, 46d, 53, 113, 166

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: 53, 113, 166

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: 53, 113, 166

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: 7d, 46d, 53, 60e, 113e

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: 7d, 46d, 53, 60e, 113e

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

Optimal GPV sequence53, 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: [1 3 6 -17 36], 0 -5 -13 70 -115]]

POTE generator: ~243/200 = 339.554

Optimal GPV sequence: 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: [1 3 6 -17 36 17], 0 -5 -13 70 -115 -47]]

POTE generator: ~243/200 = 339.554

Optimal GPV sequence: 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: [1 3 6 -17 36 17 -31], 0 -5 -13 70 -115 -47 124]]

POTE generator: ~243/200 = 339.555

Optimal GPV sequence: 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: [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: 53, 205deg, 258g, 311, 675, 986, 1661cfh

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

Optimal GPV sequence14c, 32c, 46, 60, 106d

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: 14c, 32c, 46, 60e, 106de

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: 14cf, 32cf, 46, 106def, 152def

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

Optimal GPV sequence14c, 39d, 53

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: 14c, 39d, 53

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: 14cf, 39df, 53

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

Optimal GPV sequence46, 113, 159

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: 46, 113, 159

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: 46, 113, 159

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: 46, 113, 159

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

Optimal GPV sequence152, 311, 463, 774

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: 152, 311, 463, 774, 1237e

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: 152f, 311

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: 152f, 159, 311, 1092cdg, 1403cdg, 1714cdeg

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: 152f, 159, 311, 1403cdgh, 1714cdegh, 2025cdefgghh, 2336bccdefgghh

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: 152f, 159, 311, 1092cdgh, 1403cdgh, 1714cdeghi

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: 152fj, 159, 311, 781dh, 1092cdgh, 1403cdgh

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

Optimal GPV sequence39d, 74cd, 113, 152, 265, 417, 986d

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: 39d, 74cd, 113, 152, 417, 569de, 721de

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: 39df, 74cdf, 113, 152f, 265, 417f

Badness: 0.038473