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. If you are looking for a different kind of neutral third this could be the temperament for you.

Amity

Main article: Amity

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 a pure classical major third. Mos scales of 11, 18, 25, 32, 39, 46 or 53 notes are available.

Subgroup: 2.3.5

Comma list: 1600000/1594323

Mapping: [⟨1 3 6], ⟨0 -5 -13]]

Mapping generators: ~2, ~243/200

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.519

Optimal ET sequence: 7, 39, 46, 53, 152, 205, 463, 668, 873

Badness: 0.021960

Overview to 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, 2401/2400 for amicable, and 16875/16807 for familia.

Temperaments discussed elsewhere include:

Septimal amity

Main article: Amity

Septimal amity can be described as the 46 & 53 temperament, which tempers out 4375/4374 and 5120/5103 in the 7-limit. 99edo is a good tuning, with generator 28\99.

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]]

Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.432

Optimal ET sequence: 7, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.464

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.481

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.390

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.419

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.366

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.407

Optimal ET sequence: 7, 39h, 46, 53, 99h

Badness: 0.017513

Catamite

The catamite temperament (46 & 99ef) 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]]

Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.340

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~128/105 = 339.313

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.313

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~17/14 = 339.325

Optimal ET 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

Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.561

Optimal ET 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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~64/55 = 260.583

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 338.993

Optimal ET sequence: 7d, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.047

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763

Optimal ET sequence: 7d, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.763

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~39/32 = 339.764

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.814

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 339.784

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.553

Optimal ET sequence: 53, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.554

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~243/200 = 339.555

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~208/171 = 339.555

Optimal ET 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]]

Optimal tuning (POTE): ~343/240 = 1\2, ~7/6 = 260.402

Optimal ET sequence: 14c, 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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~7/6 = 260.393

Optimal ET 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]]

Optimal tuning (POTE): ~55/39 = 1\2, ~7/6 = 260.618

Optimal ET 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 amity.

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]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.219

Optimal ET sequence: 14c, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.192

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~9/7 = 430.216

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~189/160 = 286.787

Optimal ET sequence: 46, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 286.797

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.789

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 286.795

Optimal ET sequence: 46, 113, 159

Badness: 0.022036

Trinity

The trinity temperament (152 & 159) tempers out the meter, 703125/702464. It splits the 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]]

Optimal tuning (POTE): ~2 = 1\1, ~168/125 = 513.178

Optimal ET sequence: 152, 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 ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.182

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.185

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~35/26 = 513.186

Optimal ET sequence: 152fj, 159, 311, 781dh, 1092cdgh, 1403cdgh

Badness: 0.012038

Amicable

The amicable temperament tempers out the amity comma and the canousma in addition to the breedsma, and is closely associated with the canou temperament.

While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.

Subgroup: 2.3.5.7

Comma list: 2401/2400, 1600000/1594323

Mapping: [⟨1 3 6 5], ⟨0 -20 -52 -31]]

Wedgie: ⟨⟨20 52 31 36 -7 -74]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.880

Optimal ET sequence: 99, 212, 311, 410, 1131, 1541b

Badness: 0.045473

Amical

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 131072/130977, 1600000/1594323

Mapping: [⟨1 3 6 5 -8], ⟨0 -20 -52 -31 162]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8843

Optimal ET sequence: 99, 212e, 311, 410, 721, 1032, 1343

Badness: 0.100668

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2401/2400, 4096/4095, 741125/739206

Mapping: [⟨1 3 6 5 -8 -5], ⟨0 -20 -52 -31 162 123]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8838

Optimal ET sequence: 99, 212ef, 311, 410, 721, 1032

Badness: 0.049893

Amorous

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 6250/6237, 19712/19683

Mapping: [⟨1 3 6 5 14], ⟨0 -20 -52 -31 -149]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8896

Optimal ET sequence: 99e, 212, 311, 1145c, 1456cd

Badness: 0.048924

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 625/624, 2080/2079, 2401/2400, 10648/10647

Mapping: [⟨1 3 6 5 14 17], ⟨0 -20 -52 -31 -149 -188]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8910

Optimal ET sequence: 99ef, 212, 311, 834, 1145c

Badness: 0.034681

Pseudoamical

Subgroup: 2.3.5.7.11

Comma list: 385/384, 1375/1372, 1600000/1594323

Mapping: [⟨1 3 6 5 -1], ⟨0 -20 -52 -31 63]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9091

Optimal ET sequence: 99, 113, 212, 961ccdeee

Badness: 0.085837

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 385/384, 1375/1372, 19773/19712

Mapping: [⟨1 3 6 5 -1 2], ⟨0 -20 -52 -31 63 24]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9127

Optimal ET sequence: 99, 113, 212, 537cdeff, 749ccdeefff

Badness: 0.047025

Pseudoamorous

Subgroup: 2.3.5.7.11

Comma list: 243/242, 441/440, 980000/970299

Mapping: [⟨1 3 6 5 7], ⟨0 -20 -52 -31 -50]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.8917

Optimal ET sequence: 99e, 212e

Badness: 0.056583

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 243/242, 364/363, 441/440, 1875/1859

Mapping: [⟨1 3 6 5 7 10], ⟨0 -20 -52 -31 -50 -89]]

Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 84.9164

Optimal ET sequence: 99ef, 113, 212ef

Badness: 0.042826

Floral

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 9801/9800, 14641/14580

Mapping: [⟨2 6 12 10 13], ⟨0 -20 -52 -31 -43]]

Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8788

Optimal ET sequence: 198, 212, 410

Badness: 0.065110

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 1716/1715, 14641/14580

Mapping: [⟨2 6 12 10 13 19], ⟨0 -20 -52 -31 -43 -82]]

Optimal tuning (POTE): ~99/70 = 1\2, ~21/20 = 84.8750

Optimal ET sequence: 198, 410

Badness: 0.037013

Humorous

Subgroup: 2.3.5.7.11

Comma list: 2401/2400, 3025/3024, 1600000/1594323

Mapping: [⟨1 3 6 5 3], ⟨0 -40 -104 -62 13]]

Optimal tuning (POTE): ~2 = 1\1, ~4096/3993 = 42.4391

Optimal ET sequence: 85c, 113, 198, 311, 509, 820

Badness: 0.058249

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2200/2197, 2401/2400, 3025/3024

Mapping: [⟨1 3 6 5 3 6], ⟨0 -40 -104 -62 13 -65]]

Optimal tuning (POTE): ~2 = 1\1, ~40/39 = 42.4391

Optimal ET sequence: 85c, 113, 198, 311, 509, 820f

Badness: 0.028267

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]]

Optimal tuning (POTE): ~2 = 1\1, ~11907/10000 = 307.941

Optimal ET sequence: 39d, 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]]

Optimal tuning (POTE): ~2 = 1\1, ~3200/2673 = 307.906

Optimal ET 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]]

Optimal tuning (POTE): ~2 = 1\1, ~143/120 = 307.913

Optimal ET sequence: 39df, 74cdf, 113, 152f, 265, 417f

Badness: 0.038473

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