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

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

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

Vals: 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

Vals: 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

Vals: 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

Vals: Template:Val list

Badness: 0.022448

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

Vals: Template:Val list

Badness: 0.031307

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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: 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

Vals: Template:Val list

Badness: 0.022036

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

Vals: Template:Val list

Badness: 0.051740