Stearnsmic clan

The stearnsmic clan tempers out the stearnsma, the no-fives comma [1 10 0 -6⟩ = 118098/117649.

Stearnsmic temperaments not listed include:

• Hedgehog, {50/49, 245/243} → Porcupine family
• Wizard, {225/224, 118098/117649} → Marvel temperaments
• Echidna, {1728/1715, 2048/2025} → Diaschismic family
• Harry, {2401/2400, 19683/19600} → Gravity family and Breedsmic temperaments
• Octoid, {4375/4374, 16875/16807} → Ragismic microtemperaments
• Septisuperfourth, {6144/6125, 118098/117649} → Escapade family

Considered below are pogo, supers, stearnscape, garistearn and decistearn.

No-five stearnsmic

Subgroup: 2.3.7

Comma list: 118098/117649

Sval mapping: [⟨2 1 2], ⟨0 3 5]]

Gencom mapping: [⟨2 1 0 2], ⟨0 3 0 5]]

POTE generator: ~9/7 = 433.888

Optimal ET sequence: 14, 22, 36, 94, 130, 224, 354, 484, 838

Pogo

See also: Schismatic family § Pogo

The pogo temperament (94&130) tempers out the schisma, whose amount of tempering of the fifth is just about right for the stearnsma.

Subgroup: 2.3.5.7

Comma list: 32805/32768, 118098/117649

Mapping: [⟨2 1 22 2], ⟨0 3 -24 5]]

Mapping generators: ~343/243, ~9/7

Wedgie: ⟨⟨ 6 -48 10 -90 -1 158 ]]

POTE generator: ~9/7 = 433.901

Optimal ET sequence: 36, 94, 130, 224, 354

Badness: 0.079635

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 32805/32768

Mapping: [⟨2 1 22 2 25], ⟨0 3 -24 5 -25]]

Mapping generators: ~99/70, ~9/7

POTE generator: ~9/7 = 433.911

Vals: Template:Val list

Badness: 0.031857

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 4096/4095

Mapping: [⟨2 1 22 2 25 -2], ⟨0 3 -24 5 -25 13]]

Mapping generators: ~99/70, ~9/7

POTE generator: ~9/7 = 433.911

Vals: Template:Val list

Badness: 0.017514

Supers

Subgroup: 2.3.5.7

Comma list: 5120/5103, 118098/117649

Mapping: [⟨2 1 -12 2], ⟨0 3 23 5]]

Wedgie: ⟨⟨ 6 46 10 59 -1 -106 ]]

POTE generator: ~9/7 = 434.218

Optimal ET sequence: 58, 94, 152

Badness: 0.092748

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 5120/5103

Mapping: [⟨2 1 -12 2 -9], ⟨0 3 23 5 22]]

POTE generator: ~9/7 = 434.217

Optimal ET sequence: 58, 94, 152

Badness: 0.028240

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1575/1573

Mapping: [⟨2 1 -12 2 -9 -2], ⟨0 3 23 5 22 13]]

POTE generator: ~9/7 = 434.221

Optimal ET sequence: 58, 94, 152f

Badness: 0.021645

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 170/169, 289/288, 352/351, 442/441, 561/560

Mapping: [⟨2 1 -12 2 -9 -2 6], ⟨0 3 23 5 22 13 3]]

POTE generator: ~9/7 = 434.181

Optimal ET sequence: 58, 94, 152f

Badness: 0.021316

Stearnscape

Subgroup: 2.3.5.7

Comma list: 118098/117649, 250047/250000

Mapping: [⟨6 3 2 6], ⟨0 6 11 10]]

Mapping generators: ~2450/2187, ~567/500

Wedgie: ⟨⟨ 36 66 60 21 -6 -46 ]]

POTE generator: ~567/500 = 216.942

Optimal ET sequence: 72, 210, 282, 354

Badness: 0.090467

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 137781/137500

Mapping: [⟨6 3 2 6 11], ⟨0 6 11 10 9]]

POTE generator: ~567/500 = 216.950

Optimal ET sequence: 72, 282, 354

Badness: 0.032096

Garistearn

The garistearn temperament (94&282) has a period of 1/94 octave and tempers out 118098/117649 and garischisma, 33554432/33480783.

Subgroup: 2.3.5.7

Comma list: 118098/117649, 33554432/33480783

Mapping: [⟨94 149 0 264], ⟨0 0 1 0]]

Wedgie: ⟨⟨ 0 94 0 149 0 -264 ]]

POTE generator: ~5/4 = 386.7805

Optimal ET sequence: 94, 282, 658d, 940dd

Badness: 0.307043

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 4000/3993, 33554432/33480783

Mapping: [⟨94 149 0 264 107], ⟨0 0 1 0 1]]

POTE generator: ~5/4 = 386.5968

Optimal ET sequence: 94, 282, 376, 658de

Badness: 0.082255

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 729/728, 1575/1573, 28672/28561

Mapping: [⟨94 149 0 264 107 348], ⟨0 0 1 0 1 0]]

POTE generator: ~5/4 = 386.8141

Optimal ET sequence: 94, 282

Badness: 0.045941

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 540/539, 729/728, 1156/1155, 1575/1573, 2880/2873

Mapping: [⟨94 149 0 264 107 348 166], ⟨0 0 1 0 1 0 1]]

POTE generator: ~5/4 = 386.8420

Optimal ET sequence: 94, 282

Badness: 0.027608

Decistearn

See also: Trisedodge family

The decistearn temperament (80&130) has a period of 1/10 octave and tempers out the hemimean comma, 3136/3125 as well as the linus comma.

Subgroup: 2.3.5.7

Comma list: 3136/3125, 118098/117649

Mapping: [⟨10 17 24 30], ⟨0 -3 -2 -5]]

Wedgie: ⟨⟨ 30 20 50 -38 -5 60 ]]

POTE generator: ~6/5 = 313.960

Optimal ET sequence: 50, 80, 130, 470cd, 600cd, 730cd, 860ccd

Badness: 0.095543

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 3136/3125, 4000/3993

Mapping: [⟨10 17 24 30 35], ⟨0 -3 -2 -5 -1]]

POTE generator: ~6/5 = 314.079

Optimal ET sequence: 50, 80, 130, 210e, 340ce

Badness: 0.038556

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 364/363, 540/539, 3136/3125

Mapping: [⟨10 17 24 30 35 37], ⟨0 -3 -2 -5 -1 0]]

POTE generator: ~6/5 = 313.947

Optimal ET sequence: 50, 80, 130

Badness: 0.026895

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 221/220, 289/288, 351/350, 540/539, 1632/1625

Mapping: [⟨10 17 24 30 35 37 42], ⟨0 -3 -2 -5 -1 0 -3]]

POTE generator: ~6/5 = 313.931

Optimal ET sequence: 50, 80, 130

Badness: 0.024234

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 221/220, 289/288, 351/350, 361/360, 456/455, 476/475

Mapping: [⟨10 17 24 30 35 37 42 44], ⟨0 -3 -2 -5 -1 0 -3 -4]]

POTE generator: ~6/5 = 313.949

Optimal ET sequence: 50, 80, 130

Badness: 0.018232