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 or 245/243) → Porcupine family
• Wizard (+225/224) → Marvel temperaments
• Echidna (+1728/1715 or 2048/2025) → Diaschismic family
• Harry (+2401/2400 or 19683/19600) → Gravity family and Breedsmic temperaments
• Octoid (+4375/4374 or 16875/16807 → Ragismic microtemperaments
• Septisuperfourth (+6144/6125) → 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]]

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

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

Optimal tuning (POTE): ~343/243 = 1\2, ~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]]

Wedgie: ⟨⟨ 6 -48 10 -90 -1 158 ]]

Optimal tuning (POTE): ~343/243 = 1\2, ~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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911

Optimal ET sequence: 36, 94, 130, 224, 354, 578

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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~9/7 = 433.911

Optimal ET sequence: 36, 94, 130, 224, 354, 578

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 ]]

Optimal tuning (POTE): ~343/243 = 1\2, ~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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~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]]

Optimal tuning (POTE): ~99/70 = 1\2, ~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]]

Optimal tuning (POTE): ~17/12 = 1\2, ~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 ]]

Optimal tuning (POTE): ~2450/2187 = 1\6, ~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]]

Optimal tuning (POTE): ~121/108 = 1\6, ~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 the 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 ]]

Optimal tuning (POTE): ~1029/1024 = 1\94, ~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]]

Optimal tuning (POTE): ~1029/1024 = 1\94, ~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]]

Optimal tuning (POTE): ~169/168 = 1\94, ~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]]

Optimal tuning (POTE): ~169/168 = 1\94, ~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 2 14 5], ⟨0 3 2 5]]

mapping generators: ~15/14, ~135/98

Wedgie: ⟨⟨ 30 20 50 -38 -5 60 ]]

Optimal tuning (CTE): ~15/14 = 1\10, ~135/98 = 553.810 (~36/35 = 46.190)

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 2 14 5 30], ⟨0 3 2 5 1]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.783 (~36/35 = 46.217)

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 2 14 5 30 37], ⟨0 3 2 5 1 0]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.783 (~36/35 = 46.217)

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 2 14 5 30 37 27], ⟨0 3 2 5 1 0 3]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.862 (~36/35 = 46.138)

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 2 14 5 30 37 27 24], ⟨0 3 2 5 1 0 3 4]]

Optimal tuning (CTE): ~15/14 = 1\10, ~11/8 = 553.913 (~36/35 = 46.087)

Optimal ET sequence: 50, 80, 130

Badness: 0.018232