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
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
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
Badness: 0.027608
Decistearn
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 ]]
Optimal tuning (POTE): ~15/14 = 1\10, ~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]]
Optimal tuning (POTE): ~15/14 = 1\10, ~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]]
Optimal tuning (POTE): ~15/14 = 1\10, ~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]]
Optimal tuning (POTE): ~15/14 = 1\10, ~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]]
Optimal tuning (POTE): ~15/14 = 1\10, ~6/5 = 313.949
Optimal ET sequence: 50, 80, 130
Badness: 0.018232