Wizmic microtemperaments
This is a collection of microtemperaments which tempers out the wizma, [-6 -8 2 5⟩ = 420175/419904.
Discussed elsewhere are:
- Superpyth, {64/63, 245/243} → Archytas clan
- Cloudtone, {81/80, 16875/16384} → Meantone family
- Oolong, {126/125, 117649/116640} → Starling temperaments
- Wizard, {225/224, 118098/117649} → Marvel temperaments
- Hemiseven, {1029/1024, 19683/19600} → Gamelismic clan
- Ennealimmal, {2401/2400, 4375/4374} → Ragismic microtemperaments
- Sengagen, {3136/3125, 420175/419904} → Hemimean clan
- Septiquarter, {5120/5103, 420175/419904} → Hemifamity temperaments
- Hendecatonic, {6144/6125, 10976/10935} → Porwell temperaments
- Sqrtphi, {15625/15552, 16875/16807} → Kleismic family
- Tsaharuk, {32805/32768, 420175/419904} → Schismatic family
- Fifthplus, {65625/65536, 420175/419904} → Horwell temperaments
- Octowerck, {321489/320000, 420175/419904} → Varunismic temperaments
- Quinwell, {420175/419904, 2109375/2097152} → Semicomma family
- Decavish, {420175/419904, 2202927104/2197265625} → Vishnuzmic family
Considered below are qak, tokko, tertiathirds, and witch.
Qak
Subgroup: 2.3.5.7
Comma list: 420175/419904, 703125/702464
Mapping: [⟨1 27 11 40], ⟨0 -41 -14 -60]]
Mapping generators: ~2, ~192/125
Wedgie: ⟨⟨ 41 14 60 -73 -20 100 ]]
POTE generator: ~192/125 = 743.856
Badness: 0.029267
Tokko
Subgroup: 2.3.5.7
Comma list: 420175/419904, 5250987/5242880
Mapping: [⟨1 12 56 -2], ⟨0 -13 -67 6]]
Mapping generators: ~2, ~256/147
Wedgie: ⟨⟨ 13 67 -6 76 -46 -202 ]]
POTE generator: ~256/147 = 961.401
Badness: 0.044417
Tertiathirds
The tertiathirds temperament (121&270) tempers out the quasiorwellisma, 29360128/29296875 in the 7-limit, as well as the wizma. This temperament splits the interval of 5/4 into three 14/13 generators.
Subgroup: 2.3.5.7
Comma list: 420175/419904, 29360128/29296875
Mapping: [⟨1 48 5 76], ⟨0 -52 -3 -82]]
Mapping generators: ~2, ~6272/3375
Wedgie: ⟨⟨ 52 3 82 -116 -16 182 ]]
POTE generator: ~6272/3375 = 1071.1121
Badness: 0.093005
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 117649/117612
Mapping: [⟨1 48 5 76 107], ⟨0 -52 -3 -82 -116]]
POTE generator: ~245/132 = 1071.1102
Vals: Template:Val list
Badness: 0.033322
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Mapping: [⟨1 48 5 76 107 76], ⟨0 -52 -3 -82 -116 -81]]
POTE generator: ~13/7 = 1071.1098
Vals: Template:Val list
Badness: 0.019494
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224
Mapping: [⟨1 48 5 76 107 76 63], ⟨0 -52 -3 -82 -116 -81 -66]]
POTE generator: ~13/7 = 1071.1088
Vals: Template:Val list
Badness: 0.019107
Witch
The witch temperament (99&166) tempers out wizma (420175/419904) and the amity comma (1600000/1594323) as well as the hemfiness comma (4096000/4084101, saquinru-atriyo).
Subgroup: 2.3.5.7
Comma list: 420175/419904, 1600000/1594323
Mapping: [⟨1 18 45 12], ⟨0 -25 -65 -14]
Mapping generators: ~2, ~63/40
Wedgie: ⟨⟨ 25 65 14 45 -48 -150 ]]
POTE generator: ~63/40 = 787.902
Badness: 0.080608
Semiwitch
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 41503/41472, 585640/583443
Mapping: [⟨2 11 25 10 16], ⟨0 -25 -65 -14 -29]]
Mapping generators: ~99/70, ~49/44
POTE generator: ~49/44 = 187.904
Vals: Template:Val list
Badness: 0.088189
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 2200/2197, 17303/17280
Mapping: [⟨2 11 25 10 16 24], ⟨0 -25 -65 -14 -29 -53]]
POTE generator: ~39/35 = 187.904
Vals: Template:Val list
Badness: 0.038009
Hitch
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 117649/117612, 1600000/1594323
Mapping: [⟨1 18 45 12 -10], ⟨0 -50 -130 -28 41]]
Mapping generators: ~2, ~1120/891
POTE generator: ~1120/891 = 393.950
Vals: Template:Val list
Badness: 0.093482
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1716/1715, 3025/3024, 1600000/1594323
Mapping: [⟨1 18 45 12 -10 71], ⟨0 -50 -130 -28 41 -205]]
POTE generator: ~1120/891 = 393.948
Vals: Template:Val list
Badness: 0.060716
Hitcher
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 13720/13689, 28672/28561
Mapping: [⟨1 18 45 12 -10 6], ⟨0 -50 -130 -28 41 -7]]
POTE generator: ~49/39 = 393.949
Vals: Template:Val list
Badness: 0.059591