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 #Superpyth
- Cloudtone, {81/80, 16875/16384} → Meantone family #Cloudtone
- Oolong, {126/125, 117649/116640} → Starling temperaments #Oolong
- Wizard, {225/224, 118098/117649} → Marvel temperaments #Wizard
- Hemiseven, {1029/1024, 19683/19600} → Gamelismic clan #Hemiseven
- Ennealimmal, {2401/2400, 4375/4374} → Ragismic microtemperaments #Ennealimmal
- Sengagen, {3136/3125, 420175/419904} → Hemimean clan #Sengagen
- Septiquarter, {5120/5103, 420175/419904} → Hemifamity temperaments #Septiquarter
- Hendecatonic, {6144/6125, 10976/10935} → Porwell temperaments #Hendecatonic
- Sqrtphi, {15625/15552, 16875/16807} → Kleismic family #Sqrtphi
- Tsaharuk, {32805/32768, 420175/419904} → Schismatic family #Tsaharuk
- Fifthplus, {65625/65536, 420175/419904} → Horwell temperaments #Fifthplus
- Octowerck, {321489/320000, 420175/419904} → Varunismic temperaments #Octowerck
- Quinwell, {420175/419904, 2109375/2097152} → Semicomma family #Quinwell
- Decavish, {420175/419904, 2202927104/2197265625} → Vishnuzmic family #Decavish
Qak
Subgroup: 2.3.5.7
Comma list: 420175/419904, 703125/702464
Mapping: [⟨1 -14 -3 -20], ⟨0 41 14 60]]
Wedgie: ⟨⟨ 41 14 60 -73 -20 100 ]]
POTE generator: ~125/96 = 456.144
Badness: 0.029267
Tokko
Subgroup: 2.3.5.7
Comma list: 420175/419904, 5250987/5242880
Mapping: [⟨1 -1 -11 4], ⟨0 13 67 -6]]
Wedgie: ⟨⟨ 13 67 -6 76 -46 -202 ]]
POTE generator: ~147/128 = 238.599
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 -4 2 -6], ⟨0 52 3 82]]
Wedgie: ⟨⟨ 52 3 82 -116 -16 182 ]]
POTE generator: ~3375/3136 = 128.8879
Badness: 0.093005
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 117649/117612
Mapping: [⟨1 -4 2 -6 -9], ⟨0 52 3 82 116]]
POTE generator: ~264/245 = 128.8898
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 -4 2 -6 -9 -5], ⟨0 52 3 82 116 81]]
POTE generator: ~14/13 = 128.8902
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 -4 2 -6 -9 -5 -3], ⟨0 52 3 82 116 81 66]]
POTE generator: ~14/13 = 128.8912
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 -7 -20 -2], ⟨0 25 65 14]
Wedgie: ⟨⟨ 25 65 14 45 -48 -150 ]]
POTE generator: ~80/63 = 412.098
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]]
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]]
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