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
• Decavish, {420175/419904, 2202927104/2197265625} → Vishnuzmic family #Decavish

Considered below are qak, tokko and tertiathirds.

Qak

Subgroup: 2.3.5.7

Comma list: 420175/419904, 703125/702464

Mapping: [⟨1 -14 -3 -20], ⟨0 41 14 60]]

⟨⟨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]]

⟨⟨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]]

⟨⟨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

See also: Amity family

The witch temperament (99&166) tempers out wizma (420175/419904) and amity comma (1600000/1594323) as well as hemfiness comma (4096000/4084101).

Subgroup: 2.3.5.7

Comma list: 420175/419904, 1600000/1594323

Mapping: [⟨1 -7 -20 -2], ⟨0 25 65 14]

⟨⟨25 65 14 45 -48 -150]]

POTE generator: ~80/63 = 412.098

Badness: 0.080608