Wizmic microtemperaments

A wizmic temperament is one which tempers out the wizma, [-6 -8 2 5⟩ = 420175/419904.

Discussed elsewhere are decavish, ennealimmal, fifthplus, hemiseven, hendecatonic, octowerck, sengagen, septiquarter, tsaharuk, and wizard.

Qak

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

Template:Val list

Badness: 0.029267

Tokko

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

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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.

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

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Badness: 0.093005

11-limit

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

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

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