Parkleiness temperaments

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Parkleiness rank-two temperaments temper out the parkleiness comma, 1959552/1953125 = [7 7 -9 1 (zotritrigu).

Temperaments dicussed elsewhere include:

Majvamic

The majvamic temperament (183&217) is an extension of the majvam temperament which tempers out the parkleiness comma and the decovulture comma (67108864/66976875, sasabirugugu) in the 7-limit.

Subgroup: 2.3.5.7

Comma list: 1959552/1953125, 67108864/66976875

Mapping: [1 10 5 -32], 0 -22 -7 91]]

Wedgie⟨⟨22 7 -91 -40 -206 -231]]

POTE generator: ~125/96 = 459.001

Optimal GPV sequence34, 149d, 183, 217, 400

Badness: 0.188996

11-limit

Subgroup: 2.3.5.7.11

Comma list: 5632/5625, 46656/46585, 131072/130977

Mapping: [1 10 5 -32 31], 0 -22 -7 91 -72]]

POTE generator: ~125/96 = 459.002

Vals: 34, 149d, 183, 400, 983c, 1383ce, 1783cce

Badness: 0.055046

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 676/675, 1001/1000, 4096/4095, 39366/39325

Mapping: [1 10 5 -32 31 19], 0 -22 -7 91 -72 -40]]

POTE generator: ~125/96 = 459.000

Vals: 34, 149d, 183, 217, 400

Badness: 0.033963

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 676/675, 936/935, 1001/1000, 1156/1155, 4096/4095

Mapping: [1 10 5 -32 31 19 6], 0 -22 -7 91 -72 -40 -5]]

POTE generator: ~125/96 = 459.000

Vals: 34, 149d, 183, 217, 400

Badness: 0.019543

Octogintic

The octogintic temperament has a period of 1/80 octave and tempers out the parkleiness comma and the starscape comma (645700815/645657712), as well as linus comma, 578509309952/576650390625.

Subgroup: 2.3.5.7

Comma list: 1959552/1953125, 645700815/645657712

Mapping: [80 127 186 225], 0 -1 -1 -2]]

Wedgie⟨⟨80 80 160 -59 29 147]]

POTE generator: ~3/2 = 701.940

Optimal GPV sequence80, 320, 400

Badness: 0.307033

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 46656/46585, 391314/390625

Mapping: [80 127 186 225 277], 0 -1 -1 -2 -1]]

POTE generator: ~3/2 = 701.982

Vals: 80, 320, 400

Badness: 0.067939

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 1001/1000, 4225/4224, 4459/4455, 46656/46585

Mapping: [80 127 186 225 277 296], 0 -1 -1 -2 -1 0]]

POTE generator: ~3/2 = 701.796

Vals: 80, 320, 400, 720, 1120

Badness: 0.046158

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 936/935, 1001/1000, 1377/1375, 4225/4224, 4459/4455

Mapping: [80 127 186 225 277 296 327], 0 -1 -1 -2 -1 0 0]]

POTE generator: ~3/2 = 701.800

Vals: 80, 320, 400, 720, 1120

Badness: 0.029279

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 936/935, 969/968, 1001/1000, 1377/1375, 1521/1520, 3136/3135

Mapping: [80 127 186 225 277 296 327 340], 0 -1 -1 -2 -1 0 0 -1]]

POTE generator: ~3/2 = 701.784

Vals: 80, 320, 400, 720h, 1120h

Badness: 0.021470