Parkleiness temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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]]
POTE generator: ~125/96 = 459.001
Optimal ET sequence: 34, 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
Optimal ET sequence: 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
Optimal ET sequence: 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
Optimal ET sequence: 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]]
POTE generator: ~3/2 = 701.940
Optimal ET sequence: 80, 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
Optimal ET sequence: 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
Optimal ET sequence: 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
Optimal ET sequence: 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
Optimal ET sequence: 80, 320, 400, 720h, 1120h
Badness: 0.021470