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Parkleiness temperaments: Difference between revisions

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'''Parkleiness''' rank-two temperaments temper out the ''parkleiness'' comma, 1959552/1953125 = {{monzo|7 7 -9 1}} (zotritrigu).
{{Technical data page}}
'''Parkleiness''' [[rank two temperaments]] temper out the ''parkleiness'' comma, 1959552/1953125 = {{monzo|7 7 -9 1}} (zotritrigu).


Temperaments dicussed elsewhere include:  
Temperaments dicussed elsewhere include:  
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[[Mapping]]: [{{val|1 10 5 -32}}, {{val|0 -22 -7 91}}]
[[Mapping]]: [{{val|1 10 5 -32}}, {{val|0 -22 -7 91}}]
{{Multival|legend=1|22 7 -91 -40 -206 -231}}


[[POTE generator]]: ~125/96 = 459.001
[[POTE generator]]: ~125/96 = 459.001


{{Val list|legend=1| 34, 149d, 183, 217, 400 }}
{{Optimal ET sequence|legend=1| 34, 149d, 183, 217, 400 }}


[[Badness]]: 0.188996
[[Badness]]: 0.188996
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POTE generator: ~125/96 = 459.002
POTE generator: ~125/96 = 459.002


Vals: {{Val list| 34, 149d, 183, 400, 983c, 1383ce, 1783cce }}
{{Optimal ET sequence|legend=1| 34, 149d, 183, 400, 983c, 1383ce, 1783cce }}


Badness: 0.055046
Badness: 0.055046
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POTE generator: ~125/96 = 459.000
POTE generator: ~125/96 = 459.000


Vals: {{Val list| 34, 149d, 183, 217, 400 }}
{{Optimal ET sequence|legend=1| 34, 149d, 183, 217, 400 }}


Badness: 0.033963
Badness: 0.033963
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POTE generator: ~125/96 = 459.000
POTE generator: ~125/96 = 459.000


Vals: {{Val list| 34, 149d, 183, 217, 400 }}
{{Optimal ET sequence|legend=1| 34, 149d, 183, 217, 400 }}


Badness: 0.019543
Badness: 0.019543


[[Category:Temperament]]
== Octogintic ==
[[Category:Temperament collection]]
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]]: [{{val|80 127 186 225}}, {{val|0 -1 -1 -2}}]
 
[[POTE generator]]: ~3/2 = 701.940
 
{{Optimal ET sequence|legend=1| 80, 320, 400 }}
 
[[Badness]]: 0.307033
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 9801/9800, 46656/46585, 391314/390625
 
Mapping: [{{val|80 127 186 225 277}}, {{val|0 -1 -1 -2 -1}}]
 
POTE generator: ~3/2 = 701.982
 
{{Optimal ET sequence|legend=1| 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: [{{val|80 127 186 225 277 296}}, {{val|0 -1 -1 -2 -1 0}}]
 
POTE generator: ~3/2 = 701.796
 
{{Optimal ET sequence|legend=1| 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: [{{val|80 127 186 225 277 296 327}}, {{val|0 -1 -1 -2 -1 0 0}}]
 
POTE generator: ~3/2 = 701.800
 
{{Optimal ET sequence|legend=1| 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: [{{val|80 127 186 225 277 296 327 340}}, {{val|0 -1 -1 -2 -1 0 0 -1}}]
 
POTE generator: ~3/2 = 701.784
 
{{Optimal ET sequence|legend=1| 80, 320, 400, 720h, 1120h }}
 
Badness: 0.021470
 
[[Category:Temperament collections]]
[[Category:Pages with mostly numerical content]]
[[Category:Rank 2]]
[[Category:Rank 2]]
Retrieved from "https://en.xen.wiki/w/Parkleiness_temperaments"