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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== Majvamic ==
== 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.
The ''majvamic'' temperament (183&217) is an extension of the [[Subgroup temperaments #No-sevens subgroup|majvam]] temperament which tempers out the parkleiness comma and the decovulture comma (67108864/66976875, sasabirugugu) in the 7-limit.


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
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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
Line 50: Line 49:
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
Line 63: Line 62:
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]]

Latest revision as of 01:40, 11 August 2025

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

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