Wizmic microtemperaments: Difference between revisions
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Discussed elsewhere are [[Vishnuzmic family #Decavish|decavish]], [[ennealimmal]], [[Horwell temperaments #Fifthplus|fifthplus]], [[Gamelismic clan #Hemiseven|hemiseven]], [[Porwell temperaments #Hendecatonic|hendecatonic]], [[Varunismic temperaments #Octowerck|octowerck]], [[Hemimean clan #Sengagen|sengagen]], [[Hemifamity temperaments #Septiquarter|septiquarter]], [[tsaharuk]], and [[wizard]]. | Discussed elsewhere are [[Vishnuzmic family #Decavish|decavish]], [[ennealimmal]], [[Horwell temperaments #Fifthplus|fifthplus]], [[Gamelismic clan #Hemiseven|hemiseven]], [[Porwell temperaments #Hendecatonic|hendecatonic]], [[Varunismic temperaments #Octowerck|octowerck]], [[Hemimean clan #Sengagen|sengagen]], [[Hemifamity temperaments #Septiquarter|septiquarter]], [[tsaharuk]], and [[wizard]]. | ||
== Qak | == Qak == | ||
[[Comma list]]: 420175/419904, 703125/702464 | [[Comma list]]: 420175/419904, 703125/702464 | ||
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[[Badness]]: 0.029267 | [[Badness]]: 0.029267 | ||
== Tokko | == Tokko == | ||
[[Comma list]]: 420175/419904, 5250987/5242880 | [[Comma list]]: 420175/419904, 5250987/5242880 | ||
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[[Badness]]: 0.044417 | [[Badness]]: 0.044417 | ||
== Tertiathirds | == Tertiathirds == | ||
The ''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 | [[Comma list]]: 420175/419904, 29360128/29296875 | ||
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[[Badness]]: 0.093005 | [[Badness]]: 0.093005 | ||
=== 11-limit | === 11-limit === | ||
Comma list: 3025/3024, 5632/5625, 117649/117612 | Comma list: 3025/3024, 5632/5625, 117649/117612 | ||
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Badness: 0.033322 | Badness: 0.033322 | ||
=== 13-limit | === 13-limit === | ||
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224 | Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224 | ||
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Badness: 0.019494 | Badness: 0.019494 | ||
=== 17-limit | === 17-limit === | ||
Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224 | Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224 | ||
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[[Category:Temperament]] | [[Category:Temperament]] | ||
[[Category:Temperament collection]] | |||
[[Category:Rank 2]] | [[Category:Rank 2]] | ||
[[Category:Wizmic]] | [[Category:Wizmic]] | ||
Revision as of 01:18, 6 June 2021
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
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
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
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