Wizmic microtemperaments: Difference between revisions

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__FORCETOC__
A wizmic temperament is one which tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904.
A wizmic temperament is one which tempers out the wizma, |-6 -8 2 5> = 420175/419904.


Discussed elsewhere are [[ennealimmal]], [[fifthplus]], [[hemiseven]], [[hendecatonic]], [[sengagen]], [[septiquarter]], [[tsaharuk]], and [[wizard]].
Discussed elsewhere are [[Vishnuzmic family #Decavish|decavish]], [[Ragismic microtemperaments #Ennealimmal|ennealimmal]], [[Horwell temperaments #Fifthplus|fifthplus]], [[Gamelismic clan #Hemiseven|hemiseven]], [[Porwell temperaments #Hendecatonic|hendecatonic]], [[Hemimean clan #Sengagen|sengagen]], [[Hemifamity temperaments #Septiquarter|septiquarter]], [[Schismatic family #Tsaharuk|tsaharuk]], and [[Marvel temperaments #Wizard|wizard]].


= Qak =
= Qak =
[[Comma list]]: 420175/419904, 703125/702464
[[Comma list]]: 420175/419904, 703125/702464


[[Mapping]]: [<1 -14 -3 -20|, <0 41 14 60|]
[[Mapping]]: [{{val|1 -14 -3 -20}}, {{val|0 41 14 60}}]


[[Wedgie]]: <<41 14 60 -73 -20 100||
[[Wedgie]]: {{multival|41 14 60 -73 -20 100}}


[[POTE tuning|POTE generator]]: ~125/96 = 456.144
[[POTE tuning|POTE generator]]: ~125/96 = 456.144
Line 20: Line 19:
[[Comma list]]: 420175/419904, 5250987/5242880
[[Comma list]]: 420175/419904, 5250987/5242880


[[Mapping]]: [<1 -1 -11 4|, <0 13 67 -6|]
[[Mapping]]: [{{val|1 -1 -11 4}}, {{val|0 13 67 -6}}]


[[Wedgie]]: <<13 67 -6 76 -46 -202||
[[Wedgie]]: {{multival|13 67 -6 76 -46 -202}}


[[POTE tuning|POTE generator]]: ~147/128 = 238.599
[[POTE tuning|POTE generator]]: ~147/128 = 238.599
Line 35: Line 34:
[[Comma list]]: 420175/419904, 29360128/29296875
[[Comma list]]: 420175/419904, 29360128/29296875


[[Mapping]]: [<1 -4 2 -6|, <0 52 3 82|]
[[Mapping]]: [{{val|1 -4 2 -6}}, {{val|0 52 3 82}}]


[[Wedgie]]: <<52 3 82 -116 -16 182||
[[Wedgie]]: {{multival|52 3 82 -116 -16 182}}


[[POTE tuning|POTE generator]]: ~3375/3136 = 128.8879
[[POTE tuning|POTE generator]]: ~3375/3136 = 128.8879
Line 48: Line 47:
Comma list: 3025/3024, 5632/5625, 117649/117612
Comma list: 3025/3024, 5632/5625, 117649/117612


Mapping: [<1 -4 2 -6 -9|, <0 52 3 82 116|]
Mapping: [{{val|1 -4 2 -6 -9}}, {{val|0 52 3 82 116}}]


POTE generator: ~264/245 = 128.8898
POTE generator: ~264/245 = 128.8898
Line 59: Line 58:
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224


Mapping: [<1 -4 2 -6 -9 -5|, <0 52 3 82 116 81|]
Mapping: [{{val|1 -4 2 -6 -9 -5}}, {{val|0 52 3 82 116 81}}]


POTE generator: ~14/13 = 128.8902
POTE generator: ~14/13 = 128.8902
Line 70: Line 69:
Comma list: 676/675, 715/714, 1716/1715, 2025/2023, 4225/4224
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|]
Mapping: [{{val|1 -4 2 -6 -9 -5 -3}}, {{val|0 52 3 82 116 81 66}}]


POTE generator: ~14/13 = 128.8912
POTE generator: ~14/13 = 128.8912

Revision as of 04:58, 4 May 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, 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

Template:Val list

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

Template:Val list

Badness: 0.044417

Tertiathirds

The tertiathirds temperament (121&270, named by Xenllium) 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

Template:Val list

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

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