Wizmic microtemperaments: Difference between revisions

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A wizmic temperament is one which tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904.
This is a collection of microtemperaments which tempers out the wizma, {{monzo|-6 -8 2 5}} = 420175/419904.


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 ==
Subgroup: 2.3.5.7
[[Comma list]]: 420175/419904, 703125/702464
[[Comma list]]: 420175/419904, 703125/702464


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


[[Wedgie]]: {{multival|41 14 60 -73 -20 100}}
{{Multival|legend=1| 41 14 60 -73 -20 100 }}


[[POTE tuning|POTE generator]]: ~125/96 = 456.144
[[POTE generator]]: ~125/96 = 456.144


{{Val list|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
{{Val list|legend=1| 50, 121, 171, 976, 1147, 1318, 1489, 1660, 1831, 2002c, 3833cd }}
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== Tokko ==
== Tokko ==
Subgroup: 2.3.5.7
[[Comma list]]: 420175/419904, 5250987/5242880
[[Comma list]]: 420175/419904, 5250987/5242880


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


[[Wedgie]]: {{multival|13 67 -6 76 -46 -202}}
{{Multival|legend=1| 13 67 -6 76 -46 -202 }}


[[POTE tuning|POTE generator]]: ~147/128 = 238.599
[[POTE generator]]: ~147/128 = 238.599


{{Val list|legend=1| 5, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}
{{Val list|legend=1| 5, 161c, 166, 171, 1544d, 1715d, 1886d, 2057d, 2228d, 2399d, 2570d, 2741d, 2912dd, 3083cdd }}


[[Badness]]: 0.044417
[[Badness]]: 0.044417
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== Tertiathirds ==
== 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.
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.
Subgroup: 2.3.5.7


[[Comma list]]: 420175/419904, 29360128/29296875
[[Comma list]]: 420175/419904, 29360128/29296875


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


[[Wedgie]]: {{multival|52 3 82 -116 -16 182}}
{{Multival|legend=1| 52 3 82 -116 -16 182 }}


[[POTE tuning|POTE generator]]: ~3375/3136 = 128.8879
[[POTE generator]]: ~3375/3136 = 128.8879


{{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
{{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
Line 45: Line 51:


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 117649/117612
Comma list: 3025/3024, 5632/5625, 117649/117612


Mapping: [{{val|1 -4 2 -6 -9}}, {{val|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
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=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224
Comma list: 676/675, 1716/1715, 3025/3024, 4225/4224


Mapping: [{{val|1 -4 2 -6 -9 -5}}, {{val|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 67: Line 77:


=== 17-limit ===
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
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: [{{val|1 -4 2 -6 -9 -5 -3}}, {{val|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
Line 77: Line 89:
Badness: 0.019107
Badness: 0.019107


[[Category:Temperament]]
[[Category:Regular temperament theory]]
[[Category:Temperament collection]]
[[Category:Temperament collection]]
[[Category:Wizmic microtemperaments| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Wizmic]]
[[Category:Microtemperament]]

Revision as of 15:40, 4 July 2021

This is a collection of microtemperaments 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

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7

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) 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.

Subgroup: 2.3.5.7

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

Subgroup: 2.3.5.7.11

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

Subgroup: 2.3.5.7.11.13

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

Subgroup: 2.3.5.7.11.13.17

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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