Wizmic microtemperaments: Difference between revisions

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A wizmic temperament is one which tempers out the wizma, | -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 [[ennealimmal]], [[fifthplus]], [[hemiseven]], [[hendecatonic]], [[sengagen]], [[septiquarter]], [[tsaharuk]], and [[wizard]].
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[[Badness]]: 0.044417
[[Badness]]: 0.044417
= Tertiathirds =
The ''tertiathirds'' temperament (121&270, named by [[User:Xenllium|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 tuning|POTE generator]]: ~3375/3136 = 128.8879
{{Val list|legend=1| 121, 149, 270, 2309c, 2579c, 2849c, 3119bc, 3389bc, 3659bcc, 3929bcc, 4199bcc }}
[[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: {{Val list| 121, 149, 270, 2551bc, 2821bc, 3091bc, 3361bc, 3631bbcc, 3901bbccd, 4171bbccd, 4441bbccd, 4711bbccd }}
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: {{Val list| 121, 149, 270, 1741bc, 2011bcf, 2281bcf, 2551bcf, 2821bcf, 3091bcff, 3361bcff }}
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: {{Val list| 121, 149, 270 }}
Badness: 0.019107


[[Category:Temperament]]
[[Category:Temperament]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Wizmic]]
[[Category:Wizmic]]

Revision as of 13:37, 10 April 2021

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.

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