Wizmic microtemperaments: Difference between revisions
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This is a collection of microtemperaments 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 [[ | Discussed elsewhere are: | ||
* [[Wizard]], {225/224, 118098/117649} → [[Marvel temperaments #Wizard]] | |||
* ''[[Hemiseven]]'', {1029/1024, 19683/19600} → [[Gamelismic clan #Hemiseven]] | |||
* [[Ennealimmal]], {2401/2400, 4375/4374} → [[Ragismic microtemperaments #Ennealimmal]] | |||
* ''[[Sengagen]]'', {3136/3125, 420175/419904} → [[Hemimean clan #Sengagen]] | |||
* ''[[Septiquarter]]'', {5120/5103, 420175/419904} → [[Hemifamity temperaments #Septiquarter]] | |||
* ''[[Hendecatonic]]'', {6144/6125, 10976/10935} → [[Porwell temperaments #Hendecatonic]] | |||
* [[Tsaharuk]], {32805/32768, 420175/419904} → [[Schismatic family #Tsaharuk]] | |||
* ''[[Fifthplus]]'', {65625/65536, 420175/419904} → [[Horwell temperaments #Fifthplus]] | |||
* ''[[Octowerck]]'', {321489/320000, 420175/419904} → [[Varunismic temperaments #Octowerck]] | |||
* ''[[Decavish]]'', {420175/419904, 2202927104/2197265625} → [[Vishnuzmic family #Decavish]] | |||
Considered below are qak, tokko and tertiathirds. | |||
== Qak == | == Qak == | ||
Revision as of 15:55, 4 July 2021
This is a collection of microtemperaments which tempers out the wizma, [-6 -8 2 5⟩ = 420175/419904.
Discussed elsewhere are:
- Wizard, {225/224, 118098/117649} → Marvel temperaments #Wizard
- Hemiseven, {1029/1024, 19683/19600} → Gamelismic clan #Hemiseven
- Ennealimmal, {2401/2400, 4375/4374} → Ragismic microtemperaments #Ennealimmal
- Sengagen, {3136/3125, 420175/419904} → Hemimean clan #Sengagen
- Septiquarter, {5120/5103, 420175/419904} → Hemifamity temperaments #Septiquarter
- Hendecatonic, {6144/6125, 10976/10935} → Porwell temperaments #Hendecatonic
- Tsaharuk, {32805/32768, 420175/419904} → Schismatic family #Tsaharuk
- Fifthplus, {65625/65536, 420175/419904} → Horwell temperaments #Fifthplus
- Octowerck, {321489/320000, 420175/419904} → Varunismic temperaments #Octowerck
- Decavish, {420175/419904, 2202927104/2197265625} → Vishnuzmic family #Decavish
Considered below are qak, tokko and tertiathirds.
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
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
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
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