Cataharry temperaments: Difference between revisions
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* ''[[hours]]'', {19683/19600, 33075/32768} → [[Compton family #Hours]] | * ''[[hours]]'', {19683/19600, 33075/32768} → [[Compton family #Hours]] | ||
= Swetneus = | == Swetneus == | ||
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator. | The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator. | ||
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{{Val list|legend=1| 58, 91, 149, 505d, 654bd, 803bd }} | {{Val list|legend=1| 58, 91, 149, 505d, 654bd, 803bd }} | ||
[[Badness]]: 0. | [[Badness]]: 0.133168 | ||
== 11-limit == | === 11-limit === | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
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Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcde }} | Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcde }} | ||
Badness: 0. | Badness: 0.055163 | ||
== 13-limit == | === 13-limit === | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcdef }} | Vals: {{Val list| 58, 149, 207, 356e, 563cde, 919bcdef }} | ||
Badness: 0. | Badness: 0.028876 | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 14:09, 7 August 2021
This is a collection of rank-2 temperaments tempering out the cataharry comma, [-4 9 -2 -2⟩ = 19683/19600. These include swetneus, considered below, as well as others discussed elsewhere:
- godzilla, {49/48, 81/80} → Meantone family #Godzilla
- immunized, {64/63, 8748/8575} → Immunity family #Immunized
- unicorn, {126/125, 10976/10935} → Unicorn family #Septimal unicorn
- catakleismic, {225/224, 4375/4374} → Kleismic family #Catakleismic
- hemiseven, {1029/1024, 19683/19600} → Gamelismic clan #Hemiseven
- buzzard, {1728/1715, 5120/5103} → Hemifamity temperaments #Buzzard
- harry, {2401/2400, 19683/19600} → Breedsmic temperaments #Harry
- hamity, {2430/2401, 4000/3969} → Amity family #Hamity
- subpental, {3136/3125, 19683/19600} → Hemimean clan #Subpental
- hemischis, {6144/6125, 19683/19600} → Porwell temperaments #Hemischis
- mirkat, {16875/16807, 19683/19600} → Mirkwai clan #Mirkat
- hours, {19683/19600, 33075/32768} → Compton family #Hours
Swetneus
The swetneus temperament takes its name from the fact that an approximate swetismic neutral second, ~49/45, is the generator.
Subgroup: 2.3.5.7
Comma list: 19683/19600, 50421/50000
Mapping: [⟨1 4 8 8], ⟨0 -20 -47 -43]]
Wedgie: ⟨⟨ 20 47 43 28 12 -32 ]]
POTE generator: ~49/45 = 144.956
Badness: 0.133168
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 3388/3375, 19683/19600
Mapping: [⟨1 4 8 8 13], ⟨0 -20 -47 -43 -79]]
POTE generator: ~49/45 = 144.941
Vals: Template:Val list
Badness: 0.055163
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 441/440, 676/675, 847/845
Mapping: [⟨1 4 8 8 13 13], ⟨0 -20 -47 -43 -79 -77]]
POTE generator: ~49/45 = 144.939
Vals: Template:Val list
Badness: 0.028876