Cataharry temperaments
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
Majvamoid
The majvamoid temperament (149&183) is an extension of the majvam temperament which tempers out the cataharry comma and the quasiorwellisma (29360128/29296875, sazoquinbigu) in the 7-limit.
Subgroup: 2.3.5.7
Comma list: 19683/19600, 29360128/29296875
Mapping: [⟨1 10 5 38], ⟨0 -22 -7 -92]]
Wedgie: ⟨⟨ 22 7 92 -40 84 94 ]]
POTE generator: ~125/96 = 459.031
Badness: 0.207280
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 5632/5625, 19683/19600
Mapping: [⟨1 10 5 38 31], ⟨0 -22 -7 -92 -72]]
POTE generator: ~125/96 = 459.027
Vals: Template:Val list
Badness: 0.065874
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 676/675, 1573/1568, 4225/4224
Mapping: [⟨1 10 5 38 31 19], ⟨0 -22 -7 -92 -72 -40]]
POTE generator: ~125/96 = 459.028
Vals: Template:Val list
Badness: 0.034696
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 351/350, 561/560, 676/675, 715/714, 4225/4224
Mapping: [⟨1 10 5 38 31 19 6], ⟨0 -22 -7 -92 -72 -40 -5]]
POTE generator: ~125/96 = 459.027
Vals: Template:Val list
Badness: 0.023302