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
• Immunized, {64/63, 8748/8575} → Immunity family
• Unicorn, {126/125, 10976/10935} → Unicorn family
• Catakleismic, {225/224, 4375/4374} → Kleismic family
• Hemiseven, {1029/1024, 19683/19600} → Gamelismic clan
• Buzzard, {1728/1715, 5120/5103} → Hemifamity temperaments
• Harry, {2401/2400, 19683/19600} → Breedsmic temperaments
• Hamity, {2430/2401, 4000/3969} → Amity family
• Subpental, {3136/3125, 19683/19600} → Hemimean clan
• Hemischis, {6144/6125, 19683/19600} → Porwell temperaments
• Mirkat, {16875/16807, 19683/19600} → Mirkwai clan
• Hours, {19683/19600, 33075/32768} → Compton family
• Tuskaloosa, {19683/19600, 110592/109375} → Mabila family
• Hemipental, {19683/19600, 589824/588245} → Pental family

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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: 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

Optimal GPV sequence: Template:Val list

Badness: 0.023302