Cataharry temperaments
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
This is a collection of rank-2 cataharry temperaments, which temper out the cataharry comma (monzo: [-4 9 -2 -2⟩, ratio: 19683/19600). For the family of rank-3 temperaments, see Cataharry family.
Discussed elsewhere are:
- Mite (+27/25) → Bug family
- Godzilla (+49/48 or 81/80) → Semaphoresmic clan
- Immunized (+64/63) → Immunity family
- Hemischis (+6144/6125) → Schismatic family
- Buzzard (+1728/1715) → Buzzardsmic clan
- Catakleismic (+225/224) → Kleismic family
- Hemiseven (+1029/1024) → Gamelismic clan
- Weasel (+50/49) → Tetracot family
- Unicorn (+126/125) → Unicorn family
- Hamity (+2430/2401) → Amity family
- Tuskaloosa (+110592/109375) → Mabila family
- Hemiquintile (+589824/588245) → Quintile family
- Harry (+2401/2400) → Gravity family
- Subpental (+3136/3125) → Hemimean clan
- Mirkat (+16875/16807) → Canopic clan
- Hours (+33075/32768) → Compton family
Considered below is swetneus and majvamoid, in the order of increasing badness.
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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/45 = 144.956 ¢
Optimal ET sequence: 58, 91, 149, 505d, 654bd, 803bd
Badness (Smith): 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/45 = 144.941 ¢
Optimal ET sequence: 58, 149, 207, 356e, 563cde, 919bcde
Badness (Smith): 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/45 = 144.939 ¢
Optimal ET sequence: 58, 149, 207, 356e, 563cde, 919bcdef
Badness (Smith): 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~125/96 = 459.031 ¢
Optimal ET sequence: 34d, 115d, 149, 183, 332, 515, 847, 1362bc
Badness (Smith): 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~125/96 = 459.027 ¢
Optimal ET sequence: 34d, 149, 183, 332e, 515e, 698e
Badness (Smith): 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~125/96 = 459.028 ¢
Optimal ET sequence: 34d, 149, 183, 332ef, 515ef
Badness (Smith): 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]]
Optimal tuning (POTE): ~2 = 1200.000 ¢, ~125/96 = 459.027 ¢
Optimal ET sequence: 34d, 149, 183, 332ef, 515ef, 698ef
Badness (Smith): 0.023302