Horwell temperaments
Horwell temperaments temper out the horwell comma, [-16 1 5 1⟩ = 65625/65536.
Discussed elsewhere are bisupermajor, countercata, eris, escaped, hemithirds, keen, orwell, pontiac, tertiaseptal, and worschmidt.
Mutt
Comma list: [-44 -3 21⟩
Mapping: [⟨3 5 7], ⟨0 -7 -1]]
POTE generator: ~5/4 = 385.980
Badness: 0.162467
7-limit
Comma list: 65625/65536, 250047/250000
Mapping: [⟨3 5 7 8], ⟨0 -7 -1 12]]
⟨⟨21 3 -36 -44 -116 -92]]
POTE generator: ~5/4 = 385.964
Vals: Template:Val list
Badness: 0.028406
11-limit
Comma list: 441/440, 4375/4356, 16384/16335
Mapping: [⟨3 5 7 8 10], ⟨0 -7 -1 12 11]]
POTE generator: ~5/4 = 386.020
Vals: Template:Val list
Badness: 0.058344
13-limit
Comma list: 364/363, 441/440, 625/624, 2200/2197
Mapping: [⟨3 5 7 8 10 11], ⟨0 -7 -1 12 11 3]]
POTE generator: ~5/4 = 386.022
Vals: Template:Val list
Badness: 0.029089
Fifthplus
Comma list: 65625/65536, 420175/419904
Mapping: [⟨1 11 -3 20], ⟨0 -23 13 -42]]
⟨⟨23 -13 42 -74 2 134]]
POTE generator: ~5488/3645 = 708.774
Badness: 0.025840
Emkay
Emkay (87&224) tempers out the same 5-limit comma as the emka temperament (37&50), but with the horwell (65625/65536) rather than the hemimean (3136/3125) tempered out.
Comma list: 65625/65536, 244140625/243045684
Mapping: [⟨1 14 6 -28], ⟨0 -27 -8 67]]
⟨⟨27 8 -67 -50 -182 -178]]
POTE generator: ~3125/2268 = 551.7745
Badness: 0.135696
11-limit
Comma list: 3025/3024, 4000/3993, 65625/65536
Mapping: [⟨1 14 6 -28 3], ⟨0 -27 -8 67 1]]
POTE generator: ~11/8 = 551.7746
Vals: Template:Val list
Badness: 0.035586
13-limit
Comma list: 625/624, 1575/1573, 2080/2079, 2200/2197
Mapping: [⟨1 14 6 -28 3 6], ⟨0 -27 -8 67 1 -5]]
POTE generator: ~11/8 = 551.7749
Vals: Template:Val list
Badness: 0.017853
Oquatonic
The oquatonic has a period of 1/28 octave and tempers out the horwell (65625/65536) and the dimcomp (390625/388962), as well as the hemfiness (4096000/4084101, saquinru-atriyo). In this temperament, major third of 5/4 is mapped into 9\28.
Comma list: 65625/65536, 390625/388962
Mapping: [⟨28 44 65 79], ⟨0 1 0 -1]]
⟨⟨28 0 -28 -65 -123 -65]]
POTE generator: ~126/125 = 16.3994
Badness: 0.088286