Lokismic temperaments
Lokismic rank-two temperaments temper out the loki comma, 102760448/102515625 = [21 -8 -6 2⟩ (lokisma, sasazozo-atribigu).
Temperaments dicussed elsewhere include:
Septisemitonic
The septisemitonic temperament (128&142) has a half-octave period and uses a 21/20-wide semitone (septimal semitone) as a generator.
Subgroup: 2.3.5.7
Comma list: 102760448/102515625, 200120949/200000000
Mapping: [⟨2 5 0 -1], ⟨0 -13 33 47]]
POTE generator: ~21/20 = 84.446
Badness: 0.166111
11-limit
Subgroup: 2.3.5.7.11
Comma list: 3025/3024, 131072/130977, 422576/421875
Mapping: [⟨2 5 0 -1 11], ⟨0 -13 33 47 -29]]
POTE generator: ~21/20 = 84.443
Vals: Template:Val list
Badness: 0.058273
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 2080/2079, 3025/3024, 4096/4095, 405769/405000
Mapping: [⟨2 5 0 -1 11 15], ⟨0 -13 33 47 -29 -54]]
POTE generator: ~21/20 = 84.440
Vals: Template:Val list
Badness: 0.037612
Semiquindromeda
The semiquindromeda temperament (410&422) is an extension of the quindromeda temperament with a half-octave period.
Subgroup: 2.3.5.7
Comma list: 102760448/102515625, 1220703125/1219784832
Mapping: [⟨2 4 0 -5], ⟨0 -5 28 64]]
POTE generator: ~1323/1250 = 99.521
Badness: 0.233140
11-limit
Subgroup: 2.3.5.7.11
Comma list: 5632/5625, 9801/9800, 85937500/85766121
Mapping: [⟨2 4 0 -5 -10], ⟨0 -5 28 64 102]]
POTE generator: ~1323/1250 = 99.525
Vals: Template:Val list
Badness: 0.093926
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 1716/1715, 2080/2079, 5632/5625, 831875/830466
Mapping: [⟨2 4 0 -5 -10 -13], ⟨0 -5 28 64 102 123]]
POTE generator: ~1323/1250 = 99.523
Vals: Template:Val list
Badness: 0.053361
17-limit
Subgroup: 2.3.5.7.11.13.17
Comma list: 1716/1715, 2080/2079, 2500/2499, 5632/5625, 15895/15876
Mapping: [⟨2 4 0 -5 -10 -13 10], ⟨0 -5 28 64 102 123 -11]]
POTE generator: ~18/17 = 99.522
Vals: Template:Val list
Badness: 0.034659
19-limit
Subgroup: 2.3.5.7.11.13.17.19
Comma list: 1216/1215, 1445/1444, 1716/1715, 2080/2079, 2376/2375, 2500/2499
Mapping: [⟨2 4 0 -5 -10 -13 10 8], ⟨0 -5 28 64 102 123 -11 3]]
POTE generator: ~18/17 = 99.523
Vals: Template:Val list
Badness: 0.025439