Lokismic temperaments

Lokismic rank-two temperaments temper out the loki comma, 102760448/102515625 = [21 -8 -6 2⟩ (lokisma, Sasa-bizotrigu).

Temperaments dicussed elsewhere include:

• Pajara
• Decoid
• Bischismic
• Vishnu
• Undim
• Septisuperfourth
• Bisupermajor
• Sextile
• Semiquindromeda

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

Optimal ET sequence: 128, 142, 270

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

Optimal ET sequence: 128, 142, 270

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

Optimal ET sequence: 128, 142, 270

Badness: 0.037612