Gariboh clan

The gariboh clan of rank-2 temperaments tempers out the gariboh comma, 3125/3087 = [0 -2 5 -3⟩.

Sirius

Subgroup: 3.5.7

Comma list: 3125/3087

Subgroup-val mapping: [⟨1 1 1], ⟨0 3 5]]

sval mapping generators: ~3, ~25/21

Optimal tuning (POTE): ~3 = 1\1edt, ~25/21 = 293.740

Optimal ET sequence: b6, b7, b13, b71, b84, b97, b110, b123, b136

Overview to extensions

The full 7-limit extensions' relation to sirius is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are diminished, ammonite, and maja.

The others are weak extensions. Bohpier tempers out 245/243 with a 1/13-twelfth period. Kleiboh tempers out 1728/1715 with a 1/6-twelfth period. Passion tempers out 64/63, splitting the generator in six. Garibaldi tempers out 225/224. Quasitemp tempers out 875/864. Dodecacot tempers out 10976/10935. These split the generator in five. Trismegistus tempers out 1029/1024, splitting the generator in two with a 1/5-twelfth period. Finally, semaja tempers out 6144/6125, splitting the generator in eleven.

See:

• Diminished (+36/35) → Dimipent family
• Ammonite (+250/243) → Porcupine family
• Maja (+2430/2401) → Maja family
• Bohpier (+245/243) → Sensamagic clan
• Kleiboh (+1728/1715) → Kleismic family
• Passion (+64/63) → Passion family
• Garibaldi (+225/224) → Schismatic family
• Quasitemp (+875/864) → Keemic temperaments
• Dodecacot (+10976/10935) → Tetracot family
• Trismegistus (+1029/1024) → Magic family
• Semaja (+6144/6125) → Porwell temperaments

For no-twos extensions, see No-twos subgroup temperaments.