Gariboh clan

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.

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]]

mapping generators: ~3, ~25/21

Optimal tunings:

• WE: ~3 = 1902.4455 ¢, ~25/21 = 293.7393 ¢
• CWE: ~3 = 1901.9550 ¢, ~25/21 = 293.7594 ¢

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

Badness (Sintel): 0.213

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. Submerged tempers out 525/512, splitting the generator in nine. Finally, semaja tempers out 6144/6125, splitting the generator in eleven.

See:

• Diminished (+36/35) → Diminished 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
• Submerged (+525/512) → Avicennmic temperaments
• Semaja (+6144/6125) → Porwell temperaments

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