Gariboh clan: Difference between revisions
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=== Overview to extensions === | === 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 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. These temperaments are distributed into different family pages. | ||
* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]] | |||
* ''[[Ammonite]]'' (+250/243) → [[Porcupine family #Ammonite|Porcupine family]] | |||
* ''[[Maja]]'' (+2430/2401) → [[Maja family #Septimal maja|Maja family]] | |||
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. | 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. | ||
Discussed elsewhere are: | |||
* [[Bohpier]] (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]] | * [[Bohpier]] (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]] | ||
* ''[[Kleiboh]]'' (+1728/1715) → [[Kleismic family #Kleiboh|Kleismic family]] | * ''[[Kleiboh]]'' (+1728/1715) → [[Kleismic family #Kleiboh|Kleismic family]] | ||
Revision as of 12:54, 8 August 2026
- 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 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. These temperaments are distributed into different family pages.
- Diminished (+36/35) → Diminished family
- Ammonite (+250/243) → Porcupine family
- Maja (+2430/2401) → Maja family
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.
Discussed elsewhere are:
- 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.