Gariboh clan: Difference between revisions
Intro to extensions |
+link to dodecacot and semaja |
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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. | ||
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]]. These split the generator in five. | 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: | See: | ||
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* ''[[Garibaldi]]'' (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | * ''[[Garibaldi]]'' (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | ||
* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]] | * ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]] | ||
* ''[[Dodecacot]]'' (+10976/10935) → [[Tetracot family #Dodecacot|Tetracot family]] | |||
* ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]] | * ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]] | ||
* ''[[Semaja]]'' (+6144/6125) → [[Porwell temperaments #Semaja|Porwell temperaments]] | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
Revision as of 10:09, 21 September 2023
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