Gariboh clan: Difference between revisions
Update keys |
Intro to extensions |
||
| Line 1: | Line 1: | ||
The '''gariboh clan'' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the gariboh comma, [[3125/3087]] = {{monzo| 0 -2 5 -3 }} | The '''gariboh clan''' of [[Rank-2 temperament|rank-2]] [[temperament]]s [[Tempering out|tempers out]] the gariboh comma, [[3125/3087]] = {{monzo| 0 -2 5 -3 }}. | ||
== Sirius == | == Sirius == | ||
| Line 15: | Line 13: | ||
[[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]], [[123edt|b123]], [[136edt|b136]] | [[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]], [[123edt|b123]], [[136edt|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]]. These split the generator in five. Finally, trismegistus tempers out [[1029/1024]], splitting the generator in two with a 1/5-twelfth period. | |||
See: | |||
* ''[[Diminished]]'' (+36/35) → [[Dimipent family #Diminished|Dimipent family]] | |||
* ''[[Ammonite]]'' (+250/243) → [[Porcupine family #Ammonite|Porcupine family]] | |||
* ''[[Maja]]'' (+2430/2401) → [[Maja family #Septimal maja|Maja family]] | |||
* [[Bohpier]] (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]] | |||
* ''[[Kleiboh]]'' (+1728/1715) → [[Kleismic family #Kleiboh|Kleismic family]] | |||
* ''[[Passion]]'' (+64/63) → [[Passion family #Passion|Passion family]] | |||
* ''[[Garibaldi]]'' (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]] | |||
* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]] | |||
* ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]] | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
Revision as of 09:45, 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. These split the generator in five. Finally, trismegistus tempers out 1029/1024, splitting the generator in two with a 1/5-twelfth period.
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
- Trismegistus (+1029/1024) → Magic family