Gariboh clan: Difference between revisions

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~~These are rank-2 temperaments that temper 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 }}.

~~Temperaments dicussed elsewhere include [[Porcupine family #Ammonite|ammonite]], [[Sensamagic~~ clan ~~#Bohpier|bohpier]],~~ [[~~Jubilismic clan #Diminished~~|~~diminished]], [[Schismatic family #Garibaldi|garibaldi~~]], [[~~Kleismic family #Kleiboh|kleiboh~~]], [[~~Maja family~~|~~maja~~]], [[~~Archytas clan #Passion|passion~~]]~~, [[Keemic temperaments #Quasitemp~~|~~quasitemp]], and [[Magic family #Trismegistus|trismegistus]]~~.

== Sirius ==

Subgroup: 3.5.7

[[Subgroup]]: 3.5.7

[[Comma list]]: 3125/3087

[[~~Sval~~]] [[~~mapping~~]]: [~~{{val~~| ~~1 1 1 }}~~, ~~{{val~~| 0 3 5 ~~}}]~~

: sval mapping generators: ~3, ~25/21

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

=== 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.

~~Sval mapping generators: ~3~~, ~~~25~~/21

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.

[[~~POTE generator~~]]~~: ~25~~/~~21 = 293.740~~

See:

* ''[[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]]

* [[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]]

* ''[[Dodecacot]]'' (+10976/10935) → [[Tetracot family #Dodecacot|Tetracot family]]

* ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]]

* ''[[Semaja]]'' (+6144/6125) → [[Porwell temperaments #Semaja|Porwell temperaments]]

For no-twos extensions, see [[No-twos subgroup temperaments#Sirius|No-twos subgroup temperaments]].

[[Category:Temperament]]

[[Category:Temperament clans]]

[[Category:~~Temperament~~ clan]]

[[Category:Pages with mostly numerical content]]

[[Category:Gariboh clan| ]]

[[Category:Gariboh| ]]

[[Category:Rank 2]]

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-These are rank-2 temperaments that temper out the gariboh comma, 3125/3087 = {{monzo| 0 -2 5 -3 }}.
+{{Technical data page}}
+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 }}.
-Temperaments dicussed elsewhere include [[Porcupine family #Ammonite|ammonite]], [[Sensamagic clan #Bohpier|bohpier]], [[Jubilismic clan #Diminished|diminished]], [[Schismatic family #Garibaldi|garibaldi]], [[Kleismic family #Kleiboh|kleiboh]], [[Maja family|maja]], [[Archytas clan #Passion|passion]], [[Keemic temperaments #Quasitemp|quasitemp]], and [[Magic family #Trismegistus|trismegistus]].
 == Sirius ==
-Subgroup: 3.5.7
+[[Subgroup]]: 3.5.7
 [[Comma list]]: 3125/3087
-[[Sval]] [[mapping]]: [{{val| 1 1 1 }}, {{val| 0 3 5 }}]
+{{Mapping|legend=2| 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]]: [[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.
-Sval mapping generators: ~3, ~25/21
+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.
-[[POTE generator]]: ~25/21 = 293.740
+See:
+* ''[[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]]
+* [[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]]
+* ''[[Dodecacot]]'' (+10976/10935) → [[Tetracot family #Dodecacot|Tetracot family]]
+* ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]]
+* ''[[Semaja]]'' (+6144/6125) → [[Porwell temperaments #Semaja|Porwell temperaments]]
-[[Optimal GPV sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]],  [[123edt|b123]], [[136edt|b136]]
+For no-twos extensions, see [[No-twos subgroup temperaments#Sirius|No-twos subgroup temperaments]].
-[[Category:Temperament]]
+[[Category:Temperament clans]]
-[[Category:Temperament clan]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Gariboh clan| ]] <!-- main article -->
+[[Category:Gariboh| ]] <!-- key article -->
 [[Category:Rank 2]]