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

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

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

[[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.

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) → [[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 clans]]

[[Category:Pages with mostly numerical content]]

[[Category:Gariboh clan| ]]

[[Category:Gariboh| ]]

[[Category:Rank 2]]

@@ Line 1: / Line 1: @@
-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
+: sval mapping generators: ~3, ~25/21
-[[POTE generator]]: ~25/21 = 293.740
+[[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.
+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) → [[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 clans]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Gariboh clan| ]] <!-- main article -->
+[[Category:Gariboh| ]] <!-- key article -->
 [[Category:Rank 2]]