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 }}).

== Sirius ==

~~== Sirius ==~~

[[Subgroup]]: 3.5.7

Subgroup: 3.5.7

[[Comma list]]: 3125/3087

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

: mapping generators: ~3, ~25/21

[[Optimal tuning]]s:

* [[WE]]: ~3 = 1902.4455{{c}}, ~25/21 = 293.7393{{c}}

: [[error map]]: {{val| +0.490 -2.650 +2.316 }}

* [[CWE]]: ~3 = 1901.9550{{c}}, ~25/21 = 293.7594{{c}}

: error map: {{val| 0.000 -3.080 +1.926 }}

[[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 (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]]

~~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. Submerged tempers out [[525/512]], splitting the generator in nine. Finally, semaja tempers out [[6144/6125]], splitting the generator in eleven.

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

Discussed elsewhere are:

* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]

* ''[[Passion]]'' (+64/63) → [[Passion family #Passion|Passion family]]

* [[Submerged]] (+525/512) → [[Avicennmic temperaments #Submerged|Avicennmic temperaments]]

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

* [[Bohpier]] (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]

* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]

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

* ''[[Kleiboh]]'' (+1728/1715) → [[Kleismic family #Kleiboh|Kleismic family]]

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

== Semaja ==

Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[porwell comma]] to the comma list, and may be described as the {{nowrap| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot (or alpha-heptaseph due to a much simpler [[2.5.7 subgroup|2.5.7-subgroup]] [[restriction]]). The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 3125/3087, 6144/6125

: mapping generators: ~2, ~8/7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.4860{{c}}, ~8/7 = 226.3864{{c}}

: [[error map]]: {{val| -0.514 +0.415 -2.123 +3.246 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.4697{{c}}

: error map: {{val| 0.000 +0.970 -1.026 +4.704 }}

[[Badness]] (Sintel): 2.71

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 121/120, 176/175, 3125/3087

Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}

Optimal tunings:

* WE: ~2 = 1199.9818{{c}}, ~8/7 = 226.4821{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4851{{c}}

Badness (Sintel): 1.98

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 121/120, 169/168, 176/175, 275/273

Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}

Optimal tunings:

* WE: ~2 = 1200.1020{{c}}, ~8/7 = 226.4987{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4822{{c}}

Badness (Sintel): 1.35

== References ==

[[Category:Gariboh clan| ]]

[[Category:Temperament clans]]

[[Category:~~Rank~~ 2]]

[[Category:Catalogs of rank-2 temperaments]]

@@ 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 ==
+{{Main| Sirius }}
-== 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 }}
+: mapping generators: ~3, ~25/21
+[[Optimal tuning]]s:
+* [[WE]]: ~3 = 1902.4455{{c}}, ~25/21 = 293.7393{{c}}
+: [[error map]]: {{val| +0.490 -2.650 +2.316 }}
+* [[CWE]]: ~3 = 1901.9550{{c}}, ~25/21 = 293.7594{{c}}
+: error map: {{val| 0.000 -3.080 +1.926 }}
+[[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]],  [[123edt|b123]], [[136edt|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 (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]]
-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. Submerged tempers out [[525/512]], splitting the generator in nine. Finally, semaja tempers out [[6144/6125]], splitting the generator in eleven.
-[[POTE generator]]: ~25/21 = 293.740
+Discussed elsewhere are:
+* [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
+* ''[[Passion]]'' (+64/63) → [[Passion family #Passion|Passion family]]
+* [[Submerged]] (+525/512) → [[Avicennmic temperaments #Submerged|Avicennmic temperaments]]
+* ''[[Dodecacot]]'' (+10976/10935) → [[Tetracot family #Dodecacot|Tetracot family]]
+* [[Bohpier]] (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
+* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]
+* ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]]
+* ''[[Kleiboh]]'' (+1728/1715) → [[Kleismic family #Kleiboh|Kleismic family]]
-[[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]],  [[123edt|b123]], [[136edt|b136]]
+Considered below is semaja. For no-twos extensions, see [[No-twos subgroup temperaments #Sirius|No-twos subgroup temperaments]].
+== Semaja ==
+{{See also| Llywelynsmic clan }}
+Cryptically named by [[Petr Pařízek]] in 2011, semaja adds the [[porwell comma]] to the comma list, and may be described as the {{nowrap| 37 & 53 }} temperament. Its [[ploidacot]] is gamma-19-cot (or alpha-heptaseph due to a much simpler [[2.5.7 subgroup|2.5.7-subgroup]] [[restriction]]). The name actually refers to the fact that two of its ~[[8/7]] generator steps reach a ~[[13/10]]<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 3125/3087, 6144/6125
+{{Mapping|legend=1| 1 -2 1 3 | 0 19 7 -1 }}
+: mapping generators: ~2, ~8/7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.4860{{c}}, ~8/7 = 226.3864{{c}}
+: [[error map]]: {{val| -0.514 +0.415 -2.123 +3.246 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~8/7 = 226.4697{{c}}
+: error map: {{val| 0.000 +0.970 -1.026 +4.704 }}
+{{Optimal ET sequence|legend=1| 16, 37, 53, 196d }}
+[[Badness]] (Sintel): 2.71
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 121/120, 176/175, 3125/3087
+Mapping: {{mapping| 1 -2 1 3 1 | 0 19 7 -1 13 }}
+Optimal tunings:
+* WE: ~2 = 1199.9818{{c}}, ~8/7 = 226.4821{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4851{{c}}
+{{Optimal ET sequence|legend=0| 16, 37, 53 }}
+Badness (Sintel): 1.98
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 121/120, 169/168, 176/175, 275/273
+Mapping: {{mapping| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }}
+Optimal tunings:
+* WE: ~2 = 1200.1020{{c}}, ~8/7 = 226.4987{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~8/7 = 226.4822{{c}}
+{{Optimal ET sequence|legend=0| 16, 37, 53 }}
+Badness (Sintel): 1.35
+== References ==
+[[Category:Gariboh clan| ]] <!-- main article -->
 [[Category:Temperament clans]]
-[[Category:Rank 2]]
+[[Category:Catalogs of rank-2 temperaments]]