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 }}.
{{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
[[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]]
 
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.
 
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 ==
{{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}}


Sval mapping generators: ~3, ~25/21
{{Optimal ET sequence|legend=0| 16, 37, 53 }}


[[POTE generator]]: ~25/21 = 293.740
Badness (Sintel): 1.35


[[Optimal GPV sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]],  [[123edt|b123]], [[136edt|b136]]
== References ==


[[Category:Temperament]]
[[Category:Gariboh clan| ]] <!-- main article -->
[[Category:Temperament clan]]
[[Category:Temperament clans]]
[[Category:Rank 2]]
[[Category:Catalogs of rank-2 temperaments]]

Latest revision as of 12:28, 12 September 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The gariboh clan of rank-2 temperaments tempers out the gariboh comma, 3125/3087 ([0 -2 5 -3⟩).

Sirius

Main article: Sirius

Subgroup: 3.5.7

Comma list: 3125/3087

Subgroup-val mapping: [⟨1 1 1], ⟨0 3 5]]

mapping generators: ~3, ~25/21

Optimal tunings:

  • WE: ~3 = 1902.4455 ¢, ~25/21 = 293.7393 ¢
error map: ⟨+0.490 -2.650 +2.316]
  • CWE: ~3 = 1901.9550 ¢, ~25/21 = 293.7594 ¢
error map: ⟨0.000 -3.080 +1.926]

Optimal ET sequence: b6, b7, b13, b71, b84, b97, b110, b123, 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.

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.

Discussed elsewhere are:

Considered below is semaja. For no-twos extensions, see 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 37 & 53 temperament. Its ploidacot is gamma-19-cot (or alpha-heptaseph due to a much simpler 2.5.7-subgroup restriction). The name actually refers to the fact that two of its ~8/7 generator steps reach a ~13/10[1].

Subgroup: 2.3.5.7

Comma list: 3125/3087, 6144/6125

Mapping: [⟨1 -2 1 3], ⟨0 19 7 -1]]

mapping generators: ~2, ~8/7

Optimal tunings:

  • WE: ~2 = 1199.4860 ¢, ~8/7 = 226.3864 ¢
error map: ⟨-0.514 +0.415 -2.123 +3.246]
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4697 ¢
error map: ⟨0.000 +0.970 -1.026 +4.704]

Optimal ET sequence: 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: [⟨1 -2 1 3 1], ⟨0 19 7 -1 13]]

Optimal tunings:

  • WE: ~2 = 1199.9818 ¢, ~8/7 = 226.4821 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4851 ¢

Optimal ET sequence: 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: [⟨1 -2 1 3 1 2], ⟨0 19 7 -1 13 9]]

Optimal tunings:

  • WE: ~2 = 1200.1020 ¢, ~8/7 = 226.4987 ¢
  • CWE: ~2 = 1200.0000 ¢, ~8/7 = 226.4822 ¢

Optimal ET sequence: 16, 37, 53

Badness (Sintel): 1.35

References

  1. ↑ Yahoo! Tuning Group | Suggested names for the unclasified temperaments
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