Gariboh clan: Difference between revisions
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== Sirius == | == Sirius == | ||
{{Main| Sirius }} | |||
[[Subgroup]]: 3.5.7 | [[Subgroup]]: 3.5.7 | ||
[[Comma list]]: 3125/3087 | [[Comma list]]: 3125/3087 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 1 1 | 0 3 5 }} | ||
: mapping generators: ~3, ~25/21 | : mapping generators: ~3, ~25/21 | ||
[[Optimal tuning]]s: | [[Optimal tuning]]s: | ||
* [[WE]]: ~3 = 1902.4455{{c}}, ~25/21 = 293.7393{{c}} | * [[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}} | * [[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]] | [[Optimal ET sequence]]: [[6edt|b6]], [[7edt|b7]], [[13edt|b13]], [[71edt|b71]], [[84edt|b84]], [[97edt|b97]], [[110edt|b110]], [[123edt|b123]], [[136edt|b136]] | ||
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=== Overview to extensions === | === 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 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 and collection pages. | ||
* [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]] | * [[Diminished (temperament)|Diminished]] (+36/35) → [[Diminished family #Septimal diminished|Diminished family]] | ||
* ''[[Ammonite]]'' (+250/243) → [[Porcupine family #Ammonite|Porcupine family]] | * ''[[Ammonite]]'' (+250/243) → [[Porcupine family #Ammonite|Porcupine family]] | ||
* ''[[Maja]]'' (+2430/2401) → [[Maja | * ''[[Maja]]'' (+2430/2401) → [[Nuwell temperaments #Maja|Nuwell temperaments]] | ||
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. | 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: | 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]] | * [[Bohpier]] (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]] | ||
* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]] | * ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]] | ||
* ''[[Trismegistus]]'' (+1029/1024) → [[Magic family #Trismegistus|Magic family]] | * ''[[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]]. | Considered below is semaja. For no-twos extensions, see [[No-twos subgroup temperaments #Sirius|No-twos subgroup temperaments]]. | ||
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Comma list: 121/120, 176/175, 3125/3087 | Comma list: 121/120, 176/175, 3125/3087 | ||
{{Mapping|legend=0| 1 -2 1 3 1 | 0 19 7 -1 13 }} | |||
Optimal tunings: | Optimal tunings: | ||
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Comma list: 121/120, 169/168, 176/175, 275/273 | Comma list: 121/120, 169/168, 176/175, 275/273 | ||
{{Mapping|legend=0| 1 -2 1 3 1 2 | 0 19 7 -1 13 9 }} | |||
Optimal tunings: | Optimal tunings: | ||
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== References == | == References == | ||
[[Category:Gariboh clan| ]] <!-- main article --> | |||
[[Category:Gariboh| ]] <!-- key article --> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category: | [[Category:Catalogs of rank-2 temperaments]] | ||