Olympic clan: Difference between revisions
m Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| " Tags: Mobile edit Mobile web edit |
m + link to raglympic; improve phrasing; + key category |
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[[Comma list]]: 131072/130977 | [[Comma list]]: 131072/130977 | ||
{{Mapping|legend= | {{Mapping|legend=3| 1 0 0 17 | 0 1 0 -5 | 0 0 1 -2 }} | ||
: mapping generators: ~2, ~3, ~7 | : mapping generators: ~2, ~3, ~7 | ||
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=== Overview to extensions === | === Overview to extensions === | ||
The second comma in the comma list determines how we extend olympian to include | The second comma in the comma list determines how we extend olympian to include prime 5. Akea adds [[385/384]], and finds prime 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. Orthoschismic adds [[32805/32768]], and finds prime 5 on the chain of fifths. Cassaschismic adds [[19712/19683]], giving prime 5 an independent generator. | ||
Pessoal adds [[9801/9800]], splitting the octave into two. Lif adds [[2401/2400]], splitting the perfect fifth into two. Baffin adds [[5632/5625]], splitting the perfect twelfth into two. Lux adds [[3025/3024]], splitting the ~21/16 into two. Hera adds [[6144/6125]] or [[8019/8000]], splitting the ~21/16 into three. Sophia adds [[42875/42768]], splitting the ~8/7 into three. Finally, raglympic adds [[4375/4374]], splitting the ~27/7 into four. | |||
All of them have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]]. | |||
Temperaments discussed elsewhere are: | Temperaments discussed elsewhere are: | ||
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* ''[[Baffin]]'' (+5632/5625) → [[Vishdelismic clan #Baffin|Vishdelismic clan]] | * ''[[Baffin]]'' (+5632/5625) → [[Vishdelismic clan #Baffin|Vishdelismic clan]] | ||
* ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]] | * ''[[Hera]]'' (+6144/6125) → [[Porwell family #Hera|Porwell family]] | ||
* ''[[Raglympic]]'' (+4375/4374) → [[Ragismic family #Raglympic|Ragismic family]] | |||
* ''[[Orthoschismic]]'' (+540/539) → [[Schismic rank-3 family #Orthoschismic|Schismic rank-3 family]] | * ''[[Orthoschismic]]'' (+540/539) → [[Schismic rank-3 family #Orthoschismic|Schismic rank-3 family]] | ||
* [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Undecimal septischismic (cassaschismic)|Septischismic family]] | * [[Cassaschismic]] (+19712/19683) → [[Septischismic family #Undecimal septischismic (cassaschismic)|Septischismic family]] | ||
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[[Category:Olympic clan| ]] <!-- main article --> | [[Category:Olympic clan| ]] <!-- main article --> | ||
[[Category:Olympic| ]] <!-- key article --> | |||
[[Category:Temperament clans]] | [[Category:Temperament clans]] | ||
[[Category:Catalogs of rank-3 temperaments]] | [[Category:Catalogs of rank-3 temperaments]] | ||