Olympic clan: Difference between revisions

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=== Overview to extensions ===

The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds [[385/384]], and finds the harmonic 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. 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. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]].

The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds [[385/384]], and finds the harmonic 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. Pessoal adds [[9801/9800]], splitting the octave 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. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]].

Temperaments discussed elsewhere are:

* ''[[Akea]]'' → [[Hemifamity family #Akea|Hemifamity family]]

* ''[[Pessoal]]'' → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]

* ''[[Lux]]'' → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]

* ''[[Hera]]'' → [[Porwell family #Hera|Porwell family]]

@@ Line 19: / Line 19: @@
 === Overview to extensions ===
-The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds [[385/384]], and finds the harmonic 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. 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. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]].
+The second comma in the comma list determines how we extend olympian to include the harmonic 5. Akea adds [[385/384]], and finds the harmonic 5 by equating the [[81/80|syntonic comma (81/80)]] with the septimal comma. Pessoal adds [[9801/9800]], splitting the octave 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. Finally, sophia adds 42875/42768, splitting the ~8/7 into three. These all have neat extensions to the 13-limit via tempering out both [[2080/2079]] and [[4096/4095]].
 Temperaments discussed elsewhere are:
 * ''[[Akea]]'' → [[Hemifamity family #Akea|Hemifamity family]]
+* ''[[Pessoal]]'' → [[Kalismic temperaments #Pessoal|Kalismic temperaments]]
 * ''[[Lux]]'' → [[Lehmerismic temperaments #Lux|Lehmerismic temperaments]]
 * ''[[Hera]]'' → [[Porwell family #Hera|Porwell family]]