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= Quartismic =
= Quartismic =
Comma: 117440512/117406179
Comma: 117440512/117406179


Line 20: Line 19:


== Full 11-limit extensions ==
== Full 11-limit extensions ==
Among quartismic temperaments, there are several options for 5-limit representation depending which among the various 5-limit commas is tempered out.  Adding the [[schisma]] to the list of tempered-out commas without also adding either the [[81/80|syntonic comma]] or the [[64/63|septimal comma]] results in some form Altierran temperament, other possible extensions are listed here.


Among quartismic temperaments, there are several options for 5-limit representation depending which among the various 5-limit commas is tempered out.
===Shrutar===
This is the 22&46 temperament.  See [[Diaschismic_family#Shrutar|Shrutar]].
===Escapade extension===
This is the 22&43 temperament.  See [[Escapade_family|Escapade]].
===Godzilla extension===
This is the 24&43 temperament.  See [[Semaphore_and_Godzilla|Godzilla]].


===Altierran===
= Altierran =
Arguably one of the better choices for 5-limit representation involves additionally tempering out 32805/32768- the [[schisma]]- which results in Altierran temperament.
The Altierran clan is a temperament clan consisting of those temperaments in which both schisma and the quartisma are tempered out.


Commas: 117440512/117406179, 32805/32768
Commas: 32805/32768, 117440512/117406179


Map: [<3 4 13 2 10], <0 2 -16 17 1]]
POTE generator: ~12/11 = 150.9629


POTE generator: 150.9629
Mapping generator:
 
Map: [<3 4 13 2 10|, <0 2 -16 17 1|]


EDOs: 24, 159
EDOs: 24, 159


===Shrutar===
Badness:
This is the 22&46 temperament.  See [[Diaschismic_family#Shrutar|Shrutar]].
 
===Escapade extension===
== 13-limit ==
This is the 22&43 temperament.  See [[Escapade_family|Escapade]].
Commas: 10985/10976, 32805/32768, 117440512/117406179
===Godzilla extension===
 
This is the 24&43 temperament.  See [[Semaphore_and_Godzilla|Godzilla]].
POTE generator:
 
Mapping generator:
 
Map:
 
EDOs:
 
Badness:
 
== 17-limit ==
Commas:
 
POTE generator:
 
Mapping generator:
 
Map:
 
EDOs:


== 13-limit extensions ==
Badness:
For 13-limit extensions, one could temper out 10985/10976.  However, there are other possibilities as well.


[[Category:Quartismic]]
[[Category:Quartismic]]
[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Temperament]]
[[Category:Temperament]]
Retrieved from "https://en.xen.wiki/w/Quartismic_family"