Quartismic family: Difference between revisions

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The '''quartismic family''' is built up from temperaments that temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}. Among the members of this family are Altierran, Meanquarter, Coin, Kleirtismic, and Doublefour.

The '''quartismic family''' is built up from temperaments that temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}. Among the members of this family are Quartismatic, Altierran, Meanquarter, Coin, Escapismic, Dietismic, Kleirtismic, and Doublefour.

= Quartismic =

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== Additional Options for 5-limit Representation ==

Among quartismic temperaments, there are a number of other options for 5-limit representation depending on which among the various 5-limit commas is tempered out. Adding the [[schisma]] to the list of tempered-out commas results in some form of Altierran temperament. Adding the [[81/80|meantone comma]] results in some form of Meanquarter temperament. Adding the [[Magic_comma|magic comma]] results in some form of Coin temperament. Adding the [[15625/15552|kleisma]] results in some form of Kleirtismic temperament- the "kleir-" in "Kleirtismic" is pronounced the same as "Clair". Adding the [[Tetracot_comma|tetracot comma]] results in some form of Doublefour temperament. Other possible extensions are listed here.

~~===Shrutar extension===~~

~~This is the 22&46 temperament. See [[Diaschismic_family#Shrutar|Shrutar]].~~

~~===Escapade extension===~~

~~This is the 22&43 temperament. See [[Escapade_family|Escapade]].~~

= Altierran =

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EDOs: {{EDOs|22, 25, 139cdd}}

Badness:

= Escapismic =

The Escapisimic clan is the temperament clan consisting of those temperaments in which both the escapade comma and the quartisma are tempered out, thus, it is essentially an [[Escapade_family|Escapade extension]].

Commas: 117440512/117406179, 4294967296/4271484375

POTE generators:

Map:

EDOs: {{EDOs|21, 22, 43}}

Badness:

= Dietismic =

The Dietismic clan is the temperament clan consisting of those temperaments in which both the diaschisma and the quartisma are tempered out. Dietismic can easily be extended to a form of [[Diaschismic_family#Shrutar|shrutar]]- in fact, it is quite unusual to find a Dietismic temperament that is not also a form of extended shrutar.

Commas: 2048/2025, 117440512/117406179

POTE generators:

Map:

EDOs: {{EDOs|16cdde, 22, 24, 38cdde, 46, 68, 114}}

Badness:

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-The '''quartismic family''' is built up from temperaments that temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}. Among the members of this family are Altierran, Meanquarter, Coin, Kleirtismic, and Doublefour.
+The '''quartismic family''' is built up from temperaments that temper out the [[quartisma]]- the unnoticeable comma with the ratio 117440512/117406179, and a monzo of {{monzo|24 -6 0 1 -5}}. Among the members of this family are Quartismatic, Altierran, Meanquarter, Coin, Escapismic, Dietismic, Kleirtismic, and Doublefour.
 = Quartismic =
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 == Additional Options for 5-limit Representation ==
 Among quartismic temperaments, there are a number of other options for 5-limit representation depending on which among the various 5-limit commas is tempered out.  Adding the [[schisma]] to the list of tempered-out commas results in some form of Altierran temperament.  Adding the [[81/80|meantone comma]] results in some form of Meanquarter temperament.  Adding the [[Magic_comma|magic comma]] results in some form of Coin temperament.  Adding the [[15625/15552|kleisma]] results in some form of Kleirtismic temperament- the "kleir-" in "Kleirtismic" is pronounced the same as "Clair".  Adding the [[Tetracot_comma|tetracot comma]] results in some form of Doublefour temperament.  Other possible extensions are listed here.
-===Shrutar extension===
-This is the 22&46 temperament.  See [[Diaschismic_family#Shrutar|Shrutar]].
-===Escapade extension===
-This is the 22&43 temperament.  See [[Escapade_family|Escapade]].
 = Altierran =
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 EDOs: {{EDOs|22, 25, 139cdd}}
+Badness:
+= Escapismic =
+The Escapisimic clan is the temperament clan consisting of those temperaments in which both the escapade comma and the quartisma are tempered out, thus, it is essentially an [[Escapade_family|Escapade extension]].
+Commas: 117440512/117406179, 4294967296/4271484375
+POTE generators:
+Map:
+EDOs: {{EDOs|21, 22, 43}}
+Badness:
+= Dietismic =
+The Dietismic clan is the temperament clan consisting of those temperaments in which both the diaschisma and the quartisma are tempered out.  Dietismic can easily be extended to a form of [[Diaschismic_family#Shrutar|shrutar]]- in fact, it is quite unusual to find a Dietismic temperament that is not also a form of extended shrutar.
+Commas: 2048/2025, 117440512/117406179
+POTE generators:
+Map:
+EDOs: {{EDOs|16cdde, 22, 24, 38cdde, 46, 68, 114}}
 Badness: