Dome: Difference between revisions

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A '''dome''' is ~~the~~ collection ~~of modal variants, i.e.~~ of [[Periodic scale #Rotations|rotations]], of a given [[~~periodic scale~~]]. [[Mike Battaglia]] ~~proposed~~ the term (a permutation of the letters of "mode") ~~to discuss [[Fokker block]]s~~.

A '''dome''' is a collection of [[Periodic scale #Rotations|rotations]] of a scale that comes from a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").

For example, if you look at all ~~of the periodic~~ scales that you can get with the 25/24 and 81/80 chromas, you will find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven domes obtainable from the 25/24 and 81/80 [[~~Fokker block #First definition of a Fokker block|~~Fokker arena]]. Each dome of this arena is a collection of seven periodic scales which are modally equivalent, which is to say, rotations of each other. However, every dome is independent from every other dome of the arena; the domes partition the set of scales of the arena into disjoint sets.

For example, if you look at all Fokker block scales that you can get with the 25/24 and 81/80 chromas, you will find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven (heptatonic) domes obtainable from the 25/24 and 81/80 [[Fokker arena]]. Each dome of this arena is a collection of seven periodic scales which are modally equivalent, which is to say, rotations of each other. However, every dome is independent from every other dome of the arena; the domes partition the set of scales of the arena into disjoint sets.

While we have defined a dome as a set, it should be noted it has a natural cyclic group structure.

[[Category:~~Theory~~]]

[[Category:Scale]]

[[Category:Math]]

[[Category:Fokker block]]

[[Category:~~Term~~]]

[[Category:Terms]]

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-A '''dome''' is the collection of modal variants, i.e. of [[Periodic scale #Rotations|rotations]], of a given [[periodic scale]]. [[Mike Battaglia]] proposed the term (a permutation of the letters of "mode") to discuss [[Fokker block]]s.
+{{About|a collection of scales|a type of scale|Modal union}}
+A '''dome''' is a collection of [[Periodic scale #Rotations|rotations]] of a scale that comes from a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").
-For example, if you look at all of the periodic scales that you can get with the 25/24 and 81/80 chromas, you will find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven domes obtainable from the 25/24 and 81/80 [[Fokker block #First definition of a Fokker block|Fokker arena]]. Each dome of this arena is a collection of seven periodic scales which are modally equivalent, which is to say, rotations of each other. However, every dome is independent from every other dome of the arena; the domes partition the set of scales of the arena into disjoint sets.
+For example, if you look at all Fokker block scales that you can get with the 25/24 and 81/80 chromas, you will find that you get 49 different scales. If we consider scales which are modally equivalent to be in the same dome, then the playing field reduces to seven (heptatonic) domes obtainable from the 25/24 and 81/80 [[Fokker arena]]. Each dome of this arena is a collection of seven periodic scales which are modally equivalent, which is to say, rotations of each other. However, every dome is independent from every other dome of the arena; the domes partition the set of scales of the arena into disjoint sets.
 While we have defined a dome as a set, it should be noted it has a natural cyclic group structure.
-[[Category:Theory]]
+[[Category:Scale]]
 [[Category:Math]]
 [[Category:Fokker block]]
-[[Category:Term]]
+[[Category:Terms]]