Dome - Revision history

Fredg999: Direct link to Fokker arena (new redirect)

2025-07-28T18:12:25Z

Direct link to Fokker arena (new redirect)

← Older revision		Revision as of 18:12, 28 July 2025
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	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").		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 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 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.		While we have defined a dome as a set, it should be noted it has a natural cyclic group structure.

Inthar at 16:40, 27 August 2023

2023-08-27T16:40:50Z

← Older revision		Revision as of 16:40, 27 August 2023
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	{{About\|a collection of scales\|a type of scale\|Modal union}}		{{About\|a collection of scales\|a type of scale\|Modal union}}
	A '''dome''' is ~~the~~ collection ~~of modal variants, i.e.~~ of [[Periodic scale #Rotations\|rotations]], of a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").		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 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 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 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.

Inthar at 14:13, 27 August 2023

2023-08-27T14:13:56Z

← Older revision		Revision as of 14:13, 27 August 2023
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	A '''dome''' is the collection of modal variants, i.e. of [[Periodic scale #Rotations\|rotations]], of a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").		A '''dome''' is the collection of modal variants, i.e. of [[Periodic scale #Rotations\|rotations]], of a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").

	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 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 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.

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

Inthar at 14:05, 27 August 2023

2023-08-27T14:05:17Z

← Older revision		Revision as of 14:05, 27 August 2023
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	{{About\|a collection of scales\|a type of scale\|Modal union}}		{{About\|a collection of scales\|a type of scale\|Modal union}}
	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 the collection of modal variants, i.e. of [[Periodic scale #Rotations\|rotations]], of a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").

	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 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 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.

Inthar at 14:04, 27 August 2023

2023-08-27T14:04:29Z

← Older revision		Revision as of 14:04, 27 August 2023
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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 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.

	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 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.

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

FloraC: Fix category

2023-07-08T10:24:03Z

Fix category

← Older revision		Revision as of 10:24, 8 July 2023
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	[[Category:Math]]		[[Category:Math]]
	[[Category:Fokker block]]		[[Category:Fokker block]]
	[[Category:~~Term~~]]		[[Category:Terms]]

Fredg999 category edits: Categories

2023-02-26T07:53:19Z

Fredg999: Distinguish with Modal union

2022-08-03T17:01:03Z

Distinguish with Modal union

← Older revision		Revision as of 17:01, 3 August 2022
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			{{About\|a collection of scales\|a type of scale\|Modal union}}
	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 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.

FloraC: Cleanup; +categories

2021-01-15T07:13:13Z

Cleanup; +categories

← Older revision		Revision as of 07:13, 15 January 2021
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	A '''dome''' is the collection of modal variants, ie of [[~~Periodic_scale~~#~~Definition-~~Rotations\|rotations]], of a given [[~~Periodic_scale\|~~periodic scale]]. Mike Battaglia proposed the term (a permutation of the letters of "mode") to discuss [[~~Fokker_blocks\|~~Fokker ~~blocks~~]].		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.

	~~<span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;">~~For example, if you look at all of the periodic scales that you can get with the 25/24 and 81/80 chromas, you~~'ll~~ 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_blocks~~#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 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.

	While we~~'ve~~ defined a dome as a set, it should be noted it has a natural cyclic group structure.~~</span>~~		While we have defined a dome as a set, it should be noted it has a natural cyclic group structure.

			[[Category:Theory]]
			[[Category:Math]]
			[[Category:Fokker block]]
			[[Category:Term]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+A '''dome''' is the collection of modal variants, ie of [[Periodic_scale#Definition-Rotations|rotations]], of a given [[Periodic_scale|periodic scale]]. Mike Battaglia proposed the term (a permutation of the letters of "mode") to discuss [[Fokker_blocks|Fokker blocks]].
-&lt;span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;"&gt;For example, if you look at all of the periodic scales that you can get with the 25/24 and  81/80 chromas, you'll 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 blocks#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.
+<span style="background-color: rgba(255,255,255,0.917969); color: #222222; font-family: arial,sans-serif;">For example, if you look at all of the periodic scales that you can get with the 25/24 and  81/80 chromas, you'll 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_blocks#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.
-While we've defined a dome as a set, it should be noted it has a natural cyclic group structure.&lt;/span&gt;</pre></div>
+While we've defined a dome as a set, it should be noted it has a natural cyclic group structure.</span>

← Older revision		Revision as of 16:40, 27 August 2023
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	{{About\|a collection of scales\|a type of scale\|Modal union}}		{{About\|a collection of scales\|a type of scale\|Modal union}}
	A '''dome''' is ~~the~~ collection ~~of modal variants, i.e.~~ of [[Periodic scale #Rotations\|rotations]], of a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").		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 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 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 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.

← Older revision		Revision as of 14:05, 27 August 2023
Line 1:		Line 1:
	{{About\|a collection of scales\|a type of scale\|Modal union}}		{{About\|a collection of scales\|a type of scale\|Modal union}}
	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 the collection of modal variants, i.e. of [[Periodic scale #Rotations\|rotations]], of a given [[Fokker block]] recipe. [[Mike Battaglia]] coined the term (a permutation of the letters of "mode").

	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 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 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.

← Older revision		Revision as of 07:53, 26 February 2023
Line 6:		Line 6:
	While we have defined a dome as a set, it should be noted it has a natural cyclic group structure.		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:Math]]
	[[Category:Fokker block]]		[[Category:Fokker block]]
	[[Category:Term]]		[[Category:Term]]