Dome: Difference between revisions
No edit summary |
m Direct link to Fokker arena (new redirect) |
||
| (2 intermediate revisions by one other user not shown) | |||
| 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 | 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 domes obtainable from the 25/24 and 81/80 [[ | 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. | ||
Latest revision as of 18:12, 28 July 2025
- This page is about a collection of scales. For a type of scale, see Modal union.
A dome is a collection of 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 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.