Dome

This page is about a collection of scales. For a type of scale, see Modal union.

A dome is the collection of modal variants, i.e. of rotations, of a given periodic scale. Mike Battaglia proposed the term (a permutation of the letters of "mode") to discuss Fokker blocks.

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 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.