Plainspeak:
Accidental space is new and unique to KCM. It is a way of abtracting jumps, skips, and steps and create a frequency independent map. For that reason, the flat and sharp musical operators are given an algebra and this algebra is then provided as a map. Studying this map gives us the best high level view of how the major scale and all other scales are related to one another.
Visuals supporting this axiom:
Show how axiom 3, this one, depends on axiom 1 and the accidentals set up by the major mode. Axiom 2 not really relevant here.
What is accidental space
What do constructions in accidental space tell us about accidental space?
Quality (Major, Minor, MajMin, MinMaj, dim, fulldim, aug) labels isometric clusters between scales.
Make a point to not use dominant as quality to not get confussed with dominant as movement/expectation.
Category theory and accidental space
Objects: Heptatonic Scale
Arrows: Accidental Operatiors