  Orbits of automorphism groups of partially ordered sets are not necessarily
congruence classes, i.e. images of an order homomorphism. Based on so-called
orbit categories a framework of factorisations and unfoldings is developed that
preserves the antisymmetry of the order Relation. Finally some suggestions are
given, how the orbit categories can be represented by simple directed and
annotated graphs and annotated binary relations. These relations are reflexive,
and, in many cases, they can be chosen to be antisymmetric. From these
constructions arise different suggestions for fundamental systems of partially
ordered sets and reconstruction data which are illustrated by examples from
mathematical music theory.
