To interpolate between properties of these two basic types, we must investigate C*-algebras given by softened relations, in particular with emphasis on their K-theory. A surprisingly weak correlation between the K-theory of the C*-algebras given by exact and softened relations leads to delicate problems which must be treated with care.
As an example of a set of relations which are prone to an analysis of this kind we study the pairs of unitaries commuting up to rational rotation.