  We describe a method for computing discriminants for a large class of
families of isolated determinantal singularities -- more precisely, for
subfamilies of ${\mathcal G}$-versal families. The approach intrinsically
provides a decomposition of the discriminant into two parts and allows the
computation of the determinantal and the non-determinantal loci of the family
without extra effort; only the latter manifests itself in the Tjurina
transform. This knowledge is then applied to the case of Cohen-Macaulay
codimension 2 singularities putting several known, but previously unexplained
observations into context and explicitly constructing a counterexample to
Wahl's conjecture on the relation of Milnor and Tjurina numbers for surface
singularities.
