We describe a method for computing discriminants for a large class of families of isolated determinantal singularities -more precisely, for subfamilies of 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.where J F denotes the submodule generated by the k matrices, each holding the partial derivatives of the entries of F w.r.t. one of the variables, and J op = AF + F B | A ∈ Mat(m, m; C{x}), Mat(n, n; C{x})Remark 2.10 The group G is a subgroup of the group K of Mather and coincides with it e.g. for complete intersections and Cohen-Macaulay codimension 2 singularities. It also appears as the subgroup K V of K in the literature, where