We introduce a variant of the usual K\"{a}hler forms on singular free divisors, and show that it enjoys the same depth properties as K\"{a}hler forms on isolated hypersurface singularities. Using these forms it is possible to describe analytically the vanishing cohomology, and the Gauss--Manin connection, in families of free divisors, in precise analogy with the classical description for the Milnor fibration of an isolated complete intersection singularity, due to Brieskorn and Greuel. This applies in particular to the family $\{D(f_\lambda)\}_{\lambda\in \Lambda}$ of discriminants of a versal deformation $\{f_\lambda\}_{\lambda\in\Lambda}$ of a singularity of a mapping. 1991 Mathematics Subject Classification: 14B07, 14D05, 32S40.