  In this note we provide a formula for the Tjurina number of a join of
isolated hypersurface singularities in separated variables. From this we are
able to provide a characterization of isolated hypersurface singularities whose
difference between the Milnor and Tjurina numbers is less or equal than two
arising as the join of isolated hypersurface singularities in separated
variables. Also, we are able to provide new upper bounds for the quotient of
Milnor and Tjurina numbers of certain join of isolated hypersurface
singularities. Finally, we deduce an upper bound for the quotient of Milnor and
Tjurina numbers in terms of the singularity index of any isolated hypersurface
singularity, not necessarily a join of singularities.
