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In this paper, we introduce a Z-graded variant of the periodic cyclic homology of associative algebras which generalizes the infinitesimal cohomology of affine algebras in characteristic 0 and show that it satisfies the Künneth formula (i.e. it commutes with the formation of tensor products). We also show that the Künneth formula in periodic cyclic homology holds only under the presence of certain finiteness conditions.