Rational homotopy equivalence is a weakening of the usual notion of homotopy equivalence, that is easier to study algebraically in terms of commutative differential graded algebras (like the de Rham complex of a smooth manifold). The simplest rational homotopy invariant is the rational cohomology algebra, but there can in addition be so-called Massey products between triples or higher tuples of classes that can also distinguish rational homotopy types. Defining tensors on the cohomology of a space by multiplying triple or fourfold Massey products by a further cohomology class gives an object that has less dependence on choices than the Massey products themselves, making them easier to work with. On the other hand, for a closed oriented manifold, Poincare duality allows all Massey products to be recovered from these tensors. Moreover, suitable interpretations of these tensors can capture information about the rational homotopy type even when the Massey products are undefined, and they have nice functoriality properties. For closed k-connected manifolds of dimension up to 6k+2 (k > 0), these tensors (along with the cohomology algebra itself) suffice to determine the rational homotopy type. This is based on joint work with Diarmuid Crowley and Csaba Nagy.