  We define the Bianchi-Massey tensor of a topological space X to be a linear
map from a subquotient of the fourth tensor power of H*(X). We then prove that
if M is a closed (n-1)-connected manifold of dimension at most 5n-3 (and n > 1)
then its rational homotopy type is determined by its cohomology algebra and
Bianchi-Massey tensor, and that M is formal if and only if the Bianchi-Massey
tensor vanishes.
  We use the Bianchi-Massey tensor to show that there are many (n-1)-connected
(4n-1)-manifolds that are not formal but have no non-zero Massey products, and
to present a classification of simply-connected 7-manifolds up to finite
ambiguity.
