After recalling the construction of a graded Lie bracket on the space of cyclic multilinear forms on a vector space $V$, due to Georges Pinczon, we prove the equivalence of this construction to a structure of quadratic associative algebra, up to homotopy, on $V$. In the associative case, it is easy to refind the associated usual Hochshild cohomology. By considering restriction to a subspace or a quotient space of forms, we can present in a completely similar way the cases of quadratic commutative and quadratic Lie algebras, up to homotopy, and the corresponding Harrison and Chevalley cohomologies.