  We study the notion of symplectic scalar curvature on the supermanifold over
an ordinary Fedosov manifold whose structural sheaf is that of differential
forms. In this purely geometric context, we introduce two families of odd
super-Fedosov structures, the first one is very general and uses a graded
symmetric connection, leading to a vanishing odd symplectic scalar curvature,
while the second one is based on a graded non-symmetric connection and has a
non-trivial odd symplectic scalar curvature. As a simple example of the second
case, we determine that curvature when the base Fedosov manifold is the torus.
