  It is shown that a matrix model with SO(d,d) global symmetry is derived from
a generalized Yang-Mills theory on the standard Courant algebroid. This model
keeps all the positive features of the well-studied type IIB matrix model, and
it has many additional welcome properties. We show that it does not only
capture the dynamics of spacetime, but it should be associated with the
dynamics of phase space. This is supported by a large set of classical
solutions of its equations of motion, which corresponds to phase spaces of
noncommutative curved manifolds and points to a new mechanism of emergent
gravity. The model possesses an additional symmetry that exchanges positions
and momenta, in analogy to quantum mechanics. It is argued that the emergence
of phase space in the model is an essential feature for the investigation of
the precise relation of matrix models to string theory and quantum gravity.
