  Schemes based on anticommuting scalar coordinates, corresponding to
properties, lead to generations of particles naturally. The application of
Grassmannian duality cuts down the number of states substantially and is vital
for constructing sensible Lagrangians anyhow. We apply duality to all of the
subgroups within the {\em classification} group
SU(3)$\times$SU(2)$_L\times$SU(2)$_R$, which encompasses the standard model
gauge group, and thereby determine the full state inventory; this includes the
definite prediction of quarks with charge -4/3 and other exotic states.
Assuming universal gravitational coupling to the gauge fields and parity even
property curvature, we also obtain $4\sin^2\theta_w = 1 - 2\alpha/3\alpha_s$
which is not far from the experimental value around the $M_Z$ mass.
