  We present a calculation of the Nucleon and Delta excited state spectrum on
dynamical anisotropic clover lattices. A method for operator construction is
introduced that allows for the reliable identification of the continuum spins
of baryon states, overcoming the reduced symmetry of the cubic lattice. Using
this method, we are able to determine a spectrum of single-particle states for
spins up to and including J = 7/2, of both parities, the first time this has
been achieved in a lattice calculation. We find a spectrum of states
identifiable as admixtures of SU(6) x O(3) representations and a counting of
levels that is consistent with the non-relativistic $qqq$ constituent quark
model. This dense spectrum is incompatible with quark-diquark model solutions
to the "missing resonance problem" and shows no signs of parity doubling of
states.
