  Using a new quark-field construction algorithm and a large variational basis
of operators, we extract a highly excited isovector meson spectrum on dynamical
anisotropic lattices. We show how carefully constructed operators can be used
to reliably identify the continuum spin of extracted states, overcoming the
reduced cubic symmetry of the lattice. Using this method we extract, with
confidence, excited states, states with exotic quantum numbers (0+-, 1-+ and
2+-) and states of high spin, including for the first time in lattice QCD,
spin-four states.
