  The charmonium system has several excited states below the energy threshold
for decay into $D$ and $\bar{D}$ mesons, which can in principle be studied
accurately in lattice QCD. Studies that include many states in the spectrum
have typically only been done at one value of the lattice spacing and with
relatively heavy light quarks in the sea. Here we give preliminary results for
radial and orbital excitation energies for charmonium from a calculation on
2+1+1 MILC configurations at multiple lattice spacings and including physical
values for $u/d$ quark masses. We use the HISQ formulation for $c$ to obtain
small discretisation errors and smeared operators to improve excited state
overlap.
