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.
