  We present results of a 2+1+1 flavor twisted mass lattice QCD computation of
the spectrum of $D$ mesons and $D_s$ mesons and of charmonium. Particular focus
is put on the positive parity $D$ states (so-called $D^{\ast \ast}$ mesons)
with quantum numbers $J^P = 0^+$, $1^+$ and $2^+$. Besides computing their
masses we are also separating and classifying the two $J^P = 1^+$ states
according to the angular momentum/spin of their light degrees of freedom (light
quarks and gluons) $j =1/2, 3/2$.
