  The Skyrme model of nuclear physics requires quantisation if it is to match
observed nuclear properties. A simple technique is used to find the normal mode
spectrum of the baryon number B=4 Skyrme soliton, representing the $\alpha$
particle. We find sixteen vibrational modes and classify them under the cubic
symmetry group $O_h$ of the static solution. The spectrum possesses a
remarkable structure, with the lowest energy modes lying in those
representations expected from an approximate correspondence between Skyrmions
and BPS monopoles. The next mode up is the `breather', and above that are
higher multipole breathing modes.
