Using simple and general arguments we propose an effective Hamiltonian for the description of low-energy pure QCD. The Hamiltonian is a function of spatially constant collective modes. Its eigenstates can be organized into bands classified by the irreducible representations of an O(8) group. The latter also determine parity and charge conjugation of the states. The energy spectrum agrees well with the glueball spectrum as measured on the lattice, and in particular the level ordering with respect to spin is naturally explained.