  A simple model shows how it is possible to create a gap in the vibrational
spectrum of a one-dimensional lattice. The proposed model is a host-guest chain
having, instead of point-like masses connected by spring, massive cages hosting
particles inside. We imagine the cage as a rigid box containing a mass linked
by a spring to the box inner wall. The presence of guests creates an energy gap
in the dispersion of vibrational frequencies. The gap is about the internal
resonance of the mass hidden in the cage.
