  We propose a model for the pair of electromagnon excitations observed in the
class of multiferroic materials {\it R}MnO$_3$ ({\it R} is a rare-earth ion).
The model is based on a harmonic cycloid ground state interacting with a
zone-edge magnon and its twin excitation separated in momentum space by two
times the cycloid wave vector. The pair of electromagnons is activated by cross
coupling between magnetostriction and spin-orbit interactions. Remarkably, the
spectral weight of the twin electromagnon is directly related to the presence
of a magnetically induced oscillatory polarization in the ground state. This
leads to the surprising prediction that TbMnO$_3$ has an oscillatory
polarization with amplitude 50 times larger than its uniform polarization.
