  The phenomenological theory of ferroelectricity in spiral magnets presented
in [M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006)] is generalized to describe
consistently states with both uniform and modulated-in-space ferroelectric
polarizations. A key point in this description is the symmetric part of the
magnetoelectric coupling since, although being irrelevant for the uniform
component, it plays an essential role for the non-uniform part of the
polarization. We illustrate this importance in generic examples of modulated
magnetic systems: longitudinal and transverse spin-density wave states and
planar cycloidal phase. We show that even in the cases with no uniform
ferroelectricity induced, polarization correlation functions follow to the soft
magnetic behavior of the system due to the magnetoelectric effect. Our results
can be easily generalized for more complicated types of magnetic ordering, and
the applications may concern various natural and artificial systems in
condensed matter physics (e.g., magnon properties could be extracted from
dynamic dielectric response measurements).
