  In the homogenization of composite metamaterials the role played by the
relative positions of the wires and resonators is not well understood, though
essential. We present a general argument which shows that the homogenization of
such metamaterials can be seen as the homogenization of 1D single negative
stacks. The sensitivity to the geometrical parameters is due to the fact that
light sees the harmonic mean of the dielectric constant when propagating
parallel to the layers. Since the dielectric constant is not positive definite
the harmonic mean is not bounded and presents abrupt variations. We discuss
applications of this remarkable phenomenon.
