  We consider the spectrum of a second-order elliptic operator in divergence
form with periodic coefficients, which is known to be completely described by
Bloch eigenvalues. We show that under small perturbations of the coefficients,
a multiple Bloch eigenvalue can be made simple. The Bloch wave method of
homogenization relies on the regularity of spectral edge. The spectral tools
that we develop, allow us to obtain simplicity of an internal spectral edge
through perturbation of the coefficients. As a consequence, we are able to
establish Bloch wave homogenization at an internal edge in the presence of
multiplicity by employing the perturbed Bloch eigenvalues. We show that all the
crossing Bloch modes contribute to the homogenization at the internal edge and
that higher and lower modes do not contribute to the homogenization process.
