  We investigate the structure of singular Calabi-Yau varieties in moduli
spaces that contain a Brieskorn-Pham point. Our main tool is a construction of
families of deformed motives over the parameter space. We analyze these motives
for general fibers and explicitly compute the $L-$series for singular fibers
for several families. We find that the resulting motivic $L-$functions agree
with the $L-$series of modular forms whose weight depends both on the rank of
the motive and the degree of the degeneration of the variety. Surprisingly,
these motivic $L-$functions are identical in several cases to $L-$series
derived from weighted Fermat hypersurfaces. This shows that singular Calabi-Yau
spaces of non-conifold type can admit a string worldsheet interpretation, much
like rational theories, and that the corresponding irrational conformal field
theories inherit information from the Gepner conformal field theory of the
weighted Fermat fiber of the family. These results suggest that phase
transitions via non-conifold configurations are physically plausible. In the
case of severe degenerations we find a dimensional transmutation of the
motives. This suggests further that singular configurations with non-conifold
singularities may facilitate transitions between Calabi-Yau varieties of
different dimensions.
