  The famous vanishing of the density of states (DOS) in a band gap, be it
photonic or electronic, pertains to the infinite-crystal limit. In contrast,
all experiments and device applications refer to finite crystals, which raises
the question: Upon increasing the linear size $L$ of a crystal, how fast does
the DOS approach the infinite-crystal limit? We present a theory for finite
crystals that includes Bloch-mode broadening due to the presence of crystal
boundaries. Our results demonstrate that the DOS for frequencies inside a band
gap has a $1/L$ scale dependence for crystals in one, two and three dimensions.
