  We present EMPIRE, an IRAM 30-m large program that mapped $\lambda = 3{-}4$
mm dense gas tracers at $\sim 1{-}2\,$kpc resolution across the whole
star-forming disk of nine nearby, massive, spiral galaxies. We describe the
EMPIRE observing and reduction strategies and show new whole-galaxy maps of
HCN(1-0), HCO$^+$(1-0), HNC(1-0) and CO(1-0). We explore how the HCN-to-CO and
IR-to-HCN ratios, observational proxies for the dense gas fraction and dense
gas star formation efficiency, depend on host galaxy and local environment. We
find that the fraction of dense gas correlates with stellar surface density,
gas surface density, molecular-to-atomic gas ratio, and dynamical equilibrium
pressure. In EMPIRE, the star formation rate per unit dense gas anti-correlates
with these same environmental parameters. Thus, although dense gas appears
abundant the central regions of many spiral galaxies, this gas appears
relatively inefficient at forming stars. These results qualitatively agree with
previous work on nearby galaxies and the Milky Way's Central Molecular Zone. To
first order, EMPIRE demonstrates that the conditions in a galaxy disk set the
gas density distribution and that the dense gas traced by HCN shows an
environment-dependent relation to star formation. However, our results also
show significant ($\pm 0.2$ dex) galaxy-to-galaxy variations. We suggest that
gas structure below the scale of our observations and dynamical effects likely
also play an important role.
