LVG calculations for a four-dimensional parameter space: the [HCN]/[CO] abundance ratio and gas kinetic temperature are given at the top of each panel, while the axes of each panel are the gas volume density and the ratio of column density to linewidth (or equivalently of volume density to velocity gradient). The contours show the expected line ratio based on the emitted fluxes in Jy km s^-1. The locus representing the range of parameters possible for the nucleus and ring of NGC 3227 are drawn in red and green respectively. The dashed orange lines are curves of equal velocity gradient (in km s^-1 pc^-1), and indicate which regions of the parameter space are physically plausible. In particular, the locus of self-gravitating virialised clouds is represented by the dot-dash blue line.