Instantaneous normal mode (INM) analysis of a set of bulk Morse systems is performed to monitor the changes in the curvature distribution that occur as a result of changing the range and curvature of the Morse potential. The liquids are bound by Morse pair potentials, V-alpha(r)=epsilon[e(e)(-alpha(1-(r/r)))-1](2)-epsilon, and share a common well-depth, epsilon, and equilibrium pair distance, r(e), but possess different values of range parameter, alpha, which is inversely correlated with the range and softness of the potential. INM analysis is used to index the changes in the curvature distribution of the potential energy surface that take place as the range parameter of the pair potential is varied and is shown to provide considerable insights into the accompanying dynamical changes. For example, the fraction of imaginary frequency modes, and therefore the diffusivity, is expected to rise with increasing temperature and decreasing range. In contrast, the Einstein frequency, which is a measure of the curvature of the effective potential well that traps a tagged particle in the liquid state, shows a nonmonotonic behavior with range. We also consider the behavior of INM spectra of liquids in relation to that of solids and gases. It is shown that INM analysis can be used to monitor the transition of a fluid from a liquidlike regime, dominated by collective rearrangements, to a gaslike regime, dominated by binary collisions. The transition to a collision-dominated regime is promoted by decreasing the range of the pair potential. Key INM spectral features are shown to undergo a discontinuous change on melting. Minimization of instantaneous configurations to the nearest saddle removes the imaginary frequencies in the solid phase but not in the liquid phase.