# Density of states of classical harmonic oscillator in phase space

Since all classical harmonic oscillators are ellipses in phase (position-momentum) space, and since the entire phase trajectory of a given system (with a fixed rigidity and mass factor) can be specified from either the peak momentum or displacement in the trajectory, why is it said that the number of states available to the given oscillator is proportional to the area inside the phase trajectory, and not to the peak value of the position/momentum?