Forced nonharmonic excitation of the two-dimensional flow about a circular cylinder is studied by numerical simulations at mean Reynolds numbers of 180 and 150. Moderate deviations of the forced inflow velocity waveform from a pure harmonic generate different modes of phase-locked vortex formation in the cylinder wake, involving combinations of single and/or pairs of vortices for the same forcing frequency and peak-to-peak amplitude. The dynamical response of the wake oscillator is studied by employing phase portraits of the drag and lift coefficients that display modified limit-cycle behavior due to nonharmonic excitation. It is further shown that changing solely the velocity waveform can incite transition from a quasiperiodic state to a phase-locked state. The findings demonstrate that the wake oscillator is admissible to an infinite number of phase-locked and/or modulated states characterized by a single point on the frequency-amplitude plane.