We introduce a new harmonic/percussive source separation (HPSS) method based on recently introduced local AM-FM estimators which were originally designed for synchrosqueezing techniques. Here, we show that these estimators can also be used to discriminate the harmonic part from the percussive part of a musical audio mixture. Our method blindly operates in the time-frequency plane and assigns each point to a source according to its local modulation rate that is expected to be higher for percussive sounds than for harmonic components. Our technique offers a simple and elegant mathematical formulation of the HPSS problem that can provide competitive results in comparison to state-of-the-art blind methods when comparatively evaluated on a music dataset.