Power spectra of magnetic pulsations observed at synchronous orbit by the ATS 6 satellite often show several spectral peaks simultaneously. Such pulsations, which we call harmonic events because of the nearly constant separation between successive peaks, are continuously observed in the dayside in the Pc 3--4 frequency range (6.6--100 mHz). The harmonic events are seen clearly only in the east-west magnetic field component. The spectral peaks are regularly spaced with a typical minimum separation of 14 mHz in the morining gradually decreasing to 10 mHz in the afternoon. In the dynamic spectra of harmonic events, the fundamental mode is usually absent. In addition, the relative amplitudes of the higher harmonics depend on the magnetic latitude. These observed features can be explained by a standing Alfv¿n wave consisting of many discrete harmonic frequencies. A statistical analysis of power spectra demonstrates that at least 10--30% of Pc 3 pulsations can be classified as harmonic events. Using the harmonic events, we are able to estimate the plasma mass density. For a selected event on August 7, 1975, the plasma mass density at the synchronous orbit is estimated to be 3--8 hydrogen mass/cm3.