At the introductory level, the demonstration and analysis of sound beating is usually limited to the superposition of two purely sinusoidal waves with equal amplitudes and very similar frequencies. Under such conditions, an observer hears the periodic variation of the loudness of a sound with an unchanging timbre. On the other hand, when complex waves with very similar frequencies are superimposed, each harmonic beats with a frequency proportional to the frequency of the harmonic. Consequently, the resulting sound exhibits a subtle variation of timbre with time. This article extends the normal introductory discussion of beating and explains why electronic phase shifters, devices familiar to many musicians, can produce the sound of beating complex waves.