TapSongs are presented, which enable user authentication on a single "binary" sensor (e.g., button) by matching the rhythm of tap down/up events to a jingle timing model created by the user. We describe our matching algorithm, which employs absolute match criteria and learns from successful logins. We also present a study of 10 subjects showing that after they created their own TapSong models from 12 examples (< 2 minutes), their subsequent login attempts were 83.2% successful. Furthermore, aural and visual eavesdropping of the experimenter's logins resulted in only 10.7% successful imposter logins by subjects. Even when subjects heard the target jingles played by a synthesized piano, they were only 19.4% successful logging in as imposters. These results are attributable to subtle but reliable individual differences in people's tapping, which are supported by prior findings in music psychology.