Motion in Magnetic Resonance Imaging (MRI) scans results in image corruption and remains a barrier to clinical imaging. Motion correction algorithms require accurate sensing, but existing sensors are limited in sensitivity, comfort, or general usability. We propose Beat Pilot Tone (BPT), a radio frequency (RF) motion sensing system that is sensitive, comfortable, versatile, and scalable. BPT operates by a novel mechanism: two or more transmitted RF tones form standing wave patterns that are modulated by motion and sensed by the same receiver coil arrays used for MR imaging. By serendipity, the tones are mixed through nonlinear intermodulation in the receiver chain and digitized simultaneously with the MRI data. We demonstrate BPT's mechanism in simulations and experiments. Furthermore, we show in healthy volunteers that BPT can sense head, bulk, respiratory, and cardiac motion, including small vibrations such as displacement ballistocardiograms. BPT can distinguish between different motion types, achieve greater sensitivity than other methods, and operate as a multiple-input multiple-output (MIMO) system. Thus, BPT can enable motion-robust MRI scans at high spatiotemporal resolution in many applications.