This paper presents the concept of Resonant Bits, an interaction technique for encouraging engaging, slow and skilful interaction with tangible, mobile and ubiquitous devices. The technique is based on the resonant excitation of harmonic oscillators and allows the exploration of a number of novel types of tangible interaction including: ideomotor control, where subliminal micro-movements accumulate over time to produce a visible outcome; indirect tangible interaction, where a number of devices can be controlled simultaneously through an intermediary object such as a table; and slow interaction, with meditative and repetitive gestures being used for control. The Resonant Bits concept is tested as an interaction method in a study where participants resonate with virtual pendulums on a mobile device. The Harmonic Tuner, a resonance-based music player, is presented as a simple example of using resonant bits. Overall, our ambition in proposing the Resonant Bits concept is to promote skilful, engaging and ultimately rewarding forms of interaction with tangible devices that takes time and patience to learn and master.