Fresnoite, a piezoelectric mineral, develops a modulation in its basal plane below ~ 433 K that is incommensurable with the tetragonal lattice. Such transitions can be understood in terms of forming a regular lattice of solitons, where each soliton adds a phase shift to the translational periodicity. Dynamic modulations of the phase are called phasons, and are expected gapless excitations with acoustic-like linear dispersion, but with a velocity distinct from that of sound. Although recognized in 1954, observations of propagating phasons have been limited because of typically strong mode damping. We observed sharp propagating phasons in fresnoite using inelastic neutron scattering. They are supersonic with velocities 2.8 to 4.3 times faster than sound. These results have interesting implications for thermal and transport properties. For example, designing incommensurable modulations into a device might enable the ballistic channeling of lattice energy at speeds beyond the limits phonons.