I consider the general class of theories in which there is a new ultralight scalar field that mediates an equivalence principle violating, long-range force. In such a framework, the Sun and Earth act as sources of the scalar field, leading to potentially observable location-dependent effects on atomic and nuclear spectra. The sensitivity of current and next-generation atomic and nuclear clocks to these effects is determined and the results compared against the existing laboratory and astrophysical constraints on equivalence principle violating fifth forces. It is shown that, in the future, the annual modulation in the frequencies of atomic and nuclear clocks in the laboratory caused by the eccentricity of Earth’s orbit around the Sun may offer the most sensitive probe of this general class of equivalence principle violating theories.