Femtosecond (fs) x-ray pulses are a key tool to study the structure and dynamics of matter on its natural length and time scale. To complement radio-frequency accelerator-based large-scale facilities, novel laser-based mechanisms hold promise for compact laboratory-scale x-ray sources. Laser-plasma driven undulator radiation in particular offers high peak-brightness, optically synchronized few-fs pulses reaching into the few-nanometer (nm) regime. To date, however, few experiments have successfully demonstrated plasma-driven undulator radiation. Those that have, typically operated at single and comparably long wavelengths. Here we demonstrate plasma-driven undulator radiation with octave-spanning tuneability at discrete wavelengths reaching from 13 nm to 4 nm. Studying spontaneous undulator radiation is an important step towards a plasma-driven free-electron laser. Our specific setup creates a photon pulse, which closely resembles the plasma electron bunch length and charge profile and thus might enable novel methods to characterize the longitudinal electron phase space.