relation (CφR) of Josephson junctions (JJs) fails to fully describe the energy spectra of transmon artificial atoms across various samples and laboratories. While the microscopic theory of JJs contains higher harmonics in the CφR, these have generally been assumed to give insignificant corrections for tunnel JJs, due to the low transparency of the conduction channels. However, this assumption might not be justified given the disordered nature of the commonly used AlOx tunnel barriers. Indeed, a mesoscopic model of tunneling through an inhomogeneous AlOx barrier predicts contributions from higher Josephson harmonics of several %. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The measurement of Josephson harmonics in the CφR of standard tunnel junctions prompts a reevaluation of current models for superconducting hardware and it offers a highly sensitive probe towards optimizing tunnel barrier uniformity.