The search for the universal laws of human brain function is still on-going but progress is being made. Here we describe the novel concepts of connectome harmonics and connectome-harmonic decomposition, which can be used to characterize the brain activity associated with any mental state. We use this new frequency-specific language to describe the brain activity elicited by psilocybin and LSD and find remarkably similar effects in terms of increases in total energy and power, as well as frequency-specific energy changes and repertoire expansion. In addition, we find enhanced signatures of criticality suggesting that the brain dynamics tune toward criticality in both psychedelic elicited states. Overall, our findings provide new evidence for the remarkable ability of psychedelics to change the spatiotemporal dynamics of the human brain.