Full Text Info/History Metrics Abstract The human brain is a complex system, whose activity exhibits flexible and continuous reorganisation across space and time. The decomposition of whole-brain recordings into harmonic modes has revealed a repertoire of gradient-like activity patterns associated with distinct brain functions. However, the way these activity patterns are expressed over time with their changes in various brain states remains unclear. In this study, we develop the Harmonic Decomposition of Spacetime (HADES) framework that characterises how different harmonic modes defined in space are expressed over time, and, as a proof-of-principle, demonstrate the sensitivity and robustness of this approach to specific changes induced by the serotonergic psychedelic N,N-Dimethyltryptamine (DMT) in healthy participants. HADES demonstrates significant decreases in contributions across most low-frequency harmonic modes in the DMTinduced brain state. When normalizing the contributions by condition (DMT and non-DMT), we detect a decrease specifically in the second functional harmonic, which represents the uni- to transmodal functional hierarchy of the brain, supporting the hypothesis that functional hierarchy is changed in psychedelics. Moreover, HADES’ dynamic spacetime measures of fractional occupancy, life time and latent space provide a precise description of the significant changes of the spacetime hierarchical organization of brain activity in the psychedelic state.