Our moment-to-moment conscious experience is paced by transitions between states, each one corresponding to a change in the electromagnetic brain activity. One consolidated analytical choice is to characterize these changes in the frequency domain, such that the transition from one state to the other corresponds to a difference in the strength of oscillatory power, often in pre-defined, theory-driven frequency bands of interest. Nonetheless, recent computational advances allow us to explore new ways to characterize electromagnetic brain activity and its changes. Here, we assembled a set of multiple transformations aiming to describe time series in a multidimensional feature space. On an MEG dataset with 29 human participants, we tested how the features extracted in this way described some of those state transitions known to elicit prominent changes in the frequency spectrum, such as eyes-closed versus eyes-open resting-state or the occurrence of visual stimulation. We then compared the informativeness of multiple sets of features by submitting them to a multivariate classifier (SVM). We found that the new features outperformed traditional ones in generalizing states classification across participants. Moreover, some of these new features yielded systematically better decoding accuracy than the power in canonical frequency bands that has been often considered a landmark in defining these state changes. Critically, we replicated these findings, after pre-registration, in an independent EEG dataset (N = 210). In conclusion, the present work highlights the importance of enriching our perspective on the characteristics of electromagnetic brain activity, by considering other features of the signal on top of power in theory-driven frequency bands of interest.