The origin of the human alpha rhythm has been a matter of debate since Lord Adrian attributed it to synchronous neural populations in the occipital cortex. Although some authors have pointed out the Gaussian characteristics of the alpha rhythm, their results have been repeatedly disregarded in favor of Adrian’s interpretation; even though the first EEG Gaussianity reports can be traced back to the origins of the field. Here we revisit this problem using the envelope analysis — a method that relies on the fact that the coefficient of variation of the envelope (CVE) for continuous-time zero-mean Gaussian noise (as well as for any filtered sub-band) is equal to , thus making the CVE a fingerprint for Gaussianity. As a consequence, any significant deviation from is linked to synchronous neural dynamics. We analyzed occipital EEG and iEEG data from massive public databases. Our results showed the human alpha rhythm can be characterized either as a synchronous or as a Gaussian signal based on the value of its CVE. Furthermore, Fourier analysis showed the canonical spectral peak at ≈ 10[Hz] is present in both the synchronous and Gaussian cases, thus demonstrating this same peak can be produced by different underlying neural dynamics. This study confirms the original interpretation of Adrian regarding the origin of the alpha rhythm but also opens the door for the study of Gaussianity in brain dynamics. These results suggest a broader interpretation for event-related synchronization/desynchronization (ERS/ERD) may be needed. Envelope analysis constitutes a novel complement to Fourier-based methods for neural signal analysis relating amplitude modulation patterns (CVE) to signal energy.