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. While 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 EEG. 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 white noise (as well as for any filteredsub-band) is equal to √(4−π)/π≈0.523, thus making the CVE a fingerprint for Gaussianity. As a consequence, any significant deviation from Gaussianity is linked to synchronous neural dynamics. Low-CVE signals come from phase-locking dynamics, while mid-CVE signals constitute Gaussian noise. High-CVE signals have been linked to unsteady dynamics in populations of nonlinear oscillators. We analyzed occipital EEG and iEEG data from massive public databases and the order parameter of a population of weakly coupled oscillators using the envelope analysis. Our results showed that the human alpha rhythm can be characterized as a rhythmic, Gaussian, or pulsating signal due to intra- and inter-subject variability. Furthermore, Fourier analysis showed that the canonical spectral peak at≈10[Hz] is present in all three CVE classes, thus demonstrating that this same peak can be produced by rhythms, Gaussian noise, and pulsating ripples. Alpha-like signals obtained from a population of non-linear oscillators showed a different CVE depending only on the coupling constant, suggesting that the same neural population can produce the amplitude modulation patterns observed in experimental data. iEEG data, however, was found to be mostly Gaussian, specially the signals recorded from the calcarine cortex. These results suggest that a new interpretation for EEG event-related synchronization/desynchronization (ERS/ERD) may be needed. Envelope analysis constitutes a novel complement to traditional Fourier-based methods for neural signal analysis relating amplitude modulations (CVE) to signal energy.