During rest, envelopes of band-limited on-going MEG signals co-vary across the brain in consistent patterns, which have been related to resting-state fMRI functional networks. To investigate the genesis of such envelope correlations, we consider a whole-brain network model assuming two distinct fundamental scenarios: one where each brain area generates oscillations in a single frequency, and a novel one where each brain area can generate oscillations in multiple frequency bands. The models share, as a common generator of damped oscillations, the normal form of a supercritical Hopf bifurcation operating at the critical border between the steady state and the oscillatory regime. The envelopes of the simulated signals are compared with empirical MEG data using new methods to analyse the envelope dynamics in terms of their phase coherence and stability across the spectrum of carrier frequencies. Considering the whole-brain model with a single frequency generator in each brain area, we obtain the best fit with the empirical MEG data when the fundamental frequency is tuned at 12Hz. However, when multiple frequency generators are placed at each local brain area, we obtain an improved fit of the spatio-temporal structure of on-going MEG data across all frequency bands. Our results indicate that the brain is likely to operate on multiple frequency channels during rest, introducing a novel dimension for future models of large-scale brain activity.