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In the brain, cross-frequency coupling has been hypothesized to result from the activity of specialized microcircuits. For example, theta-gamma coupling is assumed to be generated by specialized cell pairs (PING and ING mechanisms), or special cells (e.g., fast bursting neurons). However, this implies that the generating mechanisms is uniquely specific to the brain. In fact, cross-scale coupling is a phenomenon encountered in the physics of all large, multi-scale systems: phase and amplitude correlations between components of different scales arise as a result of nonlinear interaction. Because the brain is a multi-scale system too, a similar mechanism must be active in the brain. Here, we represent brain activity as a superposition of nonlinearly interacting patterns of spatio-temporal activity (collective activity), supported by populations of neurons. Cross-frequency coupling is a direct consequence of the nonlinear interactions, and does not require specialized cells or cell pairs. It is therefore universal, and must be active in neural fields of any composition. To emphasize this, we demonstrate the phenomenon in excitatory fields. While there is no doubt that specialized cells play a role in theta-gamma coupling, our results suggest that the coupling mechanism is at the same time simpler and richer: simpler because it involves the universal principle of nonlinearity; richer, because nonlinearity of collective activity is likely modulated by specialized-cell populations in ways to be yet understood.