We present a unified model for connected antenna arrays with a large number of tightly integrated (i.e., coupled) antennas in a compact space within the context of massive multiple-input multiple-output (MIMO) communication. We refer to this system as tightly-coupled massive MIMO. From an information-theoretic perspective, scaling the design of tightly-coupled massive MIMO systems in terms of the number of antennas, the operational bandwidth, and form factor was not addressed in prior art. We investigate this open research problem using a physically consistent modeling approach for far-field (FF) MIMO communication based on multi-port circuit theory. In doing so, we turn mutual coupling (MC) from a foe to a friend of MIMO systems design, thereby challenging a basic percept in antenna systems engineering that promotes MC mitigation/compensation. We show that tight MC widens the operational bandwidth of antenna arrays thereby unleashing a missing MIMO gain that we coin "bandwidth gain". Furthermore, we derive analytically the asymptotically optimum spacing-to-antenna-size ratio by establishing a condition for tight coupling in the limit of large-size antenna arrays with quasi-continuous apertures. We also optimize the antenna array size while maximizing the achievable rate under fixed transmit power and inter-element spacing. Then, we study the impact of MC on the achievable rate of MIMO systems under line-of-sight (LoS) and Rayleigh fading channels. These results reveal new insights into the design of tightly-coupled massive antenna arrays as opposed to the widely-adopted "disconnected" designs that disregard MC by putting faith in the half-wavelength spacing rule.