We measured a change in the current transport of an antenna-coupled, multigate, GaAs/AlGaAs field-effect transistor when terahertz electromagnetic waves irradiated the transistor and attribute the change to bolometric heating of the electrons in the two dimensional electron channel. The observed terahertz absorption spectrum indicates coherence between plasmons excited under adjacent biased device gates. The experimental results agree quantitatively with a theoretical model we developed that is based on a generalized plasmonic transmission line formalism and describes an evolution of the plasmonic spectrum with increasing electron density modulation from homogeneous to the crystal limit. These results demonstrate an electronically induced and dynamically tunable plasmonic band structure.