A definition of inertial mass is advanced which views this mass property as being due to intrinsic periodic electromagnetic processes characterized by an amplitude R and an angular frequency co. The existence of a stable ElM composite mass unit, called a hylon, is then postulated composed of two or more of these primitive processes. Selected spacetime coherence relations are then imposed on to and R through ad hoc quantizations based on notions borrowed from historical physical theories. Elementary particles are then investigated to test the efficacy of the mass definition and coherence relations. It is found that by equating the postulated hylon mass with the experimental pion masses, a mass spectrum emerges which has a close correspondence with many of the more stable particles and resonances. A case is then made for considering these particles as being primarily electromagnetic in nature and exhibiting an underlying space-time structure in terms of the theory advanced.