The lifetimes of the long-lived threshold-state elementary particles exhibit a clear-cut spacing in powers of the. ne structure constant a. The uncertainly principle leads to a reciprocal 1/alpha similar or equal to 137 quantization of the mass-widths, and hence the masses, of these particles, which is evident in the experimental data. This empirical alpha-dependence includes all types of particle states-leptons, quarks, hadrons, and gauge bosons- and reveals that they share a common mass structure. The masses of the threshold-state particles (where the various quark combinations first appear) are accurately reproduced as multiples of three basic a- generated mass quanta: the. rst-order boson and fermion a- masses m(b) similar or equal to 70 MeV and m(f) similar or equal to 105 MeV, and the second- order fermion a- mass ma f = 14,394 MeV (which is produced at the Tevatron). By adding distinctively-patterned multiples of these masses to the electron ground state, we reproduce the isospin- averaged masses of the mu and tau leptons, the Standard Model constituent quarks (including the t), the proton, the B-c and Upsilon mesons, and the WZ gauge boson doublet, to better than 1% accuracy.