The apparatus, method of data analysis, and results of a spark-chamber experiment on the production of muon pairs by 12-GeV/c w~ and K~ mesons incident on carbon and iron are discussed in detail. Based on these measurements, the best values for the p°-meson mass and width are M p = 765±7 MeV and T p = 95±19 MeV, while the branching ratio r(p°-*MV")/r(p°-• TT + TT) = (5.6zbl.l)XlO" 5 . Values of the spin-density matrix elements p\x' for the dimuon system in the mass range 600 n + n~)/r(° -> all) and upper limits on decay modes T (rf*-+fi + }T)/T (if-> all) and r0?°-> TT°}I + H~)/T (r)°-^ all) are also given. The invariant-mass spectrum of the muon pairs shows no evidence for the existence of a / = 1"" isovector meson, other than the p°, up to 1300 MeV.