Data on pbar-p -> 3eta for beam momenta 600--1940 MeV/c are presented. The strongest channel is f_0(1500)-eta from the initial pbar-p state 1S0. Together with eta-pizero-pizero data, the 3eta data determine the branching ratio BR[f_0(1500) -> eta-eta]/BR[f_0(1500) -> pizero-pizero] = 0.42+-0.09. They are consistent with a dominant contribution from an I=0, C=+1 J^{PC} = 0^{-+} resonance observed earlier in the eta-pizero-pizero data; from the combined eta-pizero-pizero and 3eta data, its mass is M = 2320 pm 15 MeV and its width Gamma = 230+-35 MeV.
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