Using 2.45x10;{7} psi(2S) decays collected with the CLEO-c detector at the Cornell Electron Storage Ring we present the most precise measurements of magnetic dipole transitions in the charmonium system. We measure B(psi(2S)-->gammaeta_{c})=(4.32+/-0.16+/-0.60)x10;{-3}, B(J/psi-->gammaeta_{c})/B(psi(2S)-->gammaeta_{c})=4.59+/-0.23+/-0.64, and B(J/psi-->gammaeta_{c})=(1.98+/-0.09+/-0.30)%. We observe a distortion in the eta_{c} line shape due to the photon-energy dependence of the magnetic dipole transition rate. We find that measurements of the eta_{c} mass are sensitive to the line shape, suggesting an explanation for the discrepancy between measurements of the eta_{c} mass in radiative transitions and other production mechanisms.