Transverse momentum (\(p_{\rm{T}}\)) spectra of pions, kaons, and protons up to \(p_{\rm{T}} = 20\) GeV/\(c\) have been measured in Pb-Pb collisions at \(\sqrt{s_{\rm NN}} = 2.76\) TeV using the ALICE detector for six different centrality classes covering 0-80%. The proton-to-pion and the kaon-to-pion ratios both show a distinct peak at \(p_{\rm{T}} \approx 3\) GeV/\(c\) in central Pb-Pb collisions that decreases towards more peripheral collisions. For \(p_{\rm{T}} > 10\) GeV/\(c\), the nuclear modification factor is found to be the same for all three particle species in each centrality interval within systematic uncertainties of 10-20%. This suggests there is no direct interplay between the energy loss in the medium and the particle species composition in the hard core of the quenched jet. For \(p_{\rm{T}} < 10\) GeV/\(c\), the data provide important constraints for models aimed at describing the transition from soft to hard physics.