The centrality dependence of transverse momentum distributions and yields for ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},{K}^{\ifmmode\pm\else\textpm\fi{}},p$, and $\overline{p}$ in $\text{Au}+\text{Au}$ collisions at $\sqrt{{s}_{NN}}=200\phantom{\rule{0.3em}{0ex}}\text{GeV}$ at midrapidity are measured by the PHENIX experiment at the Relativistic Heavy Ion Collider. We observe a clear particle mass dependence of the shapes of transverse momentum spectra in central collisions below $\ensuremath{\sim}2\phantom{\rule{0.3em}{0ex}}\text{GeV}∕c$ in ${p}_{T}$. Both mean transverse momenta and particle yields per participant pair increase from peripheral to midcentral and saturate at the most central collisions for all particle species. We also measure particle ratios of ${\ensuremath{\pi}}^{\ensuremath{-}}∕{\ensuremath{\pi}}^{+}$, ${K}^{\ensuremath{-}}∕{K}^{+}$, $\overline{p}∕p$, $K∕\ensuremath{\pi}$, $p∕\ensuremath{\pi}$, and $\overline{p}∕\ensuremath{\pi}$ as a function of ${p}_{T}$ and collision centrality. The ratios of equal mass particle yields are independent of ${p}_{T}$ and centrality within the experimental uncertainties. In central collisions at intermediate transverse momenta $\ensuremath{\sim}1.5--4.5\phantom{\rule{0.3em}{0ex}}\text{GeV}∕c$, proton and antiproton yields constitute a significant fraction of the charged hadron production and show a scaling behavior different from that of pions.
