The dynamic magnetic pair-density function (DymPDF) D_(rm M)(r, E) is obtained via the Fourier transform of the dynamic magnetic structure factor, S_(rm M)(Q, E), which is measured using nonpolarized inelastic neutron scattering. While there is a long history of magnetic excitation studies with S_(rm M)(Q, E), there are no reports on D_(rm M)(r, E). In this study, we examine simple magnet models and representative magnet examples, such as FeTiO₃ and YBa₂Cu₃O₆, to investigate the real-space dynamics of D_(rm M)(r, E). We derive the D_(rm M)(r, E) equations for simple magnet models in a low energy limit. By comparing these equations to the simulations, we demonstrate the characteristic energy dependence of real-space local magnon modes, including the transition of the magnon mode from acoustic to optical. Our novel analysis reveals the local magnon modes accompanied by a sign change in each spin-pair correlation at a given energy in nanoscale real space even under non-periodic conditions. This method is unique for studying local magnetic dynamics.