Oscillatory reconnection is a relaxation process in magnetized plasma, with an inherent periodicity that is exclusively dependent on the properties of the background plasma. This study focuses on the seismological prospects of oscillatory reconnection in the solar corona. We perform three sets of parameter studies (for characteristic coronal values of the background magnetic field, density, and temperature) using the PLUTO code to solve the fully compressive, resistive MHD equations for a 2D magnetic X-point. From each parameter study, we derive the period of the oscillatory reconnection. We find that this period is inversely proportional to the characteristic strength of the background magnetic field and the square root of the initial plasma temperature, while following a square root dependency upon the equilibrium plasma density. These results reveal an inverse proportionality between the magnitude of the Alfvén speed and the period, as well as the background speed of sound and the period. Furthermore, we note that the addition of anisotropic thermal conduction only leads to a small increase in the mean value for the period. Finally, we establish an empirical formula that gives the value for the period in relation to the background magnetic field, density, and temperature. This gives us a quantified relation for oscillatory reconnection, to be used as a plasma diagnostic in the solar corona, opening up the possibility of using oscillatory reconnection for coronal seismology.