We investigate a relation between the energies of nuclear excited levels and its periodic phases for nuclei with A = 14 - 244 in the energy region up to several tens MeV. These levels include neutron and proton resonances, excited levels below neutron and proton separation energies and also vibrational and rotational bands in unstable nuclei. Here we use level periods less than 50 keV. We found that series of parabolic fringes appear in the plots of level energies vs. its periodic phases in various excitation modes. Distinguished fringes can be observed for neutron and proton resonances in nuclei with neutron or proton magic numbers: 37 Cl, 59 Ni, 61 Ni and 62 Ni. For neutron and proton resonances in a wide mass range of nuclei, parabolic fringes with the same periods and scales can be observed at the same incident energies. Each fringe is separated by a phase difference of 1/n , where n is an integer. We interpret the parabolic fringes as a result of interference effects based on time; a quantized phase difference of 1/n can be connected to a discrete time delay of wave pulsations. These fringe spectra were compared between different nuclear excitation modes.