Neutron monitor counting rates and solar wind velocity, interplanetary magnetic field, sunspot number and total solar irradiance measurements from 2013 to 2018 corresponding to the end of solar maximum and the decreasing phase of the Solar Cycle 24 have been used. The main objective is to check whether the periodicities observed in the cosmic rays are affected by the magnetic rigidity or the height at which the neutron monitors are placed. A Global Neutron Monitor (GNM) has been defined as representative of the neutron monitor global network. This GNM is constructed by averaging the counting rates of a set of selected neutron monitors. The selection process is based on the combination of three new data quality criteria, which are applied to neutron monitors in the Neutron Monitor Data Base giving a final pool of 22 selected neutron monitors. Morlet wavelet analysis is applied to the GNM and the selected solar activity parameters to find the common periodicities. Short-term periodicities of 13.5, 27, 48, 92, 132 and 298 days have been observed in cosmic ray intensity. A clear inverse relationship between rigidity and spectral power has been obtained for the 13.5-, 48-, 92-, 132-day periods. A not so clear but still observed direct relationship between the height of the neutron monitors and the spectral power for the 48-, 92-, 132-day periods has been also found. The periodicity of 92 days is the one which shows the highest dependence with rigidity cutoff and height. As far as we know, this is the first time that these dependencies are reported. We think that these observations could be explained by assuming some cosmic ray intensity energy dependence in such periodicities and a competitive effect between rigidity and height.