[1] The observed modulation of galactic cosmic ray (GCR) intensity, on time and spatial scales, contains information regarding their transport in the heliosphere. One way to extract crucial information from the data is to study the rigidity dependence of modulation. A methodology is described to study the rigidity dependence of the short-term variations in galactic cosmic ray intensity Earth, in terms of the median rigidity of detector response (R m ) to cosmic ray spectrum. We define R m as the rigidity below which lies 50% of detector counting rate. For neutron monitors (NMs), it is easily calculated from the latitude survey obtained at sea level and higher elevations. We compute R m values for some NM sites; solar cycle dependence for them is shown to be small. Their practical utility is demonstrated in a study of transient cosmic ray solar modulation (Forbush decreases (FDs)), using data published in the literature. We plot the rigidity dependence of the amplitudes of three large Forbush decreases that occurred during the declining phase of three solar cycles (19, 20, and 21). We show that the Forbush decrease amplitude varies inversely with R m over a large range (1 to 300 GV) of GCR rigidities. Thereby, we rule out the existence of a ''transition rigidity'' suggested by Jokipii even for a short-term modulation (large Forbush decreases). We speculate that the force field model may be applicable to large Forbush decreases.