The Sun during the recent epoch of solar activity operated in a different way than during the last 60 years, being less active. We study temporal changes of the energy spectrum of the first three harmonics of the 27-day variation of the galactic cosmic rays (GCR) intensity during the unusual, recent solar minimum, between Solar Cycles 23 and 24 (SC 23/24) and compare with four previous minima. We show that the energy spectrum of the amplitudes of the recurrent variation of the GCR intensity is hard in the maximum epochs and is soft in the minimum epochs during Solar Cycles 20 -24, but with peculiarities during the Solar Minimum 23/24. In particular, while the energy/rigidity spectrum of the amplitudes of the first harmonic of the recurrent variation of the GCR intensity behaves practically the same as for previous epochs, the energy/rigidity spectrum of the amplitudes of the second and the third harmonics demonstrates a pronounced softening. We attribute this phenomenon to the decrease of the extension of the heliosphere caused by the decrease of the solar-wind dynamic pressure during the unusual Solar Minimum 23/24.