The slow compaction of a tapped granular packing is reminiscent of the low-temperature dynamics glasses. Here, I study the dynamics of granular compaction by means of a volumetric spectroscopy. While the specific packing volume v displays glassy aging and memory effects at low tapping amplitudes Gamma, the dynamic volumetric susceptibility chi(v)= partial differentialv/ partial differentialGamma displays minimal glassy effects, and its frequency spectrum gives no indication of a rapidly growing time scale. These features are contrast sharply with that found in the dielectric and magnetic susceptibilities of structural and spin glasses. Instead, chi(v) appears to exhibit the behavior of a dynamic configurational specific heat, such as that obtained from computer simulations of spin-glass models. This suggests that the glassy dynamics of granular compaction is controlled by statistically rare processes that diverge from the typical dynamics of the system. From modifications of the dynamical spectrum by finite system size, I suggest that these glassy processes derive from large-scale collective particle rearrangements.