  The distinctions in the mass spectra of large sodium (Na_N) and aluminum
(Al_N) clusters are discussed. A semiclassical method is used to describe the
shell effects within a spherical jellium model. It allows one to analyze the
relative role of different classical trajectories in the formation of
electronic supershells in clusters of various sizes at zero and finite
temperatures. A criterion for the hardness of the self-consistent potential is
formulated. The conjecture that the five-point-star trajectories make the main
contribution to the spectral oscillations for large soft-potential Al_N
(250<N<900) clusters is substantiated. The computational results are in
agreement with the mass spectra of the Al_N clusters at T ~ 300 K.
