  Implications of reduction procedures applied to the low energy part of the
vibrational density of states in glasses and supercooled liquids are considered
by advancing a detailed comparison between the excess - over the Debye limit -
vibrational density of states g(w) and the frequency-reduced representation
g(w)/w^2 usually referred to as the Boson peak. Analyzing representative
experimental data from inelastic neutron and Raman scattering we show that
reduction procedures distort to a great extent the otherwise symmetric excess
density of states. The frequency of the maximum and the intensity of the excess
experience dramatic changes; the former is reduced while the latter increases.
The frequency and the intensity of the Boson peak are also sensitive to the
distribution of the excess. In the light of the critical appraisal between the
two forms of the density of states (i.e. the excess and the frequency-reduced
one) we discuss changes of the Boson peak spectral features that are induced
under the presence of external stimuli such as temperature (quenching rate,
annealing), pressure, and irradiation. The majority of the Boson peak changes
induced by the presence of those stimuli can be reasonably traced back to
simple and expected modifications of the excess density of states and can be
quite satisfactorily accounted for the Euclidean random matrix theory.
Parallels to the heat capacity Boson peak are also briefly discussed.
