Conventionally, normal modes (eigenfunctions) are labeled with regard to the magnitudes of associated eigenfrequencies (eigenvalues). Linear mechanical structures governed by second order ode's possess a set of the oscillatory properties, two of which are: (i) all eigenfrequencies μkS are distinct, and (ii) the kth normal mode has exactly Nk = k − 1 nodes. Hence, under the conventional rule. μkS and NkS are in full agreement: both sets form strongly increasing sequences.It is well known that the first oscillatory property fails for linear mechanical structures governed by fourth order ODEs : they may have repeated eigenfrequencies. However, it turns out that the second oscillatory property also fails : several non-consecutive modes may have the same number of nodes. Thus. in this case, the conventional rule may lead to the complete disagreement between both sets: while μkS form an increasing (non-descending) sequence, a sequence of NkS may be disordered. Therefore, (i) higher modes may have a smaller number of nodes than lower modes (in particular, the fundamental mode may have many nodes, while any higher mode may even be nodeless) and, (ii) the normal mode response, treated as functions of a rigidity (or inertia) parameter of the structure, become discontinuous. The latter disadvantage directly relates to the problem of modal truncation : small changes in mechanical properties of the structure may lead to significant (even complete) changes in the modal responses due to the same excitation.All such spectral features are studied in the proposed paper with regard to regular continuous beams with elastic interior supports whose relative stiffness is considered as a rigidity parameter.