  The q-deformed harmonic oscillator within the framework of the recently
introduced Schwenk-Wess $q$-Heisenberg algebra is considered. It is shown, that
for "physical" values $q\sim1$, the gap between the energy levels decreases
with growing energy. Comparing with the other (real) $q$-deformations of the
harmonic oscillator, where the gap instead increases, indicates that the
formation of the macroscopic energy gap in the Schwenk-Wess $q$-Quantum
Mechanics may be avoided.
