  A systematic study of $\gamma$-bands observed in atomic nuclei is performed
using the triaxial projected shell model (TPSM) approach. The staggering phase
between the even and odd spin members of the $\gamma$-band for most the nuclei
investigated in the present work is found to have even-I-below-odd-I, which in
the framework of the collective model is considered as a signature of
$\gamma$-softness. It is observed that out of twenty-three systems studied,
only four nuclei, namely, $^{76}$Ge, $^{112}$Ru, $^{170}$Er and $^{232}$Th
depict staggering phase with odd-I-below-even-I, which is regarded as an
indication of the static $\gamma$-deformation in the collective model picture.
The inclusion of the quasiparticle excitations in the framework of
configuration mixing is shown to reverse the staggering phase from odd-I-down
to the even-I-down for all the studied nuclei, except for the aforementioned
four nuclei. Furthermore, by fitting a collective Bohr Hamiltonian to the TPSM
energies, the differences between the two models are delineated through a
comparison of the transition probabilities.
