  We report inelastic light scattering measurements of lattice dynamics related
to the incommensurate orbital order in $\mathrm{CaMn_7O_{12}}$. Below the
ordering temperature $T_\mathrm{o} \approx 250 \,\mathrm{K}$, we observe extra
phonon peaks as a result of Brillouin-zone folding, as well as a soft
vibrational mode with a power-law $T$-dependent energy, $\Omega = \Omega_{0}(1
- T/T_{\mathrm{o}})^{1/2}$. This temperature dependence demonstrates the
second-order nature of the transition at $T_\mathrm{o}$, and it indicates that
the soft mode can be regarded as the amplitude excitation of the composite
order parameter. Our result strongly suggests that the lattice degrees of
freedom are actively involved in the orbital-ordering mechanism.
