  While charge density wave (CDW) instabilities are ubiquitous to
superconducting cuprates, the different ordering wavevectors in various cuprate
families have hampered a unified description of the CDW formation mechanism.
Here we investigate the temperature dependence of the low energy phonons in the
canonical CDW ordered cuprate La$_{1.875}$Ba$_{0.125}$CuO$_{4}$. We discover
that the phonon softening wavevector associated with CDW correlations becomes
temperature dependent in the high-temperature precursor phase and changes from
a wavevector of 0.238 reciprocal space units (r.l.u.) below the ordering
transition temperature up to 0.3~r.l.u. at 300~K. This high-temperature
behavior shows that "214"-type cuprates can host CDW correlations at a similar
wavevector to previously reported CDW correlations in non-"214"-type cuprates
such as YBa$_{2}$Cu$_{3}$O$_{6+\delta}$. This indicates that cuprate CDWs may
arise from the same underlying instability despite their apparently different
low temperature ordering wavevectors.
