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.
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