Critical role of magnetic moments in the lattice dynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>YBa</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi>Cu</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mn>6</mml:mn></mml:msub></mml:math>

The role of lattice dynamics in unconventional high-temperature superconductivity is still vigorously debated. Theoretical insights into this problem have long been prevented by the absence of an accurate first-principles description of the combined electronic, magnetic, and lattice degrees of freedom. Utilizing the recently constructed ${\mathrm{r}}^{2}$SCAN density functional that stabilizes the antiferromagnetic (AFM) state of the pristine oxide ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6}$, we faithfully reproduce the experimental dispersion of key phonon modes. We further find significant magnetoelastic coupling in numerous high-energy Cu-O bond stretching optical branches, where the AFM results improve over the soft nonmagnetic phonon bands.