If the Fourier transform didn't exist I don't know that any music could exist, since lack of it would imply that sounds of different frequencies could not be linearly combined. For example, imagine if playing a drum and violin simultaneously produced crackling static!

That being said, it's a poor linkbait title for a superficial article that's missing nuance, rigor, and causality. Anyone who takes interest in this subject should read Wikipedia or an actual textbook, lest they feed their Dunning-Kruger.