FFT and PCA are totally different. FFT is a fixed linear transform - PCA finds the linear projection to k-space that retains the most variance from the original

FFT and PCA are totally different. FFT is a fixed linear transform - PCA finds the linear projection to k-space that retains the most variance from the original dataset. If you projected to the top k frequencies you'd just get a couple of tones, while PCA finds linear combinations of the original signal that are most "descriptive" in a sense. Also human hearing is much closer to a wavelet transform or STFT than FFT.