PCA can decompose sound to more accurate base functions (if you look at covariance), so if you combine a few of them together with different coefficients, you might be able to generate some cool sounds much faster than with traditional methods. Later you might feed this to a RNN and perhaps compose brand new good sounding songs automatically, make a new Vocaloid band in Japan and go on a tour, generating new music on each performance ;-)
I am actually very interested in its application to musical patterns, ie the actual notes rather than the audio. I think there's already a tool that uses this to generate rich and musically-correct MIDI on the fly but I'm having trouble remembering the name/manufacturer now. Future Retro maybe.
