Feature vector for music recommender system
For a big data, deep learning approach, you could try constructing an autoencoder from something such as WaveNet to achieve dimensionality reduction to get a feature vector. Alternatively, you could take STFT (short time Fourier transform) spectra of the songs over time and feed them into an RNN, again in autoencoder fashion. My intuition though is that, due to the immense complexity of musical genres, and current limitations of consumer hardware, any approach based on the raw audio alone is going to be very disappointing (unless you have a GPU farm). 

Really grossly, you may get some results by finding the BPM/tempo, the spectral density, overall entropy, variance in entropy over time. 

Actually, look at some of the feature extractors used in this Kaggle EEG contest. This may give you some rudimentary results, especially combined with XGB (extreme gradient boosting)

I believe most music recommendation services work like search engines, using an algorithm similar to PageRank to create a graph which associates artists.