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Open your browsers Console, goto _Network _ and filter on _XHR_. When playing a song, the url will be exposed as _"8bfe132f45b33640f499bfd91eb5a5c7f8e35552"_ or something simular. Right-click on the url and open in new tab. The song will start playing in that tab, just hit CTRL+S or Command+S and save it to your drive.
What did Spotify think of?