I don't know about Shazam's current algorithm specifically, but years ago I worked at a place with a mathematician that worked on gracenote's algorithms, and as

I don't know about Shazam's current algorithm specifically, but years ago I worked at a place with a mathematician that worked on gracenote's algorithms, and asked him for the basics on how it works. Basically, it records audio chopping it up into small segments and throwing them through a FFT. Then it takes that, and thinking of the data like a greyscale spectrograph image, runs it through a quantization filter that helps reject some noise, then converts that to locality sensitive hashes that are sent to the server. So basically FFT, filter, hash, lookup.