Acoustid

Acoustid is a database containing acoustic fingerprints.
It is an open source project by Lukáš Lalinský.
Internet databases like MusicBrainz use it to identify a song by its audio content instead of tags.

 

The basic idea is to represent music as a picture.
Transform the audio into a spectrogram using short-time Fourier transform and you have the picture.

Convert it to notes and do some filtering.

This is way too large for a database so compress it by making  a kind of audio thumbnail.

 

For a more detailed description see How does Chromaprint work?

1. Acoustid - website 
2. Computer Vision for Music Identification - Y. Ke, D. Hoiem, and R. Sukthankar
3. Google's Next Generation Music Recognition - Google AI blog