Songs are made of sounds. Sounds (more generally, any kind of wave) can be mumbled, jumbled, mixed and many things, but they have a nice property: if you mix two notes (frequencies) together even if they mix they can be mathematically divided again in a thing that is called a spectrogram, that is basically a list of all the notes that are played together at a single time. This is really nice, because even if you have sound jumbled and mumbled you still can divide it and have a nice fingerprint of the song. And each instrument, voice, and hence song has a peculiar spectrogram, which is what our brain uses to discern different sounds. Notes are like the colors of sound.
What Shazam does is calculate this fingerprint, and since different songs have different sounds, it can be used to identify a song. And like colors, it’s really difficult to distort a sound so much that it cannot be determined, because frequencies tend to stay the same even with noise or obstacles, unlike amplitude (volume) that can be used to recognize songs but only if the recording is really really accurate, because noise and obstacles have a greater impact on amplitude than on frequency
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