I’d say with respect to audio in particular, the Fourier Transform will tell you how loud (amplitude) the sounds of different pitches (frequencies) are in each short section of music.
If you make the section of music you transform at a time longer you can separate the pitches more finely, but as a result it will be an average over that longer period of time.
The Fast Fourier Transform (FFT) is just a computationally efficient way of performing a Fourier Transform with a digital computer.
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