In many ways a musical number is a chaotic system. It has a number of `attractors' and there is some sort of order about these `attractors'. For instance, there are repeating sets of chord changes and a repeating beat, or meter. Nonetheless, these patterns do not repeat themselves exactly throughout a piece of music.
The beat of the music is not sterile and exactly repeating. It is like a heart beat. It slows down or speeds up a little. Often so little that it is not noticeable. The heart beat is chaotic, it does not keep perfect time. Like the heart, if the beat gets too far out of line, the music sounds bad. But also if the beat is too repetitive, the music sounds bad and is boring.
The same logic applies to the chord progressions typically played by piano or guitar, or even an orchestra in a classical piece. Although the chord pattern may repeat, different inversions, voicings, dynamics and rhythms are used over the pattern so that it does not repeat exactly. This is what makes the music interesting.
Music is not random (chaos does NOT mean random) yet it is not periodic (repeating). It probably can be described using ideas from chaos theory.
background fractal by sidd pre duck shun