One of my favorite pieces by one of my favorite composers, here is Steve Reich’s Piano Phase performed on two pianos by a single pianist. One piano begins a simple melody and the other mirrors it, but over time the two pianos fall completely out of phase and then cycle back together again.

Here’s Reich on the piece from his classic book Writings on Music:

While this piece, Piano Phase, was later completely written out in musical notation with dotted lines between one bar and the next to indicate the gradual phase shifting, it was not necessary for us to read this notation while we played, nor is it necessary for any other musicians who play the piece. The musical material in Piano Phase may be learned and memorized in several minutes. […] I believe there are human activities that might be called “imitating machines” but that are, in reality, simply controlling your mind and body very carefully as in yoga breathing exercizes. This kind of activity turns out to be very useful physically and psychologically, as it focuses the mind to a fine point.