In the first movement of his piece, Messiaen wanted to create the strange sense of time ending. He achieved this in the most stunning manner. Time depends on things repeating, so he needed to produce a structure where you never truly hear the moment of repetition. While the clarinet imitates a blackbird and the violin a nightingale, the piano part plays a 17-note syncopated rhythm that just repeats itself over and over. But the chord sequence that the pianist plays, set to this rhythm sequence, consists of 29 chords, which are again repeated over and over. Such repeating patterns might lead to boredom and predictability, but not in this case. Because Messiaen’s choice of numbers—17 and 29—means that something rather magical… or mathematical, occurs. The numbers he chose are prime numbers, and their mutual indivisibility means that the rhythm and harmony that Messiaen has set up never get back in sync once the piece is in motion.

The two musical ideas set off at the beginning of the piece, but as the 17-note rhythm sequence begins its second cycle, the harmonic sequence is still working its way through its 29 chords. It’s only about 3/5ths through its sequence. Or, to be precise, 17/29ths of the way through. But once the harmonic sequence begins its second cycle, we are still five notes from finishing the second cycle of rhythm. The two musical ideas are kept out of sync. The choice of two prime numbers means that they don’t get back in step until you have heard 17×29=493 chords, by which time the piece has already finished. You never actually get a moment of true repetition.