A Study in the Charm of Impossibility
There is not a single note or structure in Olivier Messaien's Quartet for the End of Time without deep spiritual significance. Even the scherzo-type Intermède, composed expressly for the washrooms of Stalag VIIIA, is meaningful insofar as one may infer that it is an expression of the fight of the human spirit to rise up against the horrors of the Second World War.
The other movements all have intrinsic gematriatic connection to his Catholic faith; a faith that believed in the mystery of the divine redemption of humankind by Jesus Christ and of the mystery of Time itself, and how the eternal God, being outside of space and time as we understand it, as well as having entered into space and time, will bring us into eternity where he dwells, thus ending Time.
Nonretrogradable rhythms, notes with added values, and Messaien's Modes of Limited Transposition all point to the infinite. Messaien sought to bring the listener toward "eternity in space." A kind of surrealism pervades the Quartet; Messaien himself stated that ". . .its musical language is essentially immaterial, spiritual, and Catholic. . . special rhythms, beyond meter, contribute powerfully in dismissing the temporal."
What is a nonretrogradable rhythm?
First, let's talk about what a retrogradable rhythm might be: A rhythm that is retrogradable, if played both forward (as normal) and backward, results in two different but related patterns. A simple example of this, using letters to signify segments of rhythm, would be: