Olivier Messiaen's Quartet for the End of Time, Part 10

We now turn our attention to the “Danse de la fureur, pour les sept trompettes.” This movement features the quartet playing in unison with tessituras (the range of pitch content) that fall mostly in the staff. The movement uses a binary formal structure. And the double barline at Reh. I indicates the division between the exposition and development sections. 

Elastic Phrases and Additive Rhythms

Elastic phrase duration and rhythmic complexity characterize the opening theme of this movement. Phrases are “elastic” because Messiaen varies the number of rhythmic values in each phrase. These are known as “additive rhythms.” No meter given, so barlines are merely used to mark the end of phrases. Notice how the number of shorter rhythmic values leading up to a quarter note or half note differs from phrase to phrase in the example below.

Example: Theme of Movement VI at Rehearsal A. Brackets indicate rhythmic palindromes.

Fun With Rhythmic Palindromes

Also note the rhythmic palindromes (the same rhythm forwards or backwards) indicated by the brackets in the example above. Some rhythmic palindromes are nested within rhythmic palindromes while some overlap with other rhythmic palindromes. Others merely follow preceding rhythmic palindromes. If you like to compose music, you might find writing complicated rhythmic passages using rhythmic palindromes to be a lot of fun, too!    

Additive Rhythms Destroy Hypermeter

In the development section beginning at Reh. I, motives are treated with rhythmic augmentation (stretching out) and diminution (collapsing).  As previously discussed, the dynamic elasticity of phrase duration destroys the potential for hypermeter with the constant fluctuation of would-be hypermetric beat duration. This in turn affects the listener’s ability to accurately perceive the passage of time. 

In conclusion, the similarity between the elastic phrase durations of the fourth and sixth movements helps to unify Quatuor. While people might think that you are trying to sound like Messiaen, additive rhythms might also be a useful tool to use in your next composition. Food for thought.