I was passively analyzing Olivier Messiaen's Vingt regards sur l'enfant-Jésus and I came across the marking Valeurs progressivement ralenties (resp. Valeurs progressivement accélérées) accompanied by a sixteenth note being appended to (resp. dropped from) the next note. When I say "decelerating technique" or "accelerating technique," I am referring to these practices of adding to/subtracting from a note length. The first time one sees these things (I think) is at the beginning of the Regard de l'Onction terrible (138):
An inversion of this (in which the ralenties and accélérées swap voices) occurs at the end of this Regard (151). One also sees it in the Regard de l'Eglise d'amour (171–72):
etc. (To be honest, I noticed the second one first.)
I have experimented with the decelerating technique on some occasions, but I have no legitimate justification for using it. In "Musical Analysis of Regard de l'Onction Terrible by Olivier Messiaen: Context, Symbolism, Form and Performance," Aline da Silva Alves and Adriana Lopes Moreira cite Messiaen, who says,
Le verbe assume une certaine nature humaine: choix de la chair de Jésus par la Majesté épouvantable . . . - Une vieille tapisserie représente le Verbe de Dieu en lutte sous les traits du Christ à cheval on ne voit que ses deux mains sur la garde de épée qu'il brandit au milieu des éclairs. Cette image m'a influencé. - Dans l'Introduction et la Coda, valeurs progressivement ralenties superposées aux valeurs progressivement accélerées et inversement. (43)
The word assumes a definite human form: the choice of the flesh of Jesus by the awesome Majesty . . . - An old tapestry depicts the Word of God at war under the guise of Christ on horseback; only his two hands are seen brandishing a sword amongst thunderbolts. This image influenced me. The Introduction and Coda have progressively decelerating values superimposed on progressively accelerating values and vice versa. (43)
This merely acknowledges things. However, they reference Francisco Ciscar, who discusses the inversion in the Regard de l'Onction terrible:
Ciscar (2004: 65) suggests that the phrase "the word assumes a definite human form" is represented in the first Section of the piece where the upper staff "transforms" into the lower staff by using non-retrogradable rhythm. The following phrase, ". . . the choice of the flesh of Jesus by the awesome Majesty" is represented in the middle Sections that have the mood indication Solennel plus un peu vif (Solemn, but slightly alive), a repetitive Section with several transpositions of the musical material that, according to the Ciscar, demonstrates the search for the choice of the flesh of Jesus. This choice occurs in the last Section of the piece, in which the "human nature transforms into the Word of God," a process represented by the inversion relationship between the first and last Section of the piece. (43)
This idea of using the deceleration/acceleration technique as a mode of demonstrating a transformation is everything that I can find on it. I do not have Tome III of Messiaen's Traité de Rythme, de Couleur, et d’Ornithologie, which this paper cited and which I believe contains more insight into Messiaen's choice to use this technique. For anyone that does, I would be interested to hear any other comments that Messiaen made on it. Or what does anyone think Messiaen meant to do or wanted to evoke with this technique?
Further, where else are the deceleration/acceleration techniques found in any genre of music? I would be intrigued to hear it and the functionality thereof.
Lastly, do the deceleration/acceleration techniques have better-known names? I have a sneaking suspicion that they do and that's why I found so little on the matter.
Thank you very much.
Addendum (6 May 2023): Some time ago, I noticed that Messiaen uses this superimposition-inversion technique multiple times in movement VIII of his Turangalîla-Symphonie, for example, in the two-page excerpt below: This comes from pp. 311–312 of the Durand publication. (One can listen to this in the Myung-whun Chung recording here.)
Maybe someone knows something about the utilization of this technique in this context.
Either way, I will read Tome III (perhaps additionally Tome II) of Messiaen's Traité de Rythme, de Couleur, et d’Ornithologie, the liner notes from Myung-whun Chung's recording of the Turangalîla-Symphonie, and Technique de mon langage musical, whereafter I will come back to this post. I may also look into "Rhythmic Characters in Messiaen's 'Tristan trilogy.'" Feel free to add anything if you have any insight from these sources or in general.