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): enter image description here

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): enter image description here

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: enter image description hereenter image description here 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.

Addendum (8 March 2024): Today, I was reading and listening to Messiaen's Cantéyodjayâ and I found other instances of superimposition-inversion, namely at 5:38 and 8:32 of this YouTube video of a recording by Roger Muraro posted by Cmaj7. These instances are marked Gamme chromatique des durées, droite et rétrograde. I now realize that gamme chromatique des durées 'chromatic scale of durations' is the name that Messiaen gives to taking multiples of a base unit (in the Vingt regards, the sixteenth note, and in Cantéyodjayâ, the thirty-second note). According to this website:

La gamme chromatique de durées est faite des multiples d'une unité de base, par exemple une triple croche, deux triples croches, . . . , n triples croches. Chacune des façons différentes de grouper les valeurs de la gamme correspond à une de ses permutations.

The chromatic scale of durations is made up of multiples of a basic unit, for example one thirty-second note, two thirty-second notes, . . . , n thirty-second notes. Each of the different ways of grouping the values of the scale corresponds to one of its permutations.

These ways of grouping the values are the permutations symétriques that Messiaen discusses in Tome III of Traité de Rythme, de Couleur, et d’Ornithologie, in isolation and in his analysis of Chronochromie. The permutation in which I have been interested is simply the identity (and its "retrograde").

It's nice to have this extra nomenclature. However, Tome III does not give too much insight into the meaning of the superimposition-inversion and even the individual voices (if there is any beyond it being a serial technique). Tome II contains an analysis of the Vingt regards, so I hope to find some answers from Messiaen there.

When this question was active, I briefly analyzed the Quatuor pour la fin du temps, and I did not find anything related to the discussion there. That was a while ago, so I will give it another shot soon.

It seems that Grant Sawatzky's thesis "Olivier Messiaen's permutations symétriques in theory and practice" has useful input (in particular on examples of the permutations symétriques in practice) too.

Hopefully this provides some more opportunity for experts to jump in.

  • I'm left with the feeling that you've left your core question unstated. Which "techniques" are you asking about? The notated rhythm increasing by sixteenth-note values (sixteenth, eighth, eighth+sixteenth, quarter, ...)? (or subtracted from)
    – Aaron
    Commented Jul 31, 2022 at 23:20
  • @Aaron, I am referring to both of those things (sixteenth, eighth, eighth + sixteenth, quarter, etc. and for example half, half - sixteenth, half - eighth, etc.). I will edit my question to make that more clear. Commented Jul 31, 2022 at 23:50
  • @Aaron, I should add that I do not have one precise question in mind. I am just really curious about Messiaen's use of these deceleration/acceleration techniques and other musicians' uses of them. Commented Aug 1, 2022 at 0:06
  • At least to me, it seems much more clear now. Thanks for taking the time to update.
    – Aaron
    Commented Aug 1, 2022 at 0:55
  • I don't know everything, but I do think this is essentially unique to Messaien. These techniques do appear earlier, at least as early as Quatuor pour la fin du temps, and I think of them as a way of having compositional control over a non-periodic meter. It's not like there has been a lot of interest (though not none) in non-periodic meter before or since! Commented Aug 1, 2022 at 16:44

2 Answers 2


As composition students we gobbled up the scales of limited transposition and experimented with that "shrinking-stretching" idea from Vingt Regards. I've heard Quatuor Pour la Fin du Temps several temps but without noticing its use of the technique. (Thanks, Alexander Woo!) And I always found Messaien's tables - for example those showing all the permutations of various short rhythmic figures - useful and interesting, but he lost me when he became mystical. The words "Then we do some stained-glass work" seemed designed to throw you off the scent!

So when you ask what he meant to evoke, although I can hear the musical transformation, I can't hear human nature transforming into the Word of God. And I doubt if his students did. I'm sure Messiaen explained his techniques to them, but (with the possible exception of Stockhausen and Stimmung) the idea of the transformation of human nature doesn't seem to have rubbed off on them.

I feel it ought to be possible to find traces of the 'shrinking-stretching' idea in their work though. Boulez would be a likely place to look: especially in those early 50's pieces where he was 'serialising' duration (along with everything else). I don't think I've come across it in Knussen, whose music I know quite well.

More a long comment than an answer I'm afraid. I'd be interested to hear if you get anywhere.

By the way, there's plenty of deceleration and acceleration in gamelan, but not at the same time. The drummer always initiates it and the other isnstruments follow.

  • Thank you! I too find it hard to see some of Messiaen's mystical explanations, etc. I'll definitely start looking more closely at early 50s Boulez. Thanks for the suggestion. I'll probably start to listen to gamelan—if not for this reason, just to see what else I can find. Commented Aug 3, 2022 at 19:23

Messiaen's student Tristan Murail has composed a piano piece titled "Les Travaux et les Jours" in 2002, in which this accelerating and decelerating is a major element. It features the same independent acceleration and deceleration in the different parts (hands), but taken to extremes when compared to Messiaen's use of the technique. As you can see in this score excerpt, it is notated very differently, but also requires very precise control of the timing, not like a free-flowing rubato. The are no bar lines, but there are what appear to be regular clock ticks above the staves.

Tristan Murail, les Travaux et les Jours, excerpt

To know whether or not Murail uses this technique to signify any extra-musical concept, you'll have to look into the ancient Greek poem of the same title by Hesiod, or check whether there is more information in the introduction to the complete score.

  • Interesting how Messiaen and Murail contrast in how they accelerate (for example). Where Messiaen subtracts equal note values — giving the impression of an accelerating meter — Murail adds decreasing note values to increase the number of notes within a constant duration — maintaining the meter, but changing the rhythm.
    – Aaron
    Commented Aug 3, 2022 at 17:54
  • 1
    @Aaron Generalizing, I'd say that Messiaen thinks more like a serialist, whereas Murail is more concerned with acoustics. The version of this that I've heard (Marilyn Nonken) makes the rhythm sound more like a ball bouncing up and down, and less like "now 3 notes per time unit, now 4, now 5...".
    – guesty
    Commented Aug 3, 2022 at 18:22
  • I'll have to check that out. Where in the piece does this excerpt come from?
    – Aaron
    Commented Aug 3, 2022 at 18:25
  • 1
    @Aaron There's not much information in the score excerpt, so I don't know exactly which part it's from, but I had a quick listen to what's on YouTube, and part VI has decelerating falling arpeggios: youtube.com/watch?v=U3-E3Xx1U6c I couldn't immediately locate the rising and falling arpeggios in the score example.
    – guesty
    Commented Aug 3, 2022 at 18:43
  • 1
    @Aaron Actually, I think the excerpt comes after about a minute and a half into part I: youtube.com/watch?v=ZLnKVc_nw8Q
    – guesty
    Commented Aug 3, 2022 at 18:52

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