23 Feb 2010

The Rhythm of Reversal: Messiaen's Explanation of Polyrhythm, Retrogradable Rhythm, and Non-Retrogradable Rhythm

by Corry Shores
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[The following includes a selection (pp.141-143) from my M.Phil Thesis: The Rhythm of Sensation on the Surface of Sense: Communication in Deleuze as NonSensed and Intense. Defended and archived at the Katholieke Universiteit Leuven, 2008.]

The Rhythm of Reversal:
Messiaen's Explanation of Polyrhythm, Retrogradable Rhythm, and Non-Retrogradable Rhythm

To grasp Bacon’s triptych rhythm, which will help us understand what Deleuze means by the rhythm of sensation, we have three notions to clarify, a) the rhythm as unequal or heterogeneous, b) retrograde rhythm, and c) the three rhythmic characters (this part of the analysis is found in this entry).

Messiaen illustrates rhythms of unequal durations in his polyrhythm lessons, what he calls the superposition of rhythms of unequal length. He offers this example (from Messiaen Technique,p.4):

which I will represent using boxes whose lengths correspond to the durations of the notes. The grey-tone values of the boxes serve merely to indicate the note groupings:

The box-lines join the top and bottom sets together in an unbroken row. The smallest unit of time is 1/16 of beat (in the staff the notes with the double beams), this would be the smallest box-size. The next size is the 1/8 note (single beam), and the largest is the 3/16 (doted single beam, doted eighth note).] In the box rendition, we see that there is an uneven remainder, but the pattern repeats from the beginning, with the top line picking up at its beginning where it previously left off at its last cycle’s end. The bottom line does the same as well, thus off-setting the next sequence by 1/16 of a beat.

Thus the next cycle, beginning with the leftover of the previous is:

The remainder after this second repetition being,

when previously it was:

It will take nine repetitions of the top one before they both line up again as they do at the sequence’s beginning (Messiaen Technique, p.4). This technique allows for rhythms to be coupled without strictly chaining them to one another. In the case of Bacon’s triptychs, this is what Deleuze considers the doubled forces of isolation and coupling (Deleuze, p. 60).

Another of Messiaen’s techniques that Deleuze references in order to describe Bacon’s rhythms is the use of retrogradable and non-retrogradable rhythms, whose application to Bacon’s artwork allows Deleuze to differentiate (in some cases) the active and passive Figures in his paintings. Retrogradation is the structural capacity for a rhythmic figure’s notes to be played in reverse-order without that replay constituting the same pattern. Thus a non-retrogradable rhythm is one that plays the same in reverse, and a retrogradable rhythm plays back something different (Messiaen & Samuel, pp.43-44). When both sorts are used together in a piece, different motion effects may be accomplished. For example, when both are interchanged, the non-retrogradable stable rhythms serve well as attendant rhythms; they create a constant movement against which the non-symmetrical retrogradable rhythms seem to take flight. Messiaen offers this simple example of a non-retrogradable rhythm (Messiaen Technique, p.4):

Which of course played backward is also:

[Here is a clip from Stephen Malinowski’s truly fantastic Music Animation Machine. It is great for non-musicians like myself to understand the music better; and great musical pieces can be marvel to watch on it. The video seems blank, but the image comes up anyway after hitting play.]


The rhythmic units here are clearly the same when forward or backward.

However, retrograde rhythms are different when played backward, and produce some “curious reversals of values:” (Messiaen Technique, p.20; p.4)


When reversed it produces:


In the clip below, the forward version plays, followed by the backward version. Messiaen wants us to hear how the reversal changes the character of the rhythm. This is unlike with retrogradable rhythms, which give us the feeling that things have stayed the same, or that they remained level or flat.


Deleuze uses retrogradable and nonretrogradable rhythms to characterize the figures in Bacon's paintings. We can make-out deformed figures that look like contorted or spasming people. We discussed before how for Messiaen there are three rhythmic characters: active, passive, and attendant. Deleuze says that the figures in Bacon's paintings take-on and rotate these roles, so that one might be the attendant at one moment, then active in another, and so on. The attendant is like an observer. It is like the reference frame in physics. All the figures are interacting in relation with each other. One way we sense this is with the way our eyes feel forced in different directions. So for example, at one moment, a certain figure forces our eyes upward, and is the active character, while another one forces our eyes downward, and is the passive (as if while moving upward, the active character pushes the passive down). And then there will be an observer who watches the others from a stable frame of reference. This character will make our eyes feel forced to move in horizontal directions. Because the retrograde rhythms remain flat or horizontal in a way, Deleuze says that the attendant character in Bacon's painting has a retrogradable rhythm of motion (Deleuze 54). And the other characters will have forces in an oppositional relation. In a sense, they are the inverses of each other, but their relation is asymmetrical, with one acting upon the other. In this way, Bacon introduces a music of motion into his paintings.

Deleuze, Gilles. Francis Bacon: The Logic of Sensation. Transl. Daniel W. Smith. London/New York: Continuum, 2003.

Messiaen, Olivier. The Technique of My Musical Language, Textes. Transl. John Satterfield. Paris: Alphonse Leduc, originally published 1944.

Messiaen, Olivier, and Claude Samuel. Conversations with Olivier Messiaen. Transl. Felix Aprahamian. London: Stainer & Bell, 1976.

Thank you Stephen Malinowski for creating and sharing your incredible Music Animation Machine.

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