Deleuze and Rhythm: Klee's Grey Point (Graupunkt), Messiaen's and Bacon's Rhythmic Figures, Maldiney, Boulez, Brakhage, and Golden Ratio

by Corry Shores
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[The following is taken from my master's thesis, The Rhythm of Sensation on the Surface of Sense: Communication in Deleuze as NonSensed and Intense, pages 63-89. Completed, defended, and archived June 2008]

Deleuze and Rhythm:

Klee's Grey Point (Gray Point, Graupunkt), Messiaen's and Bacon's Rhythmic Figures (personnages rythmiques), Maldiney, Boulez, Brakhage, and Golden Ratio.

[Click on images for enlargments]

We will make Deleuze's notion of rhythm more tangible by exploring some of his visual and musical references. In Difference & Repetition, Deleuze speaks of the asymmetry in rhythm’s heterogeneous intervals, which we previously illustrated with the irregularly-ticking clock example. But before speaking of rhythm, Deleuze first makes his distinction between signal and sign: a signal is a “system” of asymmetrical levels or sets that our faculties are sensing, each one in a different way; and, a sign is the phenomenal event that occurs when something forces our faculties to communicate their intensive differences between one another, which produces a phenomenal flash: the sudden shock of sensation.^[1] Thus, the sign for Deleuze is more a matter of phenomena than of language. He offers the poetic example, “the emerald hides in its faces a bright-eyed water-sprite” (L’émeraude en ses facettes cache une ondine aux yeux clairs).[2]That is to say, a sign or phenomena is the cross-over between series, as here when two different facultative “terms” – an emerald and a water-sprite – are forced together, as a trope of sorts. However, it is not that one term substitutes the other, or that they are both synthesized together; rather, our sensations present us with both at once, on account of our disorganized faculties, causing a phenomenal flash of intensity to be communicated between them.

In his pedagogical sketchbooks, Paul Klee provides a way to visualize how a perceptual rhythm may come about through a visual asymmetrical signal system. (The rhythm of vision is perhaps different than the rhythm of sensation, but these examples serve to demonstrate heterogeneous rhythm on the perceptual level). Basing our diagram on his depictions, we might compare rhythmic arrangements of dots, with the first set being too regular to cause our eyes to move rhythmically.

Just like the ticking clock, we notice very little. No phenomena really appear, because there is no “flashing,” no asymmetrical differences which cause confusions in our faculties.

In this second case, however, the asymmetries compel our eyes to jump from place-to-place, causing phenomena to flash before us each time we move through the dissymmetries. In other words, there is a more intense phenomenal experience of this second case, on account of the rhythm of vision that it brings about.

The lack of symmetry is not a negative element, but is positivity itself; when symmetrical, there are no phenomenal flashes, and no profound activity of the faculties.[3] Thus, the asymmetry affirms the marks by affirming the differences between them; for, normally our eyes would not stop to see each one of them as they are.

Deleuze then distinguishes two types of repetition: 1) static repetition, in which a plurality is reducible to a single concept, in this case the common space between all the dots in the top set (or the shared one-second duration between the clock’s ticking), and thus for this type of repetition there is no internal difference. We might hear every tick or see every dot; yet, they are no more than one same interval between one same redundant form. And, 2) dynamic repetition, where there is an internal repetition of a difference that carries-over from point-to-point, thereby making each one distinct from the others. In this latter type, there is no unifying concept as there was with the repeating interval in the first group; for, it is a “pure dynamism” that never stagnates in sameness.^[4]

Deleuze elaborates with another distinction between 1) arithmetic symmetry, which is based on ratios or simple fractions, and 2) geometrical symmetry, based on proportions orirrational ratios, such as the golden ratio or pi. Such ratios are “irrational” surds, because they cannot be represented as one integer divided by another; for, there is always a remainder no matter how precise the calculation (as in the case of the unending sequence of decimals for pi: 3.14159265...). When such a ratio between two values is irrational, the two are consideredincommensurable with each other, because they share no measure in common, (thus the ratio of a circle’s circumference to its diameter is irrational; for, these two parts of the circle are incommensurable).^[5] Deleuze speaks of these surds in another way:

God makes the world by calculating, but his calculations never work out exactly, and this inexactitude or injustice in the result, this irreducible inequality, forms the condition of the world. The world ‘happens’ while God calculates; if the calculation were exact, there would be no world. The world can be regarded as a ‘remainder,’ and the real in the world understood in terms of fractional or even incommensurable numbers.^[6]

Dieu fait le monde en calculant, mais ses calculs ne tombent jamais juste, et c’est cette injustice dans le résultat, cette irréductible inégalité qui forme la condition du monde. Le monde « se fait » pendant que Dieu calcule ; il n’y aurait pas de monde si le calcul était juste. Le monde est toujours assimilable à un « reste », et le réel dans le monde ne peut être pensé qu’en termes de nombres fractionnaires ou même incommensurables.[7]

He further describes the static arithmetic symmetry as being rectilinear, and the dynamic as pentagonal and appearing in a “spiral line or in a geometrically progressing pulsation,” referring us to Matila C. Ghyka’s Le Nombre d’Or.^[8] Deleuze’s purpose for distinguishing these two types of geometrical forms is to explain how certain arrangements of lines do not normally create visual rhythms (e.g. squares) and others do (e.g. pentagons), because the line angles of different shapes cause our eyes to move in different ways. A square grid does not have much rhythm, because each point directs our eyes to another point in homogeneous distribution. However, some arrangements of shapes move our eyes in less orderly ways, and in some cases have a built-in infinity of possible non-redundant movements.

In Ghyka’s text, for example, we find that, on account of the irrationality of the golden ratio, the internal point to where the golden spiral is aimed can never be determined.

We can only carry out the repetition of the ratio over-and-over again, each time making a smaller box and a more precisely tipped spiral, but never arriving upon a determinate point. For, every new extension terminates with some space remaining between it and the theoretical “golden balance point,” and can thus be made more precise. (We see below that if we enlarge the small set of boxes which lie at the top-middle of the arrangement, and which encase the internal point of the spiral, we result with the same formation as the whole. We may continue to enlarge over-and-over again, never arriving at the golden point of balance toward which the line is directed).

The golden ratio in this form produces a visual rhythm by causing our eyes to move in periodic steps to an unattainable point, which is suggested merely in the proportions of the shapes.

Deleuze also refers to a way that a dynamic repetition can emerge from a static one; however, it is a mathematically complex example. And yet, it is still helpful to at least see the images Deleuze references, so that we might visually experience the rhythm of dynamic repetition, even if we do not grasp the mathematical dimensions of the example. He refers to the static repetition of a network of “double squares;” that is, squares that are paired together, but not like a grid, because the squares are of many sizes. For one reason or another, when we see Gothic cathedrals that are based on this pattern, our eyes move diagonally between the squares’ corners, which altogether makes pentagon and pentagram shapes.

On account of the irrational proportions between the pentagrams and their underlying squares, a sense of imbalance is created, which our eyes rectify by looking in the opposite direction. If we view the pentagram formation (shown immediately above), which supposedly our eyes “draw” when seeing the Gothic cathedral (shown above it), we see that the diagonals of the squares suggest a large pentagon, which itself suggests a large pentagram inscribed within it, both of which point upward. Yet, these five-pointed shapes are asymmetrical with their underlying four-pointed squares, which then pulls our eyes downward. They arrive at the smaller internal pentagon of the larger pentagram, which suggests a smaller upside-down pentagram that is likewise out-of-balance with the squares, pushing our eyes upward again. Never is symmetry attained, and our eyes might continually find pentagrams within pentagrams when viewing a Gothic cathedral.^[9] This is Deleuze's remarkable point: static geometrical forms may bear dynamic rhythms if their proportions cause our eyes to move in patterns that maintain some consistency while also being irregular, all on account of a mathematical blend of chaos and order, of rationality and irrationality. Deleuze refers us to these examples, so that we may visuallyexperience a sort of dynamic and irregular repetition, to help us grasp how sensation itself may have a heterogeneous rhythm.

Nonetheless, as we noted before when discussing Deleuze’s analysis of the rhythm of sensation in Kant’s sublime, our faculties strive to homogenize the irregular ways that things are given to us, so that objects may be properly synthesized and recognized. However, as sublime experiences demonstrate, the rhythm of sensation drowns our perception in its chaos. To account for this, Deleuze refers us to Paul Klee’s grey point, basing some of his observations on Henri Maldiney’s description of Klee’s and Cézanne’s theories of the chaos of creation.

For Klee, chaos does not lie in one pan of a scale, with order placed in the other; rather, order weighs against its opposite (whatever that may be), with chaos as the center of balance between them.[10] True chaos cannot be weighed; for, it is incommensurable. It may be considered as though it were a mathematical point, extending neither in space nor time, but lying rather between all dimensions.

This Nothing-being or being-nothing, the point, is something our minds cannot conceive. Klee considers it a non-conceptual concept of non-contradiction: it may be both itself and not itself, in one place or another, all at the same time; hence, it is not subject to the law of non-contradiction. To make this point visible, claims Klee, we must think of it as the Graupunkt, the grey-point.^[11] The grey-point in art-terminology is the place between black and white, and between one color and its opposite. When we consider color in its three dimensions, according to its hue and tone values (that is, its place along the circle of colors and its relative lightness or darkness), we may consider the grey-point as the neutral point between the tone and hue dimensions.^[12]

When we mix equal parts of pure white and pure black, we then obtain a neutral grey. Likewise, when we mix equal parts of a color and its opposite, red and green for example, we also obtain grey:^[13]

In cosmological terms, when we establish this grey point, the order of the universe may burst forth and radiate from it.^[14] In fact, all three spatial dimensions will emerge from the poles that separate-out from the chaos through the grey point.^[15]

Here we see that white and black split, one rising, one falling, thereby creating a dimension of height; the cool blue and the warm orange spread left and right to open the dimension of width, and the opposite lukewarm colors move in front and behind to create depth, all with grey remaining in the center.

Establishing order in this chaotic grey-point creates the cosmos. Before the organization, there were already natural laws and relations of movement: white to black and red to green, for example. However their motions were not yet structured and determined. In this chaos, the values and hues are not yet separated. Instead, they whirl about in such a flux of disorder that they have no fixed locations, and neighboring parts blur together so much as to be indistinguishable. All is intermixed; all is grey. In this tangled mess, white battles black, as do such opposite colors as red and green, and it is the artist’s job to establish balances between these poles.^[16]

Deleuze elaborates this by drawing from Henri Maldiney’s description of the abyss andchaos of Cézanne and Klee, which the artist confronts when beginning creation. For Klee, the painter is originally in a state of being lost within a landscape, without a reference system of orienting points.^[17] Cézanne gives a similar depiction of creation’s opening state, according to Joachim Gasquet’s recreation of his dialog with the painter. Maldiney, and as well Deleuze, emphasize the “iridescent chaos” initially enveloping Cézanne before he paints. Out from this abyss, the earth rises while the world obtains a measure of organization, but before long it caves in, collapsing back into a catastrophe: “a cataclysm has carried it all away, regenerated it.”^[18]What Cézanne calls abyss, Klee calls chaos. The first response to it is vertigo, brought about when we confuse the near and the far, causing us to become dizzy. Citing Klee’s notebooks, Maldiney then explains how the cosmos comes to be generated: the grey-point jumps over itself from its non-dimensional state into an ordered space. This occurs through rhythm, which allows for the incommensurable chaos to pass into an equalizing order; as Deleuze says, we organize a “rhythm in chaos.” ^[19]

For Klee, rhythm can emerge from the grey-point when the artist separates the hues and tones, and arranges them into relationships which maintain the endless movement of chaos, except in this case, the motion travels between more determinate zones demarcated within the canvass. If there is too much order, however, there is stasis, and no movement or rhythm. As well, if there is too much movement, so much that all the colors and tones mix back to grey, then all that remains is a world only colored grey, a world of nothing.^[20]

Before continuing with Klee’s rhythmic techniques, we might note that Deleuze explains a cinematic way that rhythm can be obtained from the chaos, but without separating opposites and ordering them. He refers to American non-narrative filmmaker Stan Brakhage as having explored a “Cézannian world before man, a dawn of ourselves, by filming all the shades of green seen by a baby in the prairie,” and refers us to Louis Marcorelles’ Éléments pour un nouveau cinéma.[21] In this text, Marcorelles quotes a passage from Brakhage’s writing:

Imagine an eye unprejudiced by compositional logic, an eye which does not respond to the name of everything, but which must know each object encountered in life through an adventure of perception. How many colors are there in a field of grass to the crawling baby unaware of “green?” How many rainbows can light create for the untutored eye? Imagine a world alive with incomprehensible objects and shimmering with an endless variety of movement and innumerable gradations of color. Imagine a world before the “beginning was the word.”[22]

Deleuze’s interest in Brakhage is the same as with Klee and Bacon; Deleuze turns to these artists with his question, what is the role of rhythm, chaos, and order in sensation? For, if he can find from these masters that sensation is at bottom a matter of disorganized perception, then we have cause to prefer his portrayal of sensation over phenomenological theories. Brakhage offers one more alternative explanation for the rhythm of sensation, to add to what Deleuze obtains from Klee and Bacon. Brakhage thinks that the colors in pre-lingual babies’ eyes are a chaotic swirl of infinitely varying hues and tones, because they have not yet learned how to differentiate any of them. In fact, Brakhage painted such Cézannian realms of color directly onto his film. However, this would seem to cause all the colors to blur together into a grey; we might presume that if colors changed rapidly before our eyes, they would all synthesize together into grey. (Below we can see Brakhage hand-painting the film, and an example strip from his Existence is Song. We can see from this strip that we would expect a sequence of such frames moving rapidly before our eyes to blur together into a homogeneous grey field).

Yet for Brakhage, the rhythm of the film projector, about 24 beats a second, is what separates the colors, so long as he can accelerate our tiny eye movements to the point where they do not stare blankly at the whole screen while colors pass-by, but rather move in tiny motions around the screen almost as rapidly as the frames change. His complaint with video media is that it “looks like a pudding that is virtually un-cutable like a gel,” rather than having “the sharp hard clarities of snapping individual frames” in film.[23] Clearly, Brakhage’s later painted-films are chaoses of color, but they are not perceived as grey, on account of the rhythm of our vision, which separates-out the differences temporally, rather than spatially as with Klee’s rhythm. Hence in this other way, our perception occurs not when passively synthesizing what we sense, but rather when we are forced to contend with a chaos that disorganizes our faculties.

Without learning its basic mechanisms, we may be unaware of the rhythm in paintings, despite it always being a part of the way we view artwork. Rhythms can be created visually by juxtaposing the tensions between forms, values, or hues, whose pairings cause our eyes to move through a series of shifts between different places on the canvass at different speeds and angles. We might look first at some of Klee’s simplest illustrations of these movements, beginning with ones brought about through tensions between forms.

This above form has even spaces, so when it is juxtaposed with another of the same sort, there is still not enough tension to move our eyes very much within the figure.

However, if they are off-set by half of an interval, already there is a tension that suggests contrary motions, which will cause our eyes to jump around the spaces a little more, in a rhythmic manner:

As the patterns become complex, so do the rhythms:

In this one below, our eyes rebound from end to end like a spring:

When we later examine Bacon’s rhythmic pairings of movements, we should keep these diagrams in mind, because he often pairs forms in a similar manner to push and pull the motion of our eyes in two opposing directions, so to animate coupled characters, to make them “wrestle.”^[24]

As we noted, hues and tones for Klee have gravitational movements such that if we faced a field made-up of a variety of colors, the opposites would naturally pair and be drawn to each other.^[25]

Thus, if green and orange were on one side of the field, and red and blue on the other, a rhythm of juxtaposed movements would result, because our eyes would be drawn dually from both ends to the other at the same time.

Klee also indicates that our eyes usually move generally first from the primary color in a complementary-pair to its secondary color companion (each primary color complements a secondary color, which is made by mixing two primary colors. In the case of red and green, the green is made by mixing the other two primaries, blue and yellow). As well, our eyes tend also to move from black to white, rather than the other way around. There is more gravity pulling our eyes to the primaries and black, so they often begin there; then afterward, most times, we jump to their complements, rather then to some other color.^[26]

From the arrow-movements shown in the far right diagram of this image from his pedagogical sketchbooks, we can see the natural eye-jumps, which when taken altogether, create a complex rhythmic motion, perhaps better exhibited in his Farbtafel Qu 1:^[27]

Hence, the artist makes use of such natural movements between colors, by separating polarities out of the grey-point and strategically arranging their orders and positions. However, the artist still should not mathematically or logically predetermine their locations, for that would limit the painting’s rhythm by homogenizing it, thus stripping the original chaos of its motive powers, and flattening all dimensions back to the grey point.

This tendency for the poles to return to the grey-point is the force of gravity that pulls them to what Klee considers the center of the earth.^[28] When the different color and tone poles are merely separated and positioned in a logically ordered fashion, they then pull back towards each other, inward toward the grey point, on account of the terrestrial-like “gravitational” forces; (in the case of our vision, our eyes move between them so much as to cause us to blur together opposite tones and colors into a neutral grey). The artist only accomplishes the construction of a work when merely determining the polar relationships. However, when she adds variations and complexities so to create rhythms, thereby preventing the collapse back to the grey point, she then has attained the work’s composition.^[29] Deleuze emphasizes this upward, gravity-defying force of expression and style which lifts us up in triumph over gravity, by organizing the chaotic rhythms into a more ordered cosmos.^[30]

While teaching at the Bauhaus – a design institute that combined studies in crafts and fine arts – Klee was encouraged to incorporate into his works and teachings the empirical findings of a color scientist, Wilhelm Ostwald, who devised precise laws of harmony for mixing and combining hues and tones. Klee took-up his findings, but obtained superior results by breaking Ostwald’s precise and logical laws of color combinations. Although Klee adopted many of Ostwald’s basic principles, he defied the rule that “harmony = obedience to law.” Ostwald designed a homogenized grayscale, placing tone values at equal intervals and assigning letters to each one. He as well determined the laws of harmony dictating precisely how those tones may be combined, much like the laws of harmony for combining notes in music.^[31]

Likewise, Klee differentiated tone values and assigned them letters, and also created combination patterns; however, his intervals between values were asymmetric and heterogeneous, and he varied the distributions of weights, sizes, and textures, so that when combined in certain ways they produced dynamic rhythms, rather than stable balance or harmony. He demonstrated the superiority of his law-defying method in his painting, Rhythmisches, which is loosely based on a “magic square” pattern. Oliver Messiaen depicts one in the following diagram:^[32]

Here we see that in a magic square, the values add up to the same number whether counting the rows, columns, or diagonals. Klee likewise performed such analysis of distributions, the most basic being the checkerboard arrangement.^[33]

Of course these patterns cause our eyes to move in zig-zag rhythms.^[34]

Klee then applies to these principles one governing asymmetrical weight:^[35]

Using this principle, Klee may distribute the tonal values (weights) of squares in irregular ways, while still maintaining some degree of balance. Thus for example, a simple row of squares made up of just one white and one black can equal the tonal “weight” of a row containing two greys of medium value. With this in mind, Klee can create a magic square of tone values, in which a variety of tone weights are distributed throughout each line, so that the total weight of vertical, horizontal, and diagonal sequences are all equal, thereby creating a perfectly balanced yet heterogeneously distributed grid. However, when putting these principles into practice to make his Rhythmisches, the result was not a perfectly constructed magic square, because he considers such designs to be more “conceptual models rather than formal proto-types intended to be rigidly imposed on pictorial ideas.”^[36] Klee believed that such theoretical calculations were only to play a secondary role in artistic creation; for, they served merely as means to help arrange the chaos of the painter’s emotions.^[37]

For the most part, Rhythmisches is arranged like a checkerboard, but with more than the two values of white and black. Yet, he mostly maintains the same interchanging pattern, which if it were merely three values would be arranged like this.^[38]

A row following underneath another one begins a single step behind the row above. However, on account of Klee’s variations in tone values & square sizes, and their slightly asymmetrical magic box distributions, he was able to accomplish “structural rhythms he described as ‘discontinuous and differential’” in his Rhythmisches.^[39]

Now having explained visual rhythm, we may now better grasp musical rhythm.

In Difference & Repetition¸ Deleuze distinguishes between two types of rhythm in music. The first is cadence-repetition, which is like the normal ticking of a clock: it divides time into regular intervals and is an “isochronic recurrence of identical elements;” that is, it is made of equal, homogeneous metrical lengths, (one tick every second). The other sort he calls rhythm-repetition, and it is like the malfunctioning clock. Its incommensurable and unequal periods create distinctive points, privileged instants which indicate a polyrhythm (illustrated in the appendix).[40] Each instant is privileged (just as each dot was seen in its individuality), because no periods of time in a heterogeneous rhythm can be reduced to such even ratios as ‘one per second.’ Instead, the rhythmic units appear chaotically and unpredictably; for, they do not follow any mechanized pattern.

Deleuze refers us to Messiaen’s and Boulez’ writings on musical rhythm for further elaboration. They likewise distinguish regular and irregular rhythms, favoring the heterogeneous sort. Composer Pierre Boulez speaks of rhythm in terms of irregularly pulsed music. The pulse is an inherent stress that falls on certain beats; so for example, when listing to the clock, we might hear “tick – tock” and not “tick – tick,” because we felt that every other beat was more stressed. This repeating stress is the pulse, and in music, different sorts of pulses can be brought about by grouping beats together in different patterns. Boulez’s technique was to divide time into such a nuanced pattern that only a machine could perform it with perfect precision. This causes the human performer to always fall short of precision; hence, the musician does not maintain a regular pulse, resulting in a less rigid, non-pulsed true rhythm.[41]

Likewise for Messiaen: rhythm is like the movements of nature, with free and unequal durations.[42] He was an ornithologist, as well as a composer, who studied intently the singing of birds. He heard the individual rhythmic character of each bird’s distinct calls, and he heard the overall rhythm of all the birds singing together. They were not in total rhythmic disorder, in which case their notes would be so unrelated as to not couple with one another; yet as well, the birds were not all synchronized to some metronome or ticking clock, as though a regular pulse emanated from the earth to allow them all to share a common beat. Some of Messiaen’s compositions were inspired by bird calls, and the musicians – when playing the bird parts – had to likewise abandon the common pulse normally shared by the whole symphony. They needed to break their habit of keeping a common time, and to instead make the rhythmic figures according to a more natural non-mechanized beat. (Composer Scott Wollschleger recounts a rehearsal of Messiaen’s Oiseaux exotiques in which three clarinets were to play the bird parts, but were playing them too precisely. When the conductor asked them to play more naturally, as the way birds sing, the performers complained that doing so causes them to lose their sense of time. The conductor reassured them that he would be able to bring them all back together with the orchestra when the time was right: “so he gave them that license to not interpret the figuration mechanically, and it sounded like a totally different piece all the sudden, it just came alive”).[43]

When music’s pulse is made up of a sequence of equal note values, the listener might take comfort in the constancy, perhaps even become hypnotized as Bergson described, as though a pocket-watch swung back-and-forth before our eyes. Yet for Messiaen and Boulez, such patterns do not have the irregularity needed to truly be rhythm. Hence, the military march isnon-rhythmic music; when instead, a truly rhythmic march involves an irregular swaying. As such, it would disrupt the listener's pulsing heart-beat and breathing patterns, clearly the opposite of Bergson’s rhythmic hypnosis. Messiaen illustrates this notion of rhythm by comparing Bach to Mozart. Bach is considered to have a very regular and mathematically precise rhythm; hence, his works appear rhythmic from the Bergsonian perspective, plunging the listener “into a state of beatific satisfaction,” when on the other hand, Mozart, whose rhythms are irregular, is more truly a rhythmician.[44]] In terms of sensation, when our faculties are synchronized and harmonious, they are likewise lulled and inactive. It is only when the rhythm of sensation throws the faculties out of coordination that a sensation sends waves of intensity through our bodies.

We saw how Klee achieved this disruptive effect by imperfectly organizing visual chaos so to create a plurality of tensions and movements in the painting. The rhythm that Deleuze finds in Bacon’s paintings likewise involves couplings of movements, but of different sorts. For example, Bacon accomplishes a diastolic and systolic rhythm by placing the Figure inside an enclosure of some sort, usually either a circle or another shape, which serves to create a contour between Figure and background-field: it is a surface or membrane through which movements are exchanged between the two zones of the painting. (Below we see his Figure at a Washbasin, 1976, in which the figure is enclosed by a white ring).

The enclosure constricts the Figure, like the systolic contraction of the heart-beat. This squeezing on the Figure applies a pressure upon it, causing its insides to push back on the contour, this movement being the diastolic.[45] As well, the pressurized and contorted Figure pushing back against the contour seeks for escape through some opening in its body, in this case, his mouth. We might imagine squeezing a balloon filled with water, with the valve still open. The contracting movement of our hand pairs with the escaping movement of the water, together making what Deleuze considers the diastolic/systolic rhythm. Our eyes here are drawn into the center, on account of the pressurizing ring, but once arriving there we encounter a Figure that is shaking in spasms. These movements suggest some sort of an explosion is pending, which means our eyes also feel compelled to move back outward, even if they remain in the center, only anticipating some release of tension. We examined before such tensions between motional tendencies in Paul Klee’s dashed-lines, whose orientational imbalances pulled our eyes in two opposing directions at once, thereby causing us to perceive motion in static forms.

The body, then, tries to escape itself through a spasm that allows it to burst from some hole on its surface, which is often depicted in Bacon’s art in acts of love, vomiting, and excretion.[46] This is the provisional organ, the point of sensation where the BwO’s inner intensive waves encounter an external force at some zone on the body’s surface, thereby exchanging intensity.

Another technique is the complex rhythm Bacon creates with the coupling of movements in his triptychs, which takes sensation to its highest possible level. This rhythm involves the exchange of roles that the Figures play in the triptychs: the active, passive, and attendant. Deleuze derives these notions from Messiaen’s detailed analysis of Stravinsky’s Rite of Spring. (The appendix explains one of Messiaen’s analyses to give concrete examples of the rhythmic figures. It is not provided to fulfill a philosophical purpose, but rather is included for those who want to know precisely what Deleuze means by the rhythmic figures).[47] Messiaen shows that there are different repeating patterns, each one like a bird call in its individual uniqueness and brevity. Some of these characters will repeat with longer duration, others recur in shorter form, and one stays the same each time. When we listen to these subtle changes, we receive the impression that the increasing patterns are doing violence to the decreasing ones, as though in a boxing match where one fighter is beat down by another, all while an audience watches the drama.

Deleuze explains that Bacon accomplishes the same effect by coupling Figures, so that the sensations they invoke are forced together, creating an even stronger intensive rhythm. When viewing the triptychs, certain Figures will pair-up, each taking one of the three possible roles. In the case of the witness-attendant rhythm in Triptych inspired by the poem “Sweeney Agonistes,” there are two character figurations, one is an intertwined figure deformed by a horizontal and flattening force, and the other is someone witnessing these deformed characters. We might begin viewing the right panel, in which a blurring technique flattens the two sleepers.^[48]

(The original paintings are quite large, so our vision does not automatically group the figures as they do when viewing this shrunken illustration above). Perhaps we notice next the man watching the horizontal forms, standing to the right. By grouping the flattened Figure with the observer, Bacon creates a coupling of movements that causes an unchanging level of disorganization in our faculties, but not because it is a homogeneous rhythm: Deleuze describes the attendant rhythm by evoking another term by Messiaen, non-retrogradable rhythm, which is a rhythmic pattern that, when played in reverse, produces the same pattern as when played forward, just as with such palindromic sentences as “fall leaves after leaves fall.” Or as Messiaen explains, “it’s as if in traversing a landscape, beginning from two opposite points, you were to meet the same things at the same times in the same positions and in the same order.” He also offers the example of the wings of a butterfly:

When butterflies are enclosed in their chrysalis, their wings are folded and stuck one against the other; the pattern on one is thus reproduced in the opposite direction on the other. Later, when the wings unfold, there will be a pattern with colours on the right wing which mirror those on the left, and the body of the butterfly, the thorax and the antennae placed between the two wings constitute the central value. These are marvelous living non-retrogradable rhythms.[49]

The non-retrogradable (palindromic) rhythms of the attendant Figure, then, are not the repetition of a common unit, but rather are more internally diverse. (More specifically, Deleuze says that the attendant rhythm is non-retrogradable, because it is “retrogradable in itself;”^[50]that is, its inverse form is implied in its forward movement, because both are the same. The appendix more thoroughly describes Messiaen’s notions of retrogradation and non-retrogradation). Thus, when viewing the attendant Figure, it could also be that we experience a rise and fall of intensity, so long as there is the non-retrogradable mirror effect which gives us the feeling that we have not really undergone any change in the process.

However, before we visually made this attendant coupling, the lying figures in the right panel – when viewed by themselves – could have been active or passive; that is to say, if we looked first at the lying figures in the left panel, which seem to be lying passively on their back, and we looked next at the coupling in the right panel, which seem to be animated, “almost whirling,” then the passive-function is taken up on the left and the active function on the right. In these cases, the active couple increases intensity, because the forces of deformation are greater, which causes the increasing movement, and which causes our faculties to be more in discord, making the job of recognizing and unifying the forms more difficult. However, the intertwined characters in the left panel, in relation to the right, have less deformative motion, and thus our faculties decrease in discord as we continue to view them. This causes us to have a decreasing intensity in comparison to the right panel. Hence in this case, the right panel takes-on the active rhythmic function, and the left the passive. In fact, we might look exclusively at the intertwined figures of the right panel, and notice that the buttocks points above the horizon, thereby assigning it the active role, while the head is lowered below the horizon, causing it to be passive.^[51]

What determines the pairings and the roles cannot be predetermined by analyzing the structural features of the triptychs: the placement of the Figures in the center or side panels has nothing to do with how the rhythmic-functions rotate around the paintings. There is no “conscious formula” that makes these determinations; rather, the rhythmic circulation of intensive tensions proceeds according to an irrational logic, a logic of sensation, which we will return-to at greater length when examining Cézanne’s logic of organized sensations, as opposed to Bacon’s logic of disorganized sensations.[52]

Thus, there is this irrational and unpredictable pattern of movement that changes depending on the case at hand, which is always complicated and unpredictable, given the changing contingent circumstances of each viewing. While sensing the painting, there is no way to pre-determine which character-functions appear in what place and at what moment. However, to experience these rhythms is to be a BwO that lets the body and faculties undergo varying levels of disarray.

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[1] Deleuze, Gilles. Difference & Repetition. Transl. Paul Patton. New York:Columbia University Press, 1994, p.20. DDeleuze, Gilles. Différence et répétition. Paris: Presses Universitaires de France,1968, p.31.

[2] Difference & Repetition, p.222. Différence et répétition, p.286. Perhaps Deleuze’s quote is a modification from Victor Hugo’s “Tout la lyre,” L'émeraude en sa facette / Cache une ondine au front clair.

[3] Difference & Repetition, p.20. Différence et répétition, p.32.

[4] Difference & Repetition, p.20. Différence et répétition, p.32.

[5] Difference & Repetition, p.20. Différence et répétition, p.32.

[6] Difference & Repetition, p.222.

[7] Différence et répétition, p.286.

[8] Difference & Repetition, p.20. Différence et répétition, p.32.

[9] Matila C. Ghyka, Le Nombre d’Or: Rites et rythmes pythagoriciens dans le développement de la civilisation occidentale, (Paris : Gallimard, 1931), p.65-70. Esthétique des proportions dans la nature et dans les arts, (Paris : Gallimard, 1927), p.298-301. Deleuze, Difference & Repetition, p.21. Différence et répétition, p.32.

[10] Images, Paul Klee, Das bildnerische Denken, (Basel : Schwabe, 1981), p.2.

[11] Das bildnerische Denken, p.3-4. “Note sur le point gris,” Théorie de l’art moderne, (Paris : Denoël et Gonthier, 1975), p.56.

[12] Image from Das bildnerische Denken, p.488.

[13] Images from Das Das bildnerische Denken, p.484-475; Paul Klee, Pädagogisches Skizzenbuch, (Mainz: Florian Kupferberg Verlag, 1965), p.50.

[14] Théorie de l’art moderne, p.56. Das bildnerische Denken, p.3-4.

[15] Image, Pädagogisches Skizzenbuch, p.50.

[16] Das bildnerische Denken, p.9-10.

[17] Henri Maldiney, Regard, parole, espace, (Lausanne: Editions l’Age d’Homme, 1994), p.149.

[18] Henri Maldiney, p.150. Joachim Gasquet, Conversations with Paul Cézanne, Transl. Julie Lawrence Cochran, Ed. Michael Doran, (Berkeley: University of California Press, 2001), p.114.

[19] Maldiney, p.151-152. Gilles Deleuze, “Cours Vincennes: synthesis and time - 28/03/1978,” webdeleuze.com.

[20] Klee, Théorie de l’art moderne, p.51. Das bildnerische Denken, p.499.

[21] Gilles Deleuze, Cinema 1: The Movement Image. Transl. Hugh Tomlinson & Barbara Habberjam, (London: The Athlone Press, 1986), p.87.

[22] Louis Marcorelles, Éléments pour un nouveau cinéma, (Paris: Unesco, 1970), 147-148.Living Cinema: New Directions in Contemporary Film-making, Transl. Isabel Quigly, (London: George Allen & Unwin Ltd., 1973), p.142.143. Stan Brakhage, “Encounters,” By Brakhage – Anthology (Criterion, 2001).

[23] Stan Brakhage, Encounters.

[24] Images from Das bildnerische Denken, p.245.

[25] Image below from Paul Klee, Pädagogisches Skizzenbuch (Mainz: Florian Kupferberg Verlag, 1965), p.50.

[26] Paul Klee, Unendliche Naturgeschickte, (Basel : Schwabe, 1970), p.146.

[27] Unendliche Naturgeschickte, p.147.

[28] Unendliche Naturgeschickte, p.31.

[29] Paul Klee, On Modern Art, Transl. Paul Findlay, (London: Faber & Faber, 1987), p.43.

[30] Deleuze, Gilles, and Félix Guattari. A Thousand Plateaus: Capitalism andSchizophrenia. London: Continuum, 1987, p.344. Deleuze, Gilles, and Félix Guattari. Capitalisme et Schizophrénie 2: MillePlateaux. Paris: Les Éditions de Minuit, 1980, p.383.

[31] K. Porter Aichele, “Paul Klee's ‘Rhythmisches’: A Recapitulation of the Bauhaus Years,”Zeitschrift für Kunstgeschichte, 57 Bd., H. 1. (1994), p.79-80. Image below is Ostwald’s “Practical grey series” from Der Kleine Farbkörper, Leipzig 1921, in Aichele p.77.

[32] Olivier Messiaen, Traité de rythme, de couleur, et d’ornithologie (1949-1992), Tome II,(Paris: Alphonse Leduc: 1995), p.17.

[33] Image, Das bildnerische Denken, p.223.

[34] Image, Pädagogisches Skizzenbuch, p.35.

[35] Image, Pädagogisches Skizzenbuch, p.33.

[36] Aichele, K. Porter. “Paul Klee's ‘Rhythmisches’: A Recapitulation of theBauhaus Years. (Zeitschrift für Kunstgeschichte, 57 Bd., H. 1., 1994), p.84.

[37] Aichele, p.85.

[38] Image, Aichele, p.85.

[39] Aichele, p.87. Image, Paul Klee, Unendliche Naturgeschickte, p.368.

[40] Difference and Repetition, p.21. Différence et répétition, p.33.

[41] “I had piled up ratios of 24:25, or 27:28, in other words, values so close together that is would be impossible to play them accurately....,” Pierre Boulez and Célestin Deliège, Pierre Boulez: Conversations with Célestin Deliège, (London: Eulenburg Books, 1975), p.68-69.

[42] Olivier Messiaen and Claude Samuel, Conversations with Olivier Messiaen, Transl. Felix Aprahamian, (London: Stainer & Bell, 1976), p.33.

[43] Occurring at Carnegie Hall, Music of Messiaen and Varèse, February 2006, conducted by David Robertson.

[44] Conversations with Olivier Messiaen, p.34.

[45] Deleuze, Gilles. Francis Bacon: Logic of Sensation. Transl. Daniel W. Smith. London: Continuum Books, 2003, p.24. Deleuze, Gilles. Francis Bacon : Logique du la sensation. Paris : Les Éditions duSeuil, 2002., p.37-38.

[46] Logic of Sensation, p.11-12. Logique de la sensation, p.23-24.

[47] Logic of Sensation, p.50-51. Logique de la sensation, p.70-71.

[48] Logic of Sensation, p.54-55. Logique de la sensation, p.74-75.

[49] Conversations with Olivier Messiaen, p.43-44.

[50] Logic of Sensation, p.57. Logique de la sensation, p.77.

[51] Logic of Sensation, p.55. Logique de la sensation, p.75.

[52] Logic of Sensation, p.59. Logique de la sensation, p.79.