Jones (1.1.2) Music Theory, “Vibrating Strings”

 

by Corry Shores

 
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George Thaddeus Jones

Music Theory

Part I
Notation, Terminology, and Basic Theory

Chapter 1
Elementary Acoustics and the Properties of Sound

1.1.2
Vibrating Strings

Brief Summary:
A stringed instrument is one whose sound is produced primarily by vibrating strings. They are further classified according to the action setting the string in motion: {1} bowed instruments (including violin) {2} plucked instruments (including harp and guitar); and {3} struck string instruments (including piano). The string vibrates on the whole by swinging back and forth. Throughout this main swing are smaller ones, dividing the string into halves, thirds, fourths, and so on, providing the overtone series. The way that an instrument accentuates certain overtones gives it its timbre.

 

 

Summary

 

 

1.1.2.1

[Stringed instruments produce their sounds with vibrating strings. The means of setting the strings in motion subclassifies them into: {1} bowed instruments (including violin) {2} plucked instruments (including harp and guitar); and {3} struck string instruments (including piano)]

 

In stringed instruments, the tones are made by making strings vibrate. There are different ways the strings can be set in motion, and the stringed instruments can be classified accordingly: {1} bowed instruments (including “violin, viola, cello, bass, and the obsolete family of viols”); {2} plucked instruments (including harp, harpsichord, guitar, lute, mandolin, and banjo); and {3} struck string instruments (piano, clavichord, and cimbalom). But “Whatever the method of setting the string in vibration, it reacts acoustically in substantially the same way for all of these instruments” (4).

 

 

 

1.1.2.2

[The string moves by making cycles from the resting position to a displaced position some distance away, rebounding to the opposite displaced position, and continuing back and forth. The ends of the string are the nodes of the wave, and the center is the loop. One cycle from the resting position through both opposite positions and back to the resting position is one wave or vibration.]

 

Jones will now explain how the physical motion of the string is involved in the physical properties of the sound waves it produces. We first consider an “elastic material” tied to two ends [perhaps we think of an elastic material generally so that these principles can apply to other sorts of things like drum heads. But it seems in this application we need to think of the elastic material as being shaped like a string.] It is relatively taut, and so it occupies the horizontal position shown in the diagram.

[Figure 1]

We then suppose that we displace it from that base-line position, drawing the center up to point A. As a result, it will rebound down to point B: “If it is moved out of its position of rest to point A by being struck, plucked, or bowed, the elasticity of the string and its momentum will carry it to point B, a distance past the point of rest approximately equal to the original displacement (A)” (4). Then the resistance from the air will gradually dampen the motion: “If it is then left free to vibrate, it will eventually be brought again to a state of rest by the friction of the medium, in this case air” (4). If the string is pulled back more, its own motions will have a greater amplitude, and the sound waves it produces will too: “The degree of displacement, which is the amplitude, determines the loudness of the sound” (4).  So the string begins at rest, moves to A, rebounds to B, then in its rebounding back toward A, will pass through its rest position, thereby making one cycle, also called one vibration or wave: “One entire cycle, from point of rest to A, then to B, and back to point of rest, is considered one vibration or wave; the ends of the string are the nodes of the wave, the center point is called the loop” (4). Certain physical properties can have some influence on the pitch of the string, like its material, thickness, and tension. However, what primarily determines the pitch is the string length (5).

 

 

 

1.1.2.3

[The full back and forth motion motion is the fundamental frequency. All the while, a series of additional motions moves through the same string. These are partials or overtones, and they bear frequencies increasing with the natural numbers.]

 

[First I will quote, then comment.]

The vibration of the entire length of the string as shown in figure 1 produces the fundamental, that is, the basic pitch we assign to this string length. However, being flexible the string vibrates also in parts of halves, thirds, quarters, and so on, and each of these segments produces a sound. These sounds are called partials, or overtones.

(5)

[There is a lot that is interesting about wave movement and overtones. See this entry where the physics of it is discussed at greater length. I will share some comments, but please consult a more reliable source on this topic. The image at the bottom of the above figure looks a lot more like what we actually see when viewing a vibrating string, and as the diagram suggests, what we normally see in all that blurry, dynamic motion is the combination of the main wave with its harmonic partial waves. All of them move through the string simultaneously, but with decreasing influence, normally, as we go down the series of partials. Were we to take an instantaneous snapshot of the string, however, it would not look like that blurry one on the bottom and most likely not like any of the ones pictured above it. It would rather be a deformation with no regularity, probably. The diagram below shows this. (Please contact me if you know the print source.)

(Image obtained from: http://nexusilluminati.blogspot.com. Many thanks to this source, and seeking the original print source.)

I am not sure of this however. But as far as I understand, at any one instant, the string takes on a deformation which expresses all the wave forces moving through it, but only over time, as those forces have periodic effect, are we able to discern the distinct wave frequencies.]

 

 

1.1.2.4

[The set of partial vibrations accompanying the fundamental is called the overtone series.]

 

The composite sound of the additional frequencies accompanying the fundamental constitutes the overtone series. For C, we obtain the “following series of pitches” resulting “from the partial vibrations” (5):

 

 

 

1.1.2.5

[The way that an instrument accentuates certain overtones determines its timbre (characteristic tone color).]

 

[I do not follow the next point about the tempered scale, but we return to it later anyway. The point might be that the notes as they have been assigned in the tempered scale have frequencies that are not precisely the doublings, triplings and so on of the original tone, but are rather approximations. As we noted above, the fundamental has the greatest intensity, with the next partials generally speaking decreasing in intensity with each one. However, that is not how it works really, because different instruments accentuate certain overtones. Let me quote:]

The pitches are shown in our “tempered scale” notation, and are only approximate; the space between the partials decreases proportionately as the series ascends. The series does not stop at the sixteenth partial, but this segment is, for practical purposes, all that we need be concerned with. The fundamental and the lower partials have greater intensity and are therefore easier to | hear than some of the more remote overtones, but it would be an oversimplification to say that the series gradually diminishes in intensity as it ascends. In the timbre or characteristic tone color, of some instruments certain of the upper partials are stronger than certain others, and it is due partly to this fact that we are able to distinguish one instrument from another – an oboe from a flute, for example.

(5-6)

 

 

 

1.1.2.6

[The fundamental is numbered as 1 and the first overtone as 2.]

 

We give the fundamental the number 1, and the first overtone is numbered 2. (6)

 

 

 

From:

Jones, George Thaddeus. Music Theory. New York: Barnes & Noble Books / Harper & Row, 1974.

 

Other images sources:

String wave overtone synthesis:

http://nexusilluminati.blogspot.com.tr/2011/06/philosophers-stone-how-to-transmute.html

Jones. (1.1.1) Music Theory, [basic terminology of sound and music: introductory material]

Corry Shores
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[The following is summary. Boldface and bracketed notes are my own.]

George Thaddeus Jones

Music Theory

Part I
Notation, Terminology, and Basic Theory

Chapter 1
Elementary Acoustics and the Properties of Sound

1.1 
[Introductory material]

Brief Summary:
Music is made out of sounds, which are air vibrations produced by vibrating material parts of musical instruments. If these vibrations are irregularly patterned and complex, they make noise. But if the vibrations are regular in their periodicities, they produce tones. A tone is characterized by four variable properties: {1} pitch (highness or lowness, depending on the wave frequency), {2} duration (the temporal extent of the tone), {3} Intensity (the volume or loudness of the tone, depending on the wave’s amplitude), and {4} timbre (the tone’s distinctive quality, depending on its overtone signature). Instruments can be classified by the primary material they are made of. But since our concern here is more acoustical, we distinguish them by whether they have vibrating strings, vibrating air columns, or vibrating bars, plates, or membranes.

Summary

We hear sound when vibrations traveling through the air strike and stimulate the eardrum. When these vibrations are irregular and complex, we normally classify them as noise. Regular vibrations, however, produce tones with a discernible pitch. (3) [Tone is not defined here, but from wikipedia: “A musical tone is a steady periodic sound”. For more on the periodicity of waves, see this entry on sine waves, and also see this entry on the physics of waves.]

The sound vibration “is produced by the oscillation of some elastic material, such as a stretched string” (3). These vibrations [of the solid material] are transmitted through the air by “forming areas of compression and rarefaction. One vibration in the air consists of one cycle or wave of high- and low-pressure  areas” (3). [See this entry for more on compression and rarefaction waves.]

“The number of these vibrations per second is called the frequency of the sound wave; the greater the frequency, the higher the pitch” (3). [A wave in water can be larger or smaller, that is, have a greater or lesser amplitude. In the air, the compression wave can also be more or less “massive” or pronounced.] “The strength or amplitude of the vibration controls the volume or intensity of the sound; the greater the amplitude the louder the sound” (3).

There are four main properties that characterize the tone:

1) Pitch: the relative sense of “high” or “low” [depending on the frequency of the sound wave’s oscillations]
2) Duration: the [temporal] length of the sound or rhythm
3) Intensity: the volume or degree of loudness [depending on the amplitude of the wave]
4) Timbre: the distinctive quality of the sound [depending on the “overtone” wave signature. Again see this entry on the physics of waves.]
(3)

There are other musical concepts that are of more interest for performance, for example “how the tone is attacked and released, how one tone is connected with another, and how a combination of tones produces a sense of density or texture” (3d).

“Musical instruments are mechanisms that produce, resonate, | amplify, and otherwise control vibrations” (3-4). Instruments can be classified in different ways. One way is to classify them according to the principal material they are made from, for example, brass and woodwind. “However, from an acoustical point of view, it is better to discuss the common musical instruments under the headings of vibrating strings, vibrating air columns, and vibrating bars, plates, or membranes” (4).

Jones, George Thaddeus. Music Theory. New York: Barnes & Noble Books / Harper & Row, 1974.

Diagram of a Slaughterhouse. [3] Deleuze on Bacon, Painting Series. Painting, 1946

by Corry Shores
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[I am profoundly grateful to the sources of these images:

askyfilledwithshootingstars.com

artnet.com

www.sai.msu.su

euroartmagazine.com

manilaartblogger.wordpress.com]

[The following is quotation. My commentary is bracketed in red.]

Diagram of a Slaughterhouse

Francis Bacon

Painting, 1946

Museum of Modern Art, New York

Painting 30 of Deleuze's

Francis Bacon: Logique de la sensation. Tome II - Peintures

Painting [3] of the English translation

and Painting [4] of the Seuil 2002 French

(thanks askyfilledwithshootingstars.com)

The contour thus assumes a new function, since it no longer lies flat, but outlines a hollow volume and has a vanishing point. Bacon's umbrellas, in this respect, are analogues of the washbasin. The two versions of Painting, 1946 and 1971 [3, 65], the Figure is clearly lodged within the round area of a balustrade, but at the same time it lets itself be grabbed by the half-spherical umbrella, and appears to be waiting to escape in its entirety through the point of the instrument: already we can no longer see anything but its abject smile. (12bc)

Le contour prend donc une nouvelle fonction, puisqu'il n'est plus à plat, mais dessine une volume creux et comporte un point de fuite. Les parapluies de Bacon, à cet égard, sont l'analogue du lavabo. Dans les deux version de « Peinture », 1946 et 1971, la Figure est bien installée dans le rond d'une balustrade, mais en même temps elle se laisse happer par le parapluie mi-sphérique, et semble attendre de s'échapper tout entière par la pointe de l'instrument : on ne voit déjà plus que son sourire abject. (24c)

[We examined the role of the sink in Bacon's Figure at a Washbasin.

(Thanks artnet.com)

It encloses the man's head, as though squeezing it like a water balloon. This causes the insides to push out-ward through his mouth. The wider ring closes in on his whole body as well, and the sink provides the escape hole for out-moving forces. Deleuze says that the umbrella in Painting 1946 serves the same role as the sink.

And the balustrade is aesthetically analogous to the white ring.

So just as the basin seems to be sucking the figure down through the drain, the umbrella gives us the impression that it is ripping-up the skeletal-figure's face, leaving just the ephemeral smile, just like the Cheshire cat's smile, last to fade away. And just as the white ring encloses and squeezes the figure crouched over the basin, the rail around the skeletal figure seems to squeeze and force him upward into the umbrella.]

The painter is certainly a butcher, but he goes to the butcher's shop as if it were a church, with the meat as the crucified victim (the Painting of 1946 [3]). (17cd)

Le peintre est boucher certes, mais il est dans cette boucherie comme dans une église, avec la viande pour Crucifié (« Peinture » de 1946). (30a)

Throughout Bacon's work, the relationship between the head and meat runs through a scale of intensity that renders it increasingly intimate. First, the meat (flesh on one side, bone on the other) is positioned on the edge of the ring or the balustrade where the Figure-head is seated [3]; but it is also the dense, fleshly rain that surrounds the head and dismantles its face beneath the umbrella [65]. (18-19)

Dans toute l'oeuvre de Bacon, le rapport tête-viande parcourt une échelle intensive qui le rend de plus en plus intime. D'abord la viande (chair d'un côté, os de l'autre) est posée sur le bord de la piste ou de la balustrade où se tient la Figure-tête ; mais elle est aussi l'épaisse pluie charnelle entourant la tête qui défait son visage sous le parapluie. (31c)

The entire body escapes through the screaming mouth. [...] Bacon suggest that beyond the scream there is the smile [...]. There is already a disquieting and disappearing smile in the head of the man underneath the umbrella in the Painting of 1946 [3], and the face is dismantled in favor of this smile, as if there were an acid eating away at the body (20d/21a)

Tout le corps s'échappe par la bouche qui crie. [...] Bacon suggère que, au-delà du cri, il y a le sourire [...] Il y a déjà un sourire tombant, inquiétant, dans la tête de l'homme au parapluie, et c'est au profit de ce sourire que le visage se défait comme sous un acide qui consume le corps (33d/34a).

(Thanks www.sai.msu.su)

[For Bacon, the flesh of our bodies is meat. Consider experiments that send electrical shocks into recently dead muscular tissue. The flesh or meat will flex, contort, twitch, spasm, and so forth. This is our body operating at its optimum, communicating intensities and forces. Sensations might be like such shocks. When we encounter things that shock us, send our bodies into disorder, we are taking within us those external differences and forces, and communicating them all throughout our bodies in chaotic ways. This would be a pure unmediated sensation, a raw sensation.

At our highest sensitivities, we are no more than meat. The less meaty we are, the less direct our sensations. So Bacon elevates the status of meat over flesh and mind. Our brains and nervous systems too are meat, serving the role of communicating intensities throughout the body and expressing them.

Deleuze writes that Bacon throughout his development comes to more strongly associate the human head with raw meat, of course in a way that elevates the status and potential of our heads. Our 'minds' at their peak performance are not meditating calmly. They are being ripped and torn all different ways by nervous shocks, expressing a brute unmediated physical reality rather than something abstract. In a sense, when our brains are meat in this way, really then do we conceive ideas, new thoughts with their own lives and storms of wrestling forces. So in the 1946 Painting, the meat and the head are put side-by-side. But slowly Bacon comes more-and-more to depict the meatness of the head and the headness of meat.]

Vibration already produces resonance. For example, the man under the umbrella of 1946 [3] is a simple Figure, corresponding to the passage of sensations from top to bottom (the meat above the umbrella) and from bottom to top (the head seized by the umbrella). But it is also a coupled Figure, corresponding to the confrontation of the sensations in the head and in the meat, to which the horrible falling smile bears witness. (47b)

La vibration se fait déjà résonance. Par exemple, l'homme sous le parapluie de 1946 est une Figure simple, d'après le passage des sensations de haut en bas (la viande au-dessus du parapluie) et de bas en haut (la tête happée par le parapluie). Mais c'est aussi une Figure accouplée, d'après l'étreinte des sensations dans la tête et dans la viande, dont témoigne l'horrible sourire tombant. (66b)

[In Bacon's works, there are not figures in the classical sense, but yet we also would not say that there is a lack of figures in his paintings. Instead there are images that take-on and change roles like actors in a play. First consider when we force together magnets, north-end to north-end. They communicate their differences to each other. One magnet does not join with the other; but each makes the other tremble and shake. This would be a sort of resonance based on the communication of differences. In the Bacon paintings, there are figures embodying certain forces that tangle and wrestle with each other. In a way, they all strike us simultaneously. In the Painting of 1946, as we noted, there is the upward force of the head being squeezed from the balustrade and sucked up through the umbrella.

There is also the heavy weight of the hanging carcass, pressing forces downward on the figure.

These are both forces that impact us, make our bodies vibrate under their influence. More concretely, we might think of our eyes being pushed upward and downward both at the same time, and as a result vibrating on account of the rapid oscillation of tendencies. Because the up and down motions rapidly succeed one another, they communicate their difference, and create a resonance, like how the magnets make each other shake. So the vibration in a way is already a resonance (because a vibration involves the communication of different forces which cause the oscillation), yet also a resonance is also already a vibration (because the trembling and shaking that accompanies the communication of difference is a vibration of sorts).

Vibration is also to be found with coupled figures. In this case, the head and the meat confront each other.

Each one affects us in its own way. But they affect us at the same time, or at least at rapid interchanges or oscillations. So the vibrations from both figures couple and together create resonance. Our bodies experience this not just through eye-motions; we are forced to put together these two things that on the one hand seem to belong together but on the other hand we cannot find any explicable account for their relation. Each one affects us in its own ways, addressing certain zones of our bodies, for example the meat might strike our stomachs with a strange combination of hunger and disgust, while the skull might be felt in our surging circulatory systems, racing out of a vague fear of death. Our own bodies become disorganized. But we make the distinctions between digestive track and circulatory system based on their organic functioning. When the parts cease to function organically, when they are thrown into divergent operations, we are no longer organic bodies. In a sense, we are bodies without organs. Yet the different disorganized zones of our bodies, hitherto divided as digestive and circulatory, still try to come back together into cooperation, so they still communicate to each other. But because what they experience are differences, they can only communicate their differences to one another, which makes each zone vibrate and resonate more profoundly. So Bacon's technique of coupling figures and juxtaposing paintings into triptychs is one way he produces sensational resonance.]

If we consider the particularly significant example of the triptychs, we see the large, brilliant fields of monochrome colors spread out before us - oranges, reds, ochers, golden yellows, greens, violets, pinks. Now if, in the beginning, modulation could still be obtained through differences of value (as in the 1944 Three Studies for Figures at the Base of a Crucifixion [1]), it quickly becomes apparent that modulation must simply consist of internal variations of intensity, or saturation, and that these variations themselves change depending on relations of proximity to this or that zone of the field. These relations of proximity are determined in several ways. Sometimes the field itself has clear-cut sections of another intensity or even another color. This technique, it is true, is rare in the triptychs, but it often appears in the simple paintings, as in the 1946 Painting [3] or the Pope No. II of 1960 [27] (violet sections in the green field). (Deleuze 103a)

Si l'on prend l'exemple particulièrement significatif des triptyques, on voit s'étendre de grands aplats monochromes et vifs, orangés, rouges, ocre, jaunes d'or, verts, violets, roses. Or si, au début, la modulation pouvait encore être obtenue par des différences de valeur (comme dans «Trois études de Figures au pied d'une crucifixion » de 1944), il apparaît vite qu'elle doit seulement consister en variations internes d'intensité ou de saturation, et que ces variations changent elles-mêmes d'après les rapports de voisinage de telle ou telle zone de l'aplat. Ces rapports de voisinage sont déterminés de plusieurs façons : tantôt l'aplat lui-même a des sections franches d'une autre intensité ou même d'une autre couleur. Il est vrai que ce procédé est rarement dans les triptyques, mais il se présente souvent dans des tableaux simples, comme dans « Peinture » de 1946, ou « Pape n 2 » de 1960 (sections violettes pour l'aplat vert). (Deleuze 138-139)

[Often we see large fields of a common color filling the ground behind the figures. Recall the red fields of Triptych, Three Studies for Figures at the Base of a Crucifixion.

(euroartmagazine.com Thanks Dr. Gerry Coulter)

Note also how the tone of the red does not remain the same. It seems to lighten as it moves from the left to the right panel. We would say then that he modulates the color; he alters some aspect of it as it spreads from place-to-place. Notice how the modulations seem to cluster together in the above triptych into zones or regions. Deleuze says that in the Painting of 1946 that the regions are more clearly sectioned off into shaped compartments.]

Let us begin with tactile-optical space [...]. Now what will disrupt this space and its consequences, in a catastrophe, is the manual "diagram," which is made up exclusively of insubordinate color-patches and traits. And something must emerge from this diagram, and present itself to view. Roughly speaking, the law of the diagram, according to Bacon, is this: one starts with a figurative form, a diagram intervenes and scrambles it, and a form of a completely different nature emerges from the diagram, which is called the Figure.

Bacon first cites two examples. [Footnote 4] In the 1946 Painting [3], he had wanted "to make a bird alighting on a field," but the lines he had drawn suddenly took on a kind of independence and suggested "something totally different," the man under the umbrella. And in the portraits of heads, the painter looks for organic resemblance, but sometimes "the paint moving from one contour into another" happens to liberate a more profound resemblance in which the organs (eyes, nose, mouth) can no longer be discerned. Precisely because the diagram is not a coded formula, these two extreme examples allow us to bring out the complementary dimensions of the operation.

We might assume that the diagram makes us pass from one form to another - for example, from a bird-form to an umbrella-form - and thus that it acts as an agent of transformation. But this is not the case in the portraits, where we move across only a single form. [109-110] And with regard to Painting [3], Bacon even states explicitly that we do not pass from one form to another. In effect, the bird exists primarily in the intention of the painter, and it gives way to the whole of the really executed painting or, if one prefers, to the umbrella series - man below, meat above. Moreover, the diagram can be found, not at the level of the umbrella, but in the scrambled zone, below and to the left, and it communicates with the whole through the black shore. It is from the diagram - at the center of the painting, at the point of close viewing - that the entire series emerges as a series of accidents "mounting on top of another." [Footnote 5] If we start with the bird as an intentional figurative form, we see that the what corresponds to this form in the painting, what is truly analogous to it, is not the umbrella-form (which merely defines a figurative analogy or an analogy or resemblance), but the series or the figural whole, which constitutes the specifically aesthetic analogy: the arms of the meat which are raised as analogues to wings, the sections of the umbrella which are falling or closing, the mouth of the man as a jagged beak. What is substituted for the bird is not another form, but completely different relations, which create a complete Figure as the aesthetic analogue of the bird (relations between the arms of the meat, the sections of the umbrella, the mouth of the man). The diagram-accident has scrambled the intentional figurative form, the bird: it imposes nonformal color-patches and traits that function only as traits of birdness, of animality. It is from these nonfigurative traits that the final whole emerges, as if from a pool; and it is they that raise to it the power of the pure Figure, beyond the figuration contained in this whole. Thus the diagram acted by imposing a zone of objective indiscernibility or indeterminability between two forms, one of which was no longer, and the other, not yet: it destroys the figuration of the first and neutralizes that of the second. And between the two, it imposes the Figure, through its original relations. There is indeed a change of form, but the change of form is a deformation; that is, a creation of original relations which are substituted for the form: the meat that flows, the umbrella that seizes, the mouth that is made jagged. As the song says, "I'm changing my shape, I feel like an accident." [footnote 6] The diagram has introduced or distributed formless forces throughout the painting, which have a necessary relation with the deformed parts, or which are made use of as, precisely, "places." (Deleuze 109b; 109c-110d)

Partons de l'espace tactile-optique [...] Or c'est avec cet espace et avec ses conséquences que le « diagramme » manuel rompt en catastrophe, lui qui consiste uniquement en taches et traits insubordonnés. Et quelque chose doit sortir du diagramme, à vue. En gros, la loi du diagramme selon Bacon est celle-ci : on part d'une forme figurative, un diagramme intervient pour la brouiller, et il doit en sortir une forme d'une tout autre nature, nommée Figure.

Bacon cite d'abord deux cas [note 146]. Dans « Peinture » de 1946, il voulait « faire un oiseau en train de se poser dans un champ », mais les traits tracés ont pris soudain une sorte d'indépendance, et suggéré « quelque chose de tout à fait différent », l'homme au parapluie. Et dans les portraits de têtes, le peintre cherche la ressemblance organique, mail il arrive que « le mouvement même de la peinture d'un contour à un autre » libère une ressemblance plus profonde où l'on ne peut plus discerner d'organes, yeux, nez ou bouche. Justement parce que le diagramme n'est pas une formule codée, ces deux cas extrêmes doivent nous permettre dégager les dimensions complémentaires de l'opération.

On pourrait croire que le diagramme nous fait passer d'une forme à une autre, par exemple d'une forme-oiseau à une forme-parapluie, et agit en ce sens comme un agent de transformation. Mais ce n'est pas le cas des portraits, où l'on va seulement d'un bord à l'autre d'une même forme. Et même pour « Peinture », Bacon dit explicitement qu'on ne passe pas d'une forme à une autre. En effet, l'oiseau existe surtout dans l'intention du peintre, et il fait place à l'ensemble du tableau réellement exécuté, ou, si l'on préfère, à la série parapluie - homme en dessous - viande au-dessus. Le diagramme d'ailleurs n'est pas au niveau du parapluie, mais dans la zone brouillée, plus bas, un peu à gauche, et communique avec l'ensemble par la plage noire : c'est lui, foyer du tableau, point de vision rapprochée, dont sort toute la série comme série d'accidents « montant les uns sur la tête des autres » [note 147]. Si l'on part de l'oiseau comme forme figurative intentionnelle, on voit ce qui correspond à cette forme dans le tableau, ce qui lui est vraiment analogue, ce n'est pas la forme-parapluie (qui définirait seulement une analogie figurative ou de ressemblance), mais c'est la série ou l'ensemble figural, qui constitue l'analogie proprement esthétique : les bras de la viande qui se lèvent comme analogues d'ailes, les tranches de parapluie qui tombent ou se ferment, la bouche de l'homme comme un bec dentelé. À l'oiseau se sont substitués, non pas une autre forme, mais des rapports tout différents, qui engendrent l'ensemble d'une Figure comme l'analogue esthétique de l'oiseau (rapports entre bras de la viande, tranches du parapluie, bouche de l'homme). Le diagramme-accident a brouillé la forme figurative intentionnelle, l'oiseau : il impose des taches et traits informels, qui fonctionnent seulement comme des traits d'oisellité, d'animalité. Et ce sont ces traits non figuratifs dont, comme d'une flaque, sort l'ensemble d'arrivée, et qui, par-delà la figuration propre à cet ensemble à son tour, l'élèvent à la puissance de pure Figure. Le diagramme a donc agi en imposant une zone d'indiscernabilité ou d'indéterminabilité objective entre deux formes, dont l'une n'était déjà plus, et l'autre, pas encore : il détruit la figuration de l'une et neutralise celle de l'autre. Et entre les deux, il impose la Figure, sous ses rapports originaux. Il y a bien changement de forme, mais le changement de forme est déformation, c'est-à-dire création de rapports originaux substitués à la forme : la viande qui ruisselle, le parapluie qui happe, la bouche qui se dentelle. Comme dit une chanson, I'm changing my shape, I feel like an accident. Le diagramme a induit ou réparti dans tout le tableau les forces informelles avec lesquelles les parties déformées sont nécessairement en rapport, ou auxquelles elles servent précisément de « lieux ». [Deleuze 146b; 146c-148b]

The essential point about the diagram is that it is made in order for something to emerge from it, and if nothing emerges from it, it fails. And what emerges from the diagram, the Figure, emerges both gradually and all at once, as in Painting [3], where the whole is given all at once, while the series is at the same time constructed gradually. [Deleuze 111d]

L'essentiel du diagramme, c'est qu'il est fait pour que quelque chose en sorte, et il rate si rien n'en sorte. Et ce qui sort du diagramme, la Figure, en sort à la fois graduellement et tout d'un coup, comme pour « Peinture » où l'ensemble est donné d'un coup, en même temps que la série, construite graduellement. [Deleuze 149cd]

(Thanks www.sai.msu.su)

[In a painting, we might very generally distinguish two basic dimensions of the painting's expression. On the one hand, there are things that we discern and recognize with our eyes and imaginations. These would include recognizable things or decodable symbolic representations. So we might call this optical space. But what we see are real physical things and markings, and not abstractions floating somewhere in another realm. Such elements as depth, contour, relief, and so on, allow our eyes and imaginations to discern abstract differences. These elements are the tactile referents. Together they make-up tactile-optical space.

There are traditions in painting which call for different parts of the canvass to play certain roles. We normally would not put the main figure at the very corner, but rather closer to the center, for example. Our eyes tend toward the center, and also, if something is at the edge, then not all of it will become depicted. Jackson Pollock broke from such tendencies by splattering the paint beyond the boundaries of the canvass. The painter has to resist more than just distributions that pre-impose themselves onto the blank canvass. She also will not be able to help having some kind of vision for what the painting will become. But often the images in our heads are also clichéd and predetermined. Bacon devised a technique that allows him to disrupt the clichés without creating an indiscernible 'mess' as with Pollock's works. Bacon begins with the preformed images on the canvass, which are either there in his imagination, or perhaps he has begun painting their general outlines already. Next, he uses some chance-based technique like splattering or smearing paint on the canvass. Then, he reads the new disruptions as if they were lines on a graph or diagram. They indicate to him the different directions and dimensions he may develop his painting. He undertakes many of these divergent impulsions at once. The result are deformed images. So the diagram disrupts the tactile-optical space which imposes clichéd patterns and recognizable imagery. What emerges then from the painting is not a recognizable figuration, but rather more of a rhythm of experience, what Deleuze calls the Figure.

In the painting, the diagram is the scrambled zone near the center.]

(Thanks www.sai.msu.su)

[Originally Bacon had in mind a bird landing on a field. We can almost see it. The outstretched hanging-carcass appendeges were the wings. The umbrella was the head. And the skull was the beak. The scrambled diagram set-off multiple chains of new divergent developments. We do not obtain for example another animal, whose parts would relate the same way that the bird's parts interrelate. Rather, we have new things with entirely new sorts of relations. The umbrella does not relate to the skull in the same way that a bird's head relates to its beak. Yet on the other hand, because this is a deformation of something that originally had an organic organization, we feel compelled to try to put the pieces together. This causes us to contract differences together, which creates in us vibrations and resonance. So we would not say that the new painting is merely analogous to the bird, because the conceptual relations do not obtain. Yet the same forces that force us to put the bird's parts together also force us to put the new painting's parts together. So it is analogous purely on the aesthetic level of the experience of sensuous forces. Hence Deleuze calls it an aesthetic analogy.]

(Thanks manilaartblogger.wordpress.com)

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

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Paris: Seuil, 2002.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Editions de la différence [Littératures], 1981.

Image Credits.

Thank you sources very much.

Painting 1946

1st instance and all fragments from:

http://www.askyfilledwithshootingstars.com/wordpress/?p=971

(c) 2009 The Estate of Francis Bacon/ARS, New York/DACS, London

Next instance from:

http://www.sai.msu.su/wm/paint/auth/bacon/

Image on wall from:

http://manilaartblogger.wordpress.com/2009/05/

Triptych, Three Studies for Figures at the Base of a Crucifixion, 1944.

http://www.euroartmagazine.com/new/?issue=6&page=1&content=140

Figure at a Washbasin, 1976

http://www.artnet.com/artwork/425743887/111884/francis-bacon-figure-at-a-washbasin.html

Ancient Chaos: Ch 2.1 of Mainzer, Thinking in Complexity: The Computational Dynamics of Matter, Mind, and Mankind

by Corry Shores
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Klaus Mainzer

Thinking in Complexity:

The Computational Dynamics

of Matter, Mind, and Mankind

2 Complex Systems and the Evolution of Matter

Matter comes in complex, irregular, and chaotic states. Order arises from it. How?

2.1 Aristotle's Cosmos and the Logos of Heraclitus

Many presocratic philosophers traced the complexity of nature back to the order of "first principles." Thales asserts that the wet is the original cause of all things.

Anaximander says it is "a boundlessly indeterminable" original matter. Out of it arises all oppositional forms of matter, such as heat & cold, and wet & dry. (18bc) Thus everything begins in a completely heterogeneous and symmetrical state. The symmetry becomes broken. Then opposites and tensions emerge. The new material states are determined and ordered.

Anaximines held that change results from the condensation and rarefaction of air.

For Heraclitus, the original matter is change. It is fire.

The ray of lightning (i.e., fire) guides the All. – This world order which is the same for all was created neither by one of the gods nor by one of the humans, but it was always, and is, and will be eternally living fire, glimmering and extinguishing according to measures. (qt. 10bc)

In the 20th century, physicists would say something similar, except speak of energy rather than fire.

But Heraclitus did not mean all was chaos. The material world "consists of opposite conditions and tendencies which, nevertheless, are held in unity by hidden harmony," which is logos. (19d, emphasis mine)

Parmenides conceived the world as being motionless, homogeneous, and timeless. (20b)

Empedocles argued that four elements "arose from nature and chance." Changes result from their intermixing. Love/attraction and hatred/repulsion are the basic forces.

Anaxagoras replaces Empedocles' four elements with an unlimited number of substances composed of seed particles. Matter is infinitely divisible, so they were unlimited in their number and smallness. Everything is contained in everything else. There is black in snow, but too little to discern. Anaxagoras also said that the cosmos proceeds from a homogeneous mixture of matter. An immaterial original spirit force "set this mixture into a whirling motion which brought about a separation of the various things depending on the speed of each of them." (21c)

Democritus posited atoms. There is full. And there is empty. Full are the atoms. Empty are the spaces between. "Atoms differ in the form (morphe), the position (thesis), and their diverse configurations (taxis) in material combinations." (21d) The atoms "move according to necessity in a constant whirl." (22a)

Plato gives a mathematical model for atomism in his Timaeus. The geometrical shapes of the basic material parts determine how they combine, and the sorts of matter that their combinations make-up. (22b-c)

For Aristotle, the most perfect motion was circular. It can go without end. (25c) The cosmos' motion is based on the circular movement of the spheres.

Taoism considers nature to be "a great organism governed by cyclical motions and rhythms." (30cd) All things are interrelated. "Rhythms follow upon each other like waves in the water." There are two opposite forces: yin and yang. (30d) Energies return to their origins. Chinese philosophy had no notions of atomistic particles. So they never developed mathematical mechanics.

Instead, at its center there was a harmonious model of nature with rhythmic waves and fields that cause everything to be connected to everything. (31b)

In this way, the Taoists resemble the Stoics.

Here too the discussion centers on effects that spread out in a great continuum like waves on water. This continuum is the Stoics' pneuma, whose tensions and vibrations are said to determine the various states of nature. The multifarious forms of nature are only transitory patterns that are formed by varied tensions of the pneuma. (31c, emphasis mine)

But the Taoist and Stoic ideas did not lead directly to the sort of wave and field sciences of today. For them,

the emergence of order from complex, irregular, and chaotic states of matter was only qualitatively described, using different models for earth and for heaven. (31c)

Mainzer, Klaus. Thinking in Complexity: The Computational Dynamics of Matter, Mind, and Mankind. Berlin: Springer, 2004.