2. The Analytic of Drawing: Second Derivatives on a Zero-Ground

Baxandall, Michael

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Appendix: Three Notes on Leonardo and Early Renaissance Shadow: 2. The Analytic of Drawing: Second Derivatives on a Zero-Ground

Michael Baxandall

Shadows and Enlightenment

For complex reasons, from the fifteenth century much more of the painters’ preparatory thought about shadow has been in the form of drawing. But graphic media are no more neutral than conceptual media, and drawing in general is a tendentious vehicle for thought about appearance. Because it dramatises the case, the episode to scrutinise here is a proliferation in the years 1465–85 of a type of drawing of single figures in two tones on paper of intermediate tone, but much of what will be said of …

Author

Michael Baxandall

PublisherYale University Press

https://doi.org/10.37862/aaeportal.00111.010

Stable URL: https://aaeportal.com/?id=-13764

Chapter subject tags:Leonardo, da Vinci, 1452-1519Relief (Art)Shades and shadows in artDrawingVision--ResearchOptics and art

2. The Analytic of Drawing: Second Derivatives on a Zero-Ground

For complex reasons, from the fifteenth century much more of the painters’ preparatory thought about shadow has been in the form of drawing. But graphic media are no more neutral than conceptual media, and drawing in general is a tendentious vehicle for thought about appearance. Because it dramatises the case, the episode to scrutinise here is a proliferation in the years 1465–85 of a type of drawing of single figures in two tones on paper of intermediate tone, but much of what will be said of this type is generalisable to other types.

Several hundred of these two-tone drawings (fig. 50) seem to be from the relatively large and intercommunicating Florentine workshops of Verrocchio, Pollaiuolo, Botticelli, Filippino Lippi and Ghirlandaio (a convenient collection in Ragghianti and Dalli Regoli, 1975). They range from much obvious apprentice work to some drawing of high skill, and there has been a long history of attempts to attribute them to hands and names, but this will be ignored here and the type treated as generic.

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Description: Recto and verso of a study sheet by Unknown

Fig. 50 Florentine, second half of the 15th century (workshop of Filippino Lippi?). Recto and verso of a study sheet. Metalpoint and biacca on blue prepared paper, each 20.7 × 29. British Museum, London (Pp. 1–15).

What they have in common is medium, period, place, general artistic ambience and also function: these are rilievo studies from the life done for self-improvement. Usually the motif is not destined for use in a particular picture. The drawings are mostly metalpoint with biacca: that is, dark marks were made by drawing with a perhaps silver or lead stylus on paper treated with a tinted bone-ash wash, often buff or reddish or pale blue, abrasive enough to cause the point to leave oxidizing traces; and, afterwards rather than before, white lead (biacca) was added with a fine brush. Since the tinted paper offers an intermediate tone, the technique might seem to have a potentiality for analysis of appearance within the three-tone structure in which artists were used to thinking and working. Three aspects of the tendency within it are here located, with recourse to terms and concepts used in current vision research.

Zero-grounds: A zero-line is a section across the visual array recording the constantly varying local average brightness values. It is registered in machine vision (figs 21–22) as a straight line, but it does not represent some one value. It might be visualised as a piece of string charged with values by having been laid along the undulating line that would chart the local brightness averages across the array, and retaining those values when pulled straight. The array is covered in two dimensions by such lines or strings, making a net. Again, the net represents not one value but a continuum of local brightness averages. One can think of a drawing ground as like this net, a zero-ground whose tone represents not some one absolute brightness value but the local average value, or tone. It is flat and even-coloured but it is charged with hills and valleys of changing average value.

The mid-toned ground of metalpoint and biacca drawings (like, in various but not always such forthright ways, the ground of almost any drawing) is really a zero-ground of this kind. It does not register an objective middle tone of stable value but rather the variable local average value from which locally lighter and darker features are registered as rising and falling. It is mainly this that enables the draughtsman to negotiate, though not in any precise sense register, a wide range of values with pigmentations – biacca and oxidized metal – that are basically each one unmixed tone with only the most limited possibility of intensity variation by such means as area hatching. So white and dark-grey in the drawing represent not white and dark grey but some optical event above or below the local average: local average plus or minus something. But the something is not simply a brightness value.

Brightness values and brightness changes: The basic units of vision are not globally calibrated brightness values, but values of brightness change from what is next, ‘spatial derivatives’. The first derivative is the gradient or rate of change between adjacent values, and then the second derivative is the rate of change in this rate of change. It is the second derivative that is used in computer vision, because it distinguishes sharp discontinuities from gentle gradients more clearly, and so (it is claimed) object edges from shadow.

Few draughtsmen have tried to draw with pure brightness values: Seurat is a rare example to come to mind. Most have introduced elements of brightness change. If the computer’s language were metalpoint and biacca rather than digits, it would represent with a white biacca mark an increase in the rate at which brightness is increasing. In a quite different medium, Cézanne was one draughtsman whose drawing of lighting also focused on the second derivative.

But the drawings are not made by computers. Most mature graphic media combine or overlay or alternate representational languages. We are very quick to pick up internal systematicity in compound graphic modes sufficiently well to read them. The Florentine drawings are drawings in which a white mark could indicate a bright value in relation to the varying average of the zero-ground behind, or an increase in brightness in relation to a value next to it, or an increase in the gradient of that increase in brightness – for instance, a place where an evenly brightening curved surface sharply increases its rate of brightening because of some kink – and often indicates more than one of these together.

Spatial frequency: The eye offers the mind both fine and coarse optical takes of things (§16 above). Machine vision tries to imitate this by combining takes of the visual array that have been passed through two or more filters, with a view to selecting those features that survive in more than one of the takes. The filters do two main things: they average out values over a chosen span or spatial frequency; and they exaggerate local variation at the chosen frequency by giving more weight to the values within the span and less weight to the values immediately next to or outside the span. Most drawings also work with preferential frequencies – that is, scales of registration and emphasis.

Physical and procedural facts of a medium play a part here. These drawings are two-tone drawing first down and then up from the notional median of the ground. The tools of the down (to darker) drawing and the up (to lighter) drawing, respectively metalpoint and brush with biacca, are radically different in their self-jigging characters – that is, the movements their physical forms easily accommodate in conjunction with natural movement of hand, arm and fingers; and so the marks they consequently like to make. Metalpoint naturally makes fine linear marks and urges linear continuity; object and plane edges can be abstracted with fine lines, and internal detail and differentiation of surface can be worked on with the help of hatching. Brush and biacca naturally accommodate the making of blobs and bars rather than fine lines, and lend themselves less readily to differentiation within their domain.

There is an imbalance between the characters of notation on the minus and the plus sides of the median, therefore. Quite often one can see a draughtsman resisting it by coarsening his point work and taking pains to refine his brush. But the metalpoint drawing is still usually done first; the drawings work from the shadowed up into the lit. Shadow is the original site of general design and is the more precisely established in form. Some drawings resist this bias by radically minimising the quantity of dark marks and maximising the light. This can be made to pay the extra and disreputable dividend of a facile effect of nocturne-like rilievo: many of the worst apprentice drawings fall for this.

However, there is also interference in these drawings from a sort of super-frequency. The drawings are of single figures, even when there are several on one piece of paper, whereas most of the paintings the artists made had several figures and objects. We are therefore coming in one tier down in the structural hierarchy of a Renaissance picture.

We do not value painting for proximity to a real visual array, but fifteenth-century painting did have imitation of the real as an important part of its ambition. Whether as a cause or a symptom, Florentine drawings in the period 1460–80 lay out a set of distortions in tonal analysis embodied also in Florentine painting, and the urgency of Leonardo’s shadow analysis is partly a reaction to this predicament, part of what is referred to by the mid-sixteenth-century critic Giorgio Vasari as ‘dryness’.

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