Three masters – Carel Fabritius, Pieter de Hooch and Johannes Vermeer – dominate the exhibition Vermeer and the Delft School, at the National Gallery until 16 September. It shows painting done in the town during the first 75 years of the 17th century. Of the three masters Fabritius is the least Delft-like. His subject-matter is not domestic, predictable or repetitious – and that of most of the Delft painters, even the very good ones, is one or all of those things. He matured quickly – we wouldn’t be able to rate him so highly if he had not, for he died at the age of 32 when the city gunpowder magazine blew up. (The ruins are recorded in a very neat painting by van der Poel.)

A substantial proportion of the dozen or so pictures safely attributed to Fabritius are on show here: two self-portraits, The Goldfinch from the Mauritshuis, a sleeping sentry and the National Gallery’s own perspective peepshow. The finish of his pictures (also unlike Delft) is painterly, not smooth. In the goldfinch you can count the strokes – one for each wing feather, one for the patch of red around the beak and so on. They achieve a lively verisimilitude with wonderful directness and economy. You have a strong feeling that Fabritius was clever, curious and interested in experiments – he was the best of Rembrandt’s pupils, and the one who was most clearly emerging from his master’s shadow. Literally so, for seen alongside Rembrandt’s portraits, his, with their pale backgrounds, suggest that a window has been opened somewhere. Light is the thing that links him with de Hooch and Vermeer and with other Delft painters who seem intellectually much less ambitious. He seems to look outward; they look inward. Yet looking inward can also be a strength, as it is in the calm, fastidious, self-abnegating intensity of the two kinds of inwardness which characterise de Hooch and Vermeer. The simple, physical looking-in at still interiors, little courtyards and small houses, at bare rooms and their self-possessed inhabitants, is the vehicle for another kind of inwardness, a quietness mirrored in these unemphatic accounts of things as they are. The character of this double quietness – quietness of subject and of style – is more mysterious in the case of Vermeer. De Hooch, like the greatest still-life painters, shows in his domestic interiors that the simpler the raw materials are (one hare, not a pile of game, three plums, not a cornucopia spilling fruit), the more likely it is that you will get a sense of the solemn actuality of the physical world. But in his case little clumsinesses of drawing and perspective and variations in finish from one part of the picture to another allow us to track the struggle of imperfect human abilities in their attempt to find a match for the look of things. His tonal judgment is wonderful. There are passages, in particular those which show transitions from one kind of lit space to another (for example, from a brighter to a dimmer room, as in the detail shown here from A Mother and Child with Its Head in Her Lap, or from the light in a courtyard in, it seems, late afternoon, to a patch of pale sky above a wall where the day fades), which are more ambitious and poignant than the uncomplicated perfection of the light in Vermeer’s cool interiors.

In Vermeer you find none of de Hooch’s provincial infelicities of drawing. But both began by making pictures of something different. De Hooch did low lifes (albeit rather polite ones) – soldiers drinking and chatting up servant girls – and Vermeer religious and historical subjects. In the earliest picture by Vermeer in the exhibition, Christ in the House of Mary and Martha, his assurance is already formidable. In The Procuress you begin to see the anonymity of surface, the determinedly uncalligraphic brush strokes, the dispassionate attention which gives every part of the canvas the same look. One effect of this is to make those parts the eye scans first – faces and hands in particular – seem a little out of focus: you expect more detail. In the later pictures the surface is so uninflected and the composition so still that they seem – even when you look back to Christ in the House of Mary and Martha, not a roistering picture in any sense – to be evidence of an abnegation of invention (no more complicatedly overlapping bodies, no kneeling and turning) and of pleasure in paint (no more expressive brush marks like those shaping the drapery). The change has a quasi-moral force – as though impressing your personality on the stuff you use to represent the world were sacrilegious.

But the change may in fact have been due to Vermeer starting to use an optical device – a camera obscura perhaps. To my eye a picture like the The Art of Painting is as good evidence that he did so as anything short of documentary proof could be. The spread-out points of brightness are like unfocused highlights on a camera’s ground-glass screen, and the perfectly controlled perspectives seem to be observed, as they would be in a projected image, rather than calculated. Optical transcription of a more or less mechanical sort would also explain the pervading calmness.

In some of de Hooch’s pictures, awkwardness subtracts from the enveloping calm. Vermeer’s figures cause no tremor of that kind – for good or for ill. You sense that the pose needs no interpretation or apology and makes no positive demands on your kinetic imagination either. But the physical ease in these images is not just a matter of optical precision. Vermeer’s pictures have an extreme abstract formality which brings to mind the intervals in a composition by Mondrian – except things are more complicated in Vermeer because the space in which they operate is extended, by chequered floors and the edges of pieces of furniture, into the third dimension. You see why people trace vanishing points and construct little models to prove that they are indeed perfect representations of possible spaces. They suggest the possibility of a kind of order which is both human and in the real world, and, at the same time, almost mathematical or musical in the way it resolves complexity.

The picture by Vermeer which is least quiet here – and thus least pleasing to modern taste – is Allegory of the Faith. His contemporaries seem to have valued it highly, but now the figure of Faith, hand on heart and eyes on heaven, sitting in front of an image of the crucifixion, is too much a piece of play-acting – and one made slightly absurd by the solid presence of the surrounding room and props. The picture we are most fortunate to see, The Art of Painting from Vienna, causes no such embarrassment. The girl dressed up as Clio is clearly an artist’s model, and the fancy-dress worn by the painter just a game. This is a painting about painting. We are in tune with that now – perhaps to the exclusion of too much else.

How far did Delft itself influence the work its painters produced? An essay by Walter Liedtke in the catalogue characterises the town and its life in ways which seem significant. Its population fluctuated, but did not increase dramatically, as Amsterdam’s did. It was close to other towns where pictures might be seen. There were fairs every year where paintings could be bought, but the local artists’ guild protected the rights of native producers.

And there are the buildings themselves. Delft had no Saenredam to make transcendent perspectives of ecclesiastical architecture, but the church interiors here by Gerard Houckgeest, Hendrick van Vliet and Emanuel de Witte are splendid, if sometimes flashy, exercises in painted perspective. Where Vermeer and de Hooch make ordinary rooms solemn, the church painters made ecclesiastical ones lively with dogs, children drawing on the floor or the columns, and figures who, even when they are listening to a sermon, have none of the gravitas Vermeer could give a milkmaid.

All the pictures here are commodities, shaped by markets and fashion. It might seem that compared with the opportunity to make whole walls alive with religious stories, or to give form to dynastic power in portraits, supplying portable wall decorations and collectibles of this sort was a limiting task. In fact it appears to have made possible, almost accidentally, an art of pure painting. While Vermeer may have been read by his contemporaries as a moralist (what we think of as a sleeping woman was seen as a warning against drunkenness, while the woman with the scales may have been thought of as an admonition to live a balanced life), we turn to them – rightly or wrongly – for the more abstract virtue which resides not in the thing shown but in the decorum and precision of the act of representation.

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