Edgar Degas, solitary, paradoxical, far-sighted, was at once the most classical and the most modern of the Impressionists and, as the Royal Academy’s outstanding new exhibition Degas and the Ballet reveals, his ballet pictures pinpoint why. Unlike his colleagues, Degas’ primary interest was the human body, which he interpreted with a formal clarity harking back to Ingres. But he was also animated by something fresh and audacious: his odd perspectives, cropped, broken compositions and free brushwork capture for the first time on canvas the flurry and rush of movement.

In “Two Dancers on the Stage” one soloist hovers en pointe, giving the illusion of weightlessness, as if she is suspended in space, while another steps away from the wings. The entire work – diaphanous tutus, sinuous legs, sloping bare boards – is bathed in a luminous glow: the perfection of artifice as achieved by both ballerina and painter.

The novelist Edmond Duranty claimed Degas as the inventor of “social chiaroscuro” – the light and dark of contemporary life, portrayed through the warm shimmer of footlights or the stark realism of the rehearsal room. “Ballet Scene from Meyerbeer’s Opera ‘Robert Le Diable’” (1876) concentrates on the moment when dead nuns rise from the grave to perform a seductive, whirling dance; their dynamism, amplified by billowing white costumes, is dramatised in broad, blurry brushstrokes contrasting with the precise foreground depictions of the orchestra. Thirty years later, the grandly austere large charcoal “Two Dancers” (1905), its only hint of colour a touch of brown pastel in the hair, is as full of life without depicting any activity – the resting girls, one leaning forward to tie her shoe, the other tilting back to adjust her hair, generate a pattern of opposing forces, while their animated limbs contrast with the solid diagonal of the bench. The first work is documentary, realist – answering Baudelaire’s demand for the painting of contemporary life. The second, in its pure form and distilled vitality, has a pared-down modernity reminding us that Picasso’s “Demoiselles” was only two years away.

This exhibition is full of the contrasts and arguments that make Degas so intellectually exciting. Monet is famous for working in series, but Degas as shown here also operates through dialogue, juxtaposition, elaboration. Of more than 200 ballet pictures, fewer than a fifth take place on stage: instead, ballet’s defining, classical tension between ideal and real is enacted in a debate between the transcendent beauty of performance – the majestic curtsying star in lilac in “Dancer with Bouquets”, the spotlit ballerinas against a dense, tapestry-like backcloth in “Three Dancers, Landscape Scenery” – and the daily grind of practice and application necessary to achieve such ephemeral perfection.

A gallery devoted to wide, shallow landscape-format depictions of the ballet workshop, recalling ancient friezes, is particularly effective. Degas, a relentlessly hard worker, loved chronicling labour: in “The Dance Lesson”, “Dancers in the Rehearsal Room” and “Dancers in the Green Room”, he evokes the oppressive interiors, uncertainty, lassitude that were the young ballerina’s lot, leading our eye across coryphées exercising at the barre, clustered at a window, resting a foot on a double bass, slumped in exhaustion, stretching, waiting, wilting. Although many figures are stationary, the pictorial form invites us to scan images from side to side, from foreground to receding depth, enlivening each composition into an almost filmic panorama.

“Picturing Movement” is this exhibition’s subtitle, and photography’s challenge to painting its recurring theme. The experiments of Eadweard Muybridge, Etienne-Jules Marey and other pioneering photographers form a separate presentation, set out like a Victorian Natural History Museum display, at the core of the show. There is no proof for or against, but I am unconvinced that their work shaped Degas’ thinking – though of course he was aware of it and sometimes used a camera himself. Rather, Degas was an artist so singular and visionary that he was pushing boundaries in myriad unexpected ways, with an instinctive feel for what the 20th century would hold.

Nothing makes this clearer than “Little Dancer Aged Fourteen”, the depiction of Marie van Goethem, daughter of a Belgian washerwoman, as a two-thirds life-size wax figure with bodice, real gauze tutu, wig and satin hair ribbon that Degas exhibited in 1881. Purists hated it as a mixed-media, high/low assault on the very essence of sculpture; others – notably J-K Huysmans – saw in it the medium’s future. They were right: the Little Dancer’s balance between insolence and innocence, sophistication and barbarity, realism and a stylisation recalling Egyptian stepping poses, heralds modernist primitivism. Rodin looks fussy and weak by comparison.

Drawings never before assembled at this stretch demonstrate how Degas made more than 20 sketches, at every possible angle, for “Little Dancer”; he would later remark of cubism’s multiple facets that “it seems even more difficult than painting”. The sensuously expressive, crusty pastels from the 1890s here are as innovative. Stippling and layering colour, applying paint in large dabs with his fingers, Degas created whole works – “Dancers in Blue”, “The Red Ballet Skirts” – dedicated to a dominant hue, its subtle variations and orchestrated harmonies: as radiant as the Fauves, and anticipating mid-20th-century gestural abstraction.

Although it lacks a few key works – the Musée d’Orsay’s “The Star”, Washington’s “The Dance Class” – this is the most enjoyable, illuminating exhibition I have seen anywhere this year, and triumphantly proves how much we can still glean from a deep, precisely focused exploration of the most familiar masters.

‘Degas and the Ballet: Picturing Movement’, Royal Academy, London, September 17-December 11, The Royal Academy

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