Mix and match has become quite the thing for museums, as curators try to break out from conventional retrospectives to themes and associations that bring widely disparate artists together. Turner, that most solitary of geniuses, has been placed alongside Claude, Whistler and the old masters. Monet crops up everywhere, including with Turner. Cy Twombly, the American abstract artist who died last year, was only recently paired with his hero, Poussin, at Dulwich Picture Gallery.
Now, Tate Liverpool has combined all three in a show called Turner Monet Twombly: Later Paintings. Twombly wasn't meant originally to be the third of the trio. Moderna Museet of Stockholm, which first commissioned the show, originally wanted Rothko as the modern partner. It was the curator, Jeremy Lewison, who suggested Twombly instead as being more contemporary and more apt.
How right he was. We all know Turner and Monet. The Tate has paired them before. But Twombly, who is increasingly being seen as the master he was since his death, brings a whole new dimension to what otherwise might have been a very correct but staid exhibition. Set against Turner's The Parting of Hero and Leander from 1837, Twombly's versions of Hero and Leandro from 150 years later seem to pick up the surging sea of Turner and make an astonishing narrative of the abstract swirls. With his swirling, spattering acrylics on paper he seems to dance hand in hand with his predecessor's astonishing watercolour sketches and half-finished oils like Turner's near abstract Rough Seas of 1840-5.
Monet seems the odd man out initially. His study of the Brittany Coast, Les Pyramides de Port-Coton, Effet de Soleil (1886), painted in deep anguish after the death of his first wife, has the roughness of the sea but not the driving sweep that draws you into the vortex of Twombly and Turner's work. Where they use thumb and palette-knife to force the paint, Monet appears tied to the short brush stroke. Where Turner would make buildings and nature part of sensation, Monet would still have form held fast beneath the effect of light he observed so acutely. Even his view of the front of Rouen Cathedral "with morning effect" of 1894 seems more a study of a building under particular light than Turner and Twombly's embrace of mood and emotion.
But as the century ends, Monet suddenly seems to learn the lesson of the Turners he has seen in London. Atmosphere and sensibility rather than motif become his subject in a series of gloriously misty and ambiguous pictures of Waterloo Bridge and the Thames from 1902 and 1904 before he goes on to his last, late obsessive pursuit of picturing his garden in Giverny while the First World War exploded around him. If in his late pictures of Venice he can't match Turner's sense of evaporation of sea mist and earthly time, in his flower studies of his old age he finds himself a whole new theme and makes it entirely his own.
Tate Liverpool is lucky enough to have five of his lily ponds, including canvases from the Albertina in Vienna and the Fondation Beyeler in Switzerland. With them and The Japanese Bridge and The Path Under the Rose Trellises painted in the 1920s in the last years of his life, Monet appears as one with Twombly's Untitled (Sunset) series of 1986 hung alongside and Turner's late studies of Sunset and Sun Setting Over a Lake nearby.
By settling on the "later" paintings of his chosen trio, Lewison is anxious to avoid any suggestion that he is subscribing to the fashionable preoccupation with late style. Instead, he pursues in a series of canvases and Twombly's three-dimensional work the common preoccupations of these artists with loss, melancholy and failing energy.
The connections are obvious to the extent that all three had the ageing artist's preoccupation with revisiting the themes of their youth and the anguish of declining libido. But there is a temptation, which the exhibition does not entirely avoid, of finding parallels and common cause simply because you've already decided to hang these figures together. It is true, but not very enlightening, to say that all three spanned different centuries and virtually overlapped each other (Turner's dates were 1775-1851, Monet's 1840-1926 and Twombly's 1928-2011).
There is an obvious link between Turner's concern with departing friends and passing time in Peace – Burial at Sea and War, The Exile and the Rock Limpet of 1842 and Twombly's assembly of an Egyptian funerary boat, Winter's Passage: Luxor and his Thermopylae anti-war sculpture of 1992 but they don't add anything to each other. Still less does the inclusion of Monet's Vétheuil of 1901 because it was of the village where his first wife was buried and fits the chosen category of Naught So Sweet as Melancholy.
You can point out, as the show does, that both Turner and Twombly had a taste for adding words to their pictures and both had a concern with the fading classical civilisation of the Italy they painted. But while Twombly's homage to an Orpheus disappearing under the paint may make a similar point, it has precious little interaction with Turner's visions of Venice. Twombly's last series, Camino Real, clearly has something sexual to it but to say Monet is declaring the same thing in Japanese Bridge is several bridges too far.
Wisely, the Tate has eschewed the didactic, with virtually no explanations on the walls. Refreshingly, it has arranged the separate parts on an open plan so that you can see forward and backward to other parts in what is, after all, a largely artificial and uncomfortably titled division into themes. For what is so exhilarating about this exhibition is the "late style" that unites these creative spirits from different eras.
By their last decades, Turner, Monet and Twombly had all abandoned fixed viewpoints and figuration. Compare and contrast by all means. But the joy of this exhibition lies simply in the conversation, as Lewison calls it, of three great painters at their fluent, fevered best.
Turner Monet Twombly: Later Paintings, Tate Liverpool (0845 604 7083), to 28 October