A family name can be a burden or a blessing. Jacopo Comin got his – Tintoretto, "little dyer" – from his father's trade, a stroke of luck for a man who would find fame as a colourist. Barocci, a painter of pretty pink Madonnas, was born Federico Fiori, or Frederick Flowers. That would have done nicely, too. Whoever dubbed his father's family Barocci did him no favours at all. Barocci, in some north Italian dialects, are ox-carts – a singularly hefty nickname for the artist now on show at the National Gallery.
One letter different, and all might have been well: barocco is the Italian for Baroque, and Barocci is famously a link between the art of that period and that of the Renaissance. I say "famously", although the Urbino-born painter is anything but famous these days, a lapse the National's show is meant to address.
The problem has been less one of name than of taste. Art history is made up of tectonic plates with labels such as Rococo or Modernism. Every now and then these shift, and artists near the edge fall off. Barocci is a case in point.
In his day (roughly 1526-1612), he was very big news indeed. To be a pioneer of the Baroque meant being at the forefront of the Counter-Reformation, toeing the line of the Council of Trent that art should be orderly, non-pagan and lust-free. In the whole of Barocci: Brilliance and Grace, there is only one secular narrative painting – of the highly edifying tale of Aeneas Fleeing Troy. All the rest are devotional works. The only bare breasts are on the Virgin Mary, and they are definitely anaphrodisiac.
If you think of what was being painted when Barocci was young – Michelangelo's Last Judgement, say – you will see how far things had come. An ox-cart he may have been, but no one would accuse him, as they did Michelangelo, of painting porcherie – pork-things, obscenities. Works such as Rest on the Return from Egypt turn their back on the High Renaissance. While the face of the elderly St Joseph is in what was, by 1570, old-fashioned sfumato, the picture's younger subjects, Mary and the Christ Child, are bathed in the shadeless light of the Counter-Reformation. A new generation is in town, and Federico Barocci is its leader.
As you look at Rest on the Return from Egypt, two things may strike you. One is that you have never heard of the man who painted it, and the other is that you have seen the picture before. Or something like it. The Virgin's soft-fleshed pink cheeks and the pixie-like face of the baby Jesus seem like an echo of Rubens. Actually, the reverse is true. When the Flemish painter came to Italy in the early 1600s, he was captivated by Barocci, particularly by the porcelain look of the Italian's female subjects. Barocci was one of the first to make finished preparatory studies for his canvases in pastel: several, including Head of the Virgin Mary, are in this show. To his decorous drawings we owe, at least in part, those big-bottomed women we think of as Rubenesque.
Rubens saw something in Barocci that succeeding generations lost sight of: an underlying humanity. He was not alone. You'll have read recently about the gift of the late Denis Mahon to British public galleries, including the National. This is of Roman Baroque pictures, so reviled when Mahon began to collect them in the 1930s that they were pretty well given away: the Irishman paid £120 for Guercino's Jacob Blessing the Sons of Joseph. The late 19th century saw Baroque art go out of fashion and the so-called Italian Primitives come in. Victorians thought of Barocci as a pretty painter, which was true, and dismissed him as shallow, which was not.
Look again at his Rest on the Return from Egypt, and then at Nude Study for the Virgin next to it. The latter is drawn not just from life, but of it. Far from being idealised, the Virgin is a woman with the beginning of a droop to her breasts, creases of cellulite in the join of her thighs. And those things are there, too, in Barocci's painting of her – a slight pull of the bodice on her nipples, a sense of mortal flesh beneath the silk.
By the end of his long career, that humanity resurfaced in a different form: Barocci's dirty-handed St Francis in Prayer has the feel of an unruly young Milanese called Caravaggio. If, like Caravaggio, Barocci had been born in 1571, he might have made the leap to a later, meatier Baroque. As it was, he was in the wrong place at the wrong time. Exhibitions often claim to rediscover forgotten geniuses, and seldom do. This one does.
To 19 May (020-7747 2885)
The impact of Marcel Duchamp, in changing the way we see art, objects and the process of creation, is explored at the Barbican's exhibition The Bride and the Bachelors: Duchamp with Cage, Cunningham, Rauschenberg and Johns (till 9 Jun). As the title suggests, it traces his influence on other media too.