

A big inspiration ... Lucien Freud's Benefits Supervisor Sleeping. Photograph: AP Photo/Christie's

The thrilling news that Lucian Freud's Benefits Supervisor Sleeping had fetched £17.2m at auction had the BBC and the Times so overexcited that they dubbed the model for the painting, Sue Tilley, Freud's muse - as if she didn't simply lie heaped on a sofa with her eyes shut while he painted her, but inspired him as well. Tilley posed for Freud a couple of days a week over a period of nine months in 1995, for the miserly sum of £20 a day. At the same time, Freud was struggling to "work off" (his own expression) the sumptuous nakedness of Australian performance artist Leigh Bowery. Bowery was the one subject Freud's ego could not subdue, partly because he wore his skin the way other people wear evening dress. Freud tried again and again to reduce him to anonymity and failed. Bowery's big, glossy body was for Freud "perfectly beautiful". He was allowed to pose standing erect, above Freud's eyeline, with his eyes open and focused, as no woman ever was. If Freud can be said to have had a muse, Bowery was it.

A muse is anything but a paid model. The muse in her purest aspect is the feminine part of the male artist, with which he must have intercourse if he is to bring into being a new work. She is the anima to his animus, the yin to his yang, except that, in a reversal of gender roles, she penetrates or inspires him and he gestates and brings forth, from the womb of the mind. Painters don't claim muses until painting begins to take itself as seriously as poetry. Andrea del Sarto, an Italian painter born in 1486, was famously married to his muse, Lucrezia, whose features so closely approached his ideal that he made all his female figures in her likeness, at a time when most other painters were building their beautiful female images on the well-loved bodies of boys. Since then, artists as different as Rubens, Bonnard, Renoir, Charles Blackman and Brett Whiteley have painted their wives over and over again, but their wives were their subjects rather than their muses.

One 20th-century wife who could claim the title of muse is Sandra Fisher, wife of RB Kitaj, not because of the role she played in life, but because of the role she played in Kitaj's intellectual life after her untimely death. Then Kitaj exalted her as the source of all his creativity, and an aspect of the divine, just as Dante had Beatrice and Petrarch, Laura.

Physical congress with one's muse is hardly possible, because her role is to penetrate the mind rather than to have her body penetrated. Dante never laid a hand on Beatrice, nor Petrarch on Laura. Gustav Klimt's "life-long companion", Emilie Flöge, the younger sister of his sister-in-law, almost certainly died a virgin. Klimt chose Flöge, who was 12 years younger than he, as his maîtresse en titre, paraded her on public occasions, often wearing fabrics of his design, but chose to have sex with women of a different class, who are supposed to have borne him at least 14 children. When he died in 1918, they received little from his estate, which was divided between Flöge and the Klimt family.

Flöge's pointed features and flat virgin body provide the type that is encountered so often in Klimt's pseudo-erotic paintings, tantalisingly glimpsed through elaborate surface patterning. Hers is the blank mask at the centre of his 1913 picture, The Virgin, now in the Národní Gallery in Prague. As so often with Klimt, the unconscious face is set at right angles to the neck, as if the model had been hanged. On her pedestal, swathed in fabric designed by the master, Flöge is a debased version of the muse as fashionista.

Monique Bourgeois, by contrast, is the real thing. In 1941, when Matisse was recovering from treatment for cancer, Bourgeois took the job of nursing him, and doubled as his model. In 1943, after they had been separated by the fortunes of war, Bourgeois entered a convent. She didn't meet Matisse again until 1946, when she came to see him to ask him to design and execute the Chapelle du Rosaire, his last and greatest complete work.

The uber-muse of the 20th century has to be Elena Ivanovna Diakonova, otherwise known as Gala, who first inspired the poet Eluard and then Salvador Dalí, whom she lived with from 1929 until her death in 1982. In this case, too, it seems that the relationship was not sexual.

Nevertheless, Dalí's dependence on his muse was absolute; with the loss of her, his stunning creativity was finally extinguished.