She was Beethoven's inspiration, Goethe's companion and caught the eye of Napoleon. But many still regard Bettina Brentano as a fraud, says Jan Swafford

"Who," asked Napoleon Bonaparte, "is that fuzzy young person?" She was Elisabeth Brentano, known simply as Bettina. Actually, Napoleon was not among her conquests, nor was he her type.

She did not jump into his lap, as she did with Goethe, or croon her name into his ear, as with Beethoven, or go for intimate walks, as with Karl Marx. Napoleon did not dedicate a battle to her, as Beethoven, Schumann and Brahms dedicated songs and the Grimms an edition of their fairy tales. But, even at a distance, Bettina Brentano drew comment.

She was sister to one famous poet, wife to another and inspiration to others, but declined to write poetry. What she did write has outraged and fascinated people ever since. She was a supreme muse, a one-woman literary movement, at once among the singular and most representative figures of the Romantic century.

Bettina was born in Frankfurt in 1785 to the large family of an Italian merchant. Her grandmother was an acclaimed sentimental novelist. Her mother had been Goethe's first great love and Bettina grew up thinking of him as family property.

When her mother died, Bettina, then aged eight, was dispatched to a convent. When she was 12 and living with her grandmother, a handsome young man turned up. It was her brother Clemens, whom she had not seen since she was five. He became her mentor and protector.

Clemens encouraged Bettina to read Goethe. She promptly went mad for the fabled character of Mignon in Wilhelm Meister's Apprenticeship. Goethe's Mignon was a little Italian dancer, stolen from her family by circus performers.

She perched on roofs; some days she would not speak and others spoke in riddles; she carried a cutlass and fought with brigands. In manner and dress, Bettina became the elfin, inexplicable Mignon. Meanwhile, for Goethe himself, she conceived a passion that would simmer until she died.

Oddly enough, it was Clemens's main concern that Bettina should marry well and become a proper hausfrau. He was afraid that his sister would hook up with a mad poet.

Clemens knew about mad poets because he was one himself. At one point he painted his room (floor to ceiling), the carpet, the curtains and his own face blue. He wrote plays and fairy tales and, with his friend Achim von Arnim (and with help from Bettina), gathered the folk poems for the epochal collection Des Knaben Wunderhorn, a touchstone of German Romanticism. As a lyric poet, Clemens rivalled Goethe.

Decades later, Bettina would publish her correspondence with her brother. We find him alternately encouraging her and trying to rein her in. She resisted relentlessly. "For heaven's sake," he chided, "don't become a Seeress... If you knew that... witches of former centuries were none other than the victims of constipation, you would take more care."

Already Bettina had a horror of the ordinary. To Clemens she wrote, in terms she would echo for the rest of her life: "It is no use telling me to be calm; to me that conveys sitting with my hands in my lap, looking forward to the broth we are having for supper... My soul is a passionate dancer; she dances to hidden music which only I can hear... Whatever police the world may prescribe to rule the soul, I refuse to obey them."

Bettina was small and delicate, with black blossoming curls, porcelain skin, fathomless brown eyes and a magnetism beyond conventional beauty. "What artist could do justice to her?" Goethe exclaimed.

Teenaged Bettina's first actual love was for a girl five years older, a beautiful, melancholy, impoverished poet, who lived in a convent: Karoline von Günderrode.

Bettina would publish their letters, too. "I can't write poetry like you, Günderrode, but I can talk with nature... And when I come back... we put our beds side by side and chat away together all night... great profound speculations which make the old world creak on its rusty hinges."

But Günderrode had a desperate passion for a married man. One day she opened her dress to show Bettina the place on her breast where a knife would find her heart. Finally the lover went back to his wife, and Günderrode put a dagger through the place on her breast. (Goethe used the incident in stories.) Bettina was devastated but not defeated. Günderrode had fallen to the dark side of the Romantic temperament: fatal longing, like Goethe's Werther. Bettina was the sunny side.

Replacements for Günderrode turned up. In 1807 Bettina befriended Goethe's mother and listened to stories of her son and the old days. Through Bettina, Goethe would mine those stories for his autobiography.

The same year Bettina finally got an introduction to Goethe: he was 58, she 21. He asked what interested her. "Nothing interests me but you," she said. He invited her to make herself at home. She jumped into his lap, threw her arms around his neck - and went to sleep. Clemens reported that, for three hours, Bettina extolled Goethe, chastised him, revitalised him.

"Don't forget, Goethe, how it was I learned to love you," she wrote to him. It was through his books. "I have been jealous [he wrote often of his loves] and sometimes I have felt myself to be the subject of your poems - and why shouldn't I dream myself into happiness? What higher reality is there than dream?"

She wanted to be his muse and his seeress. His replies were appreciative but stunned. "I have only read the first half of your letter and am too moved to continue. In the meantime, accept my thanks, go on preaching your sermons from the heights of the Rhine and let your psalms flow down to me and the fishes." He meant that, like the mystical Saint Anthony, she should preach to humans and nature alike.

Soon Bettina was stalking the other demigod of the age, Beethoven. Music to her was, like nature, a revelation beyond language and intellect, and she sang beautifully. Beethoven knew her half-brother Franz and his wife, Antonie.

One day, as the nearly deaf composer was working at the piano, he felt hands on his shoulders. He turned in anger to find an attractive young woman who spoke melodiously in his ear: "My name is Brentano." A warm smile lit up his bulldog features. Would she like to hear the song he was composing? It was none other than Goethe's Kennst du das Land: Mignon's famous lyric, Bettina's theme song.

In the next days they walked and made music. In later years, some speculated that Beethoven's mysterious Immortal Beloved was Bettina. She was not; but it was through her that he met the woman who may have been the Immortal Beloved: Bettina's half-sister-in-law Antonie Brentano.

Bettina determined to bring together Goethe and Beethoven. In letters she would publish in Goethe's Correspondence with a Child, she quoted Beethoven's ecstatic vision of his art: "Music is a higher revelation than all wisdom and philosophy, the wine which inspires one to new generative processes, and I am the Bacchus who presses out this glorious wine for humankind... Those who understand [my music] will be freed by it from all the miseries the others drag about with them."

These and other credos from Bettina's letters would become the composer's most famous utterances about music, and help build the Romantic myth of Beethoven.

But those cloud-capped words were Bettina's, not Beethoven's. She dreamed them. Beethoven did not say things like that. In the one authentic surviving letter to Bettina, he groaned of a "bacchanalia" the night before, for which he was now suffering. Bettina would turn Beethoven's hangover into a vision of Bacchus pressing transcendent wine.

She did the same in publishing the letters of Goethe, Günderrode, her brother and herself. She embroidered and invented. Scholars have long cried fraud. Recent admirers declare that Bettina created her own literary genre, the "epistolary novel". The jury is still out.

There is another, perhaps shocking, element. So far as we know, Bettina was never physically the lover of Beethoven or Goethe. She fascinated Goethe and he liked young women. Surely she aspired to be his mistress.

But in the end she was too much for him. He turned her and her letters into material for books and poems, but kept her at arm's length. We should not be surprised that she stayed loyal to him. Affairs were a fraught and risky business: witness Günderrode. Romantics managed such longing partly by spiritualising desire, and Bettina was a virtuoso at that.

Beethoven and Goethe finally did meet. Bettina was not there to see it because she had insulted Goethe's wife. (By then she was married to a poet, Clemens's friend Von Arnim.) The two men walked, talked and parted uneasily.

Bettina made up the famous story that Beethoven jostled through the Imperial party on the street while Goethe stood aside and bowed. But it is true that Beethoven criticised Goethe's deference to the nobility. Goethe wrote that Beethoven's "talent amazed me", but otherwise he found him a pain in the neck. They never met again.

Those were the years of Bettina's first glory. More were to come. With Von Arnim she produced seven children and her spirit survived the domestic life she had dreaded. She still sparkled and still collected famous admirers (Liszt, Schumann, Emerson). In 1824 she designed a memorial for Goethe that delighted the old man.

It shows him seated on a throne, and in front is a little naked muse holding a lyre. She told him it was Mignon; he knew it was Bettina. Today her monument stands in marble in Frankfurt, but, in 1830, an observer wondered: "What's the use of an elf in a commercial age? Who wants her trick dances, her treetop games and flowery palaces?"

As it turned out, many wanted them. After her husband and Goethe died, Bettina resurrected herself. Her Goethe letters made her famous. She dedicated the Günderrode letters to the student radicals whom the despotic Prussian government feared. The students gave her a torchlight parade.

She became a muse to beleaguered progressives; she was branded a communist before the Communist Manifesto; she campaigned against antisemitism. She got away with two extraordinary and dangerous political books entreating the Prussian throne to liberalise because she was a woman, and because the Prussian king was an admirer.

In her strange last book, Conversations with Demons, she imagines herself as a spirit whispering of reform to the king as he sleeps. She nearly went bankrupt publishing it and nobody read it.

Bettina died in her bed at 74, surrounded by her children, a bust of Goethe before her eyes. Long before, Clemens had drawn her in paradoxes: "Half witch, half angel... half seeress, half liar; half cat, half dove; half lizard, half butterfly... half chaste moonlight, half wanton flesh..." And so on, for a dozen more lines.

In a century rich with extravagant characters, Bettina remained unique. She was everyone's muse, she craved love from every quarter, but she was never other than her own person. To echo what was said of another extravagant Romantic, Walt Whitman: her greatest creation was herself.