A Whistling Woman is the fourth novel in the fictional sequence on which AS Byatt has been working since the late Seventies, when the first, The Virgin in the Garden, was published. Her publishers describe A Whistling Woman as "a triumphant conclusion to AS Byatt's great quartet", which sounds pretty final, though there is a tantalising passage in the text which hints at the possibility that the story of Frederica Potter is not quite over.

Frederica is the sort of strongly flavoured heroine for whom one feels an attraction, or a repulsion, that is decidedly sexual. Her person and her personality are pungently described. She is thin, with knobbly joints, freckled, red-haired, foxy, wilful and extremely clever. A marvellous passage in The Virgin in the Garden describes her getting her extraordinarily good A-level results: "No one can beat me. I can do anything, better than anyone," she exults.

This is in 1952. By 1968, the year in which A Whistling Woman is set, a violent marriage and a humiliating divorce have chastened Frederica, though only very slightly. "I've not got a first-class mind," she admits to her lover. This is probably not quite true. What she means is that there was a moment at which she could have chosen an academic career, but that she came down instead on the side of glamour and excitement, in the form of journalism.

Clever young women who make this choice often pass through a stage of regretting what they imagine to be the purer and more noble pleasures of the intellectual life. It is likely that the other thing Frederica really means is that she hasn't a first-class character: that she is obscurely aware of being dissatisfied with the life she is living because parts of it are rather frivolous and therefore not, in a conventional way, virtuous.

The dualism of cleverness versus goodness haunts the Virgin in the Garden quartet. Stephanie, Frederica's elder, gentler and equally clever sister, sacrifices cleverness to goodness, partly as a means of escaping her insistently rational father and, in effect, dies of it. Frederica, who subscribes joyfully when very young to the principle of "be clever, sweet maid, and let who will, be good", ripens rather late into uncertainty. Her internal debate reflects - and in a way also leads, since in Whistling Woman she works as the presenter of an excitingly radical television arts programme - the vivid intellectual ferment of the 1960s, which evidently seemed so rich and exciting at the time, but can appear faintly tawdry in retrospect.

Byatt herself makes Frederica reflect, in a sly flash-forward to her 60-year-old perspective on things, that the intellectual debates of the Sixties were essentially insubstantial: "The 60s were like a fishing-net woven horribly loose and slack with only the odd very bright plastic object caught in its meshes, whilst everything else had rushed and flowed through, back into the undifferentiated ocean."

This seems - which is why it makes one think that we may not have heard the last of Frederica - an odd summary of the intensely energetic and questing arguments that eddy around Frederica and her wider circle: arts v science, rules v anarchy, education v instinct, rationality v religion, Yorkshire v London, plain v fancy.

Plain versus fancy is what underpins the whole of this, and it is not a straightforward apposition. Plain, in Byatt's quartet, can mean clarity, truth, precision; it can also mean ignorance and a lack of subtle apprehension. Fancy can mean energetic, vigorous, imaginative; also mendacious, superficial and frankly bonkers.

The first two novels of the quartet are quite plain, which is to say naturalistic, with a quality of monumental simplicity, rather like a stone chapel with clear glass windows.

The later two are also monumental, but their architecture is baroque, symbolic, incantatory, explicitly informed by the rhythms of fairy tale and myth. On the whole, they seem to express a paradoxical yearning for plainness. Names are important to Byatt, and it is noticeable in A Whistling Woman that the more fanciful the name - Elvet Gander, Jonty Surtees, Paul-Zag Ottokar, Gideon Farrar - the more muddled, compromised and ultimately catastrophic the thinking.

Though one may brood on the fact that, in the end, plain old Miss Frederica Potter finds herself entangled with a chap with the fanciest name of all, the rational, anti-religious but nevertheless Romantic scientist, Luk Lysgaard-Peacock.

The comparison between George Eliot's writing and that of Byatt has been frequently and justly made. Byatt's four novels are complex, lively, muscular, moral and rather masculine books whose celebration of cleverness and strong feeling is intensely invigorating. I hope this isn't really the last of them. Those of us who love Frederica would like to know what became of her in the end.