That discrepancy — between an exquisite sensibility and a world of grubby, shallow materialism — may explain some of the temperamental quirks that Reynolds shares with his creator. Over the years, especially since “There Will Be Blood,” Mr. Anderson has repeatedly manifested his indifference to the fashions and conventions of contemporary filmmaking. In particular, he disdains the careful, self-conscious husbanding of themes and messages that preoccupies many of his peers. He always seems more interested in what his movies are than in what they’re about or who they might be for.

“Phantom Thread” is not as hermetic as “The Master” or as loosey-goosey as “Inherent Vice.” It’s a chamber piece, romantic and baroque in equal measure, with arresting harmonies and ravishing changes of tone. (This might be the place to note that Jonny Greenwood composed the score). Like “There Will Be Blood,” it casts Mr. Day-Lewis as an avatar of obsession, driven this time by the pursuit of aesthetic perfection rather than money and power. But whereas Daniel Plainview in the earlier film was a vector of pure, demonic ambition, Reynolds Woodcock bemusedly discovers himself to be one leg of a complicated emotional triangle.

The other sides are Cyril and Alma (Vicky Krieps), a non-British waitress in a provincial British restaurant who becomes Reynolds’s model, mistress and muse. Usually this is a temporary assignment. We briefly meet Alma’s predecessor, Johanna (Camilla Rutherford), who annoys Reynolds at breakfast and is dismissed offscreen by Cyril, with one of Reynolds’s old dresses as a consolation prize. Johanna’s sin is to request some of her lover’s attention, a demand he regards as intrusive and distracting.

That dynamic will repeat itself with Alma, who butters her toast too noisily, pours tea with too much splashing and boldly asserts her right to exist as something more than an ornament in the Woodcock household. The battle of wills that ensues — a two-front war for Alma, who must contend with both Woodcock siblings — is the film’s dramatic furnace and its comic engine. The three main performances are each as richly textured and subtly shaded as the clothes. Mr. Day-Lewis composes a symphony of moods: sardonic, melancholy, inspired, impatient. But he is matched by Ms. Krieps, an actress from Luxembourg as canny and unintimidated as Alma herself. Is this collaboration or competition? A tango or a tennis match? Whatever it is, this partnership is thrilling to watch: funny, wrenching, full of large and small surprises.