While longsuffering Mildred Pierce was enduring one family trial after another during HBO’s five-part miniseries, it was the composer of such Coen brothers’ movies as “True Grit” and “Fargo” who kept the mood somber and restrained.

“Mildred Pierce” was Carter Burwell’s first television score, and its three-plus hours of music was the most he has ever written for a single project.

Intimate and chamber-like, the score was conceived for just 11 musicians: string quartet, various solo woodwinds including flute and clarinet, harp and piano — “instrumentation typical of what you might call a ‘woman’s movie’ from the middle of the century,” Burwell says.

But unlike the story, the music takes its cue from the title character and never slips into melodrama. “I kept the music extremely contained,” he says. “There is hopefully a tug of drama, and of discomfort, because there are big emotional events going on, but Mildred refuses to give in to emotion.”

Burwell calls “Pierce” director Todd Haynes “very sensitive to music,” adding that, while he and Haynes spent hours discussing the jazz of the 1930s, the period and classical music heard throughout the mini were Haynes’ choices.

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