Kennedy Center Honors honoree Singer Barbara Cook at her NYC Home. (James Patrick Cooper/For The Washington Post)

Barbara Cook’s name alone has made Washington musically richer for the past five years. That’s how long the Kennedy Center has been hosting the Broadway-driven cabaret series with Cook’s signature on it, and Friday night, Cook took to the Terrace Theater in a show that repeated Saturday. At 84, she continues to bring heart and precision to the art of the song.

You could hear it in the oh-so-fluid phrasing of her opener, “Let’s Fall in Love,” her winsome high notes piping and conveying delight. Deep feeling flowed through open vowel sounds in Hoagy Carmichael’s “The Nearness of You”; holding the “i” in the phrase “my wildest dreams” suggested closely held secrets about to tumble out. The sustained “you” at the end was softly sung, yet hungry.

These are the kinds of details that have made Cook — a Tony Award winner as Marian the librarian in the original “The Music Man” many decades ago, and a nominee as recently as 2010 — such an iconic figure within the Broadway and cabaret worlds. (For still more on the nuances of the craft, watch her 6 p.m. master class with emerging singers at the Terrace on Monday; tickets are $12.) She surrounded herself with a splendidly supple quartet, led by pianist and music director Ted Rosenthal, who accompanied Cook solo for “Nearness” and “Bye Bye Blackbird.”

That latter number came attached to “House of the Rising Sun,” which Cook sang a capella; the much-recorded song couldn’t have sounded more mournful. Steve Kenyon’s easygoing clarinet cued the opening to “Georgia on my Mind,” which the quartet and Cook slowly, purposefully pushed to one of the evening’s swelling highlights.

Cook is famously direct in performance, and her conversational style swept the audience past bumps in the opening (sketchy sound mix) and forgotten lyrics in pesky “list” songs such as “Let’s Do It” (Cook consulted sheet music when she needed to). Even grousing about bad health that had her moving slowly across the stage with the use of a cane, she was good company.

And the music was sweet. The savvy Cook held back nothing in the gorgeously mature anthem “Here’s to Life” and finished with John Lennon’s “Imagine,” accompanied only by Rosenthal and sung, as Cook often ends performances, without the aid of a microphone. It’s hard to knock out an audience more delicately than that.