Pianist Carla Bley, left, with bassist Steve Swallow, center, and saxophonist Andy Sheppard, performed at the Atlas Performing Arts Center on March 22, 2019. (Caterina di Perri/ECM Records)

Carla Bley’s long association with the jazz avant-garde seems unfathomable when she performs in her trio. Sure, the titanic 82-year-old composer, arranger and pianist writes unorthodox, complicated stuff, but her melodies and harmonies are rich, consonant and exquisite. The sellout crowd at the Atlas Performing Arts Center on Friday night suggests that the avant-garde label wasn’t intimidating; the music itself was intoxicating.

Bley’s longtime trio features Steve Swallow on bass and Andy Sheppard on soprano and tenor saxophones. Swallow and Sheppard did most of the talking — Bley approached the microphone once — but there was never any doubt as to whom the attraction was. “We’re here to play music written by Carla, that’s the idea,” Swallow said at the top of the set, generating a round of applause. “She’s written a lot of it.”

The three-part “Copycat,” one of Bley’s newer compositions, set a tone for much of what followed. Its opening third was mournful, with long tones on Sheppard’s tenor against strong figures from Bley’s piano and Swallow’s bass. Parts two and three were more angular, with something of an Eastern European feel; Swallow and Sheppard, in particular, handled them gingerly — as if they were so delicate they might fall apart with one wrong note. That approach was all the more interesting because the sections weren’t delicate at all, but hardy and well put together. The illusion was as spellbinding as the music itself.

The evening was an exercise in that rotation of mournfulness and deceptive sturdiness. “Rut” was churchy and soulful, but Swallow’s bass solo had kid gloves, with subtle phrases and a careful light touch. “Beautiful Telephones” — written for President Trump, Bley explained — was doleful bordering on despairing, with Sheppard’s entrance kicking the tempo up a notch even while maintaining its darkness. (Bley lightened it a bit with humorous quotes from patriotic songs during her solo.) “Utviklingssang” was heartbreaking, with Swallow contributing a vaguely flamenco feel that both Bley and Sheppard followed. Much of Sheppard’s improvisation consisted of quiet, buzzing drones on a low A-flat note, which added to the haunting quality.

Then came a pair of tunes that hinted at Bley’s avant-garde tendencies after all. “3 Banana” was tumbling, thoroughly cockeyed and absolutely fun, with a strong solo from Bley to which Swallow gave contour and definition with his embellished lines. Swallow had also promised a tune that Bley didn’t write; Sheppard finally introduced it as her arrangement of Thelonious Monk’s “Misterioso” (“Mr. Misterioso”). It walked a very fine line: Monk’s music resists reharmonization, and Bley tweaked it a bit in her settings of his famous piano interchange. Not only did she maintain Monk’s spirit, she also extended his warmth and welcome with an opening and closing tag in which she and Sheppard did especially fine work. The encore, Bley’s “Lawns,” extended a similarly welcoming and lyrical sensibility to cap a night of beauty and magic.