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New Orleans trombonist Mark McGrain.

Ever since he was a kid, jazz trombonist Mark McGrain has heard the same request from his parents: "Play something we know."

“As someone who always pushed the envelope,” McGrain recalled recently, “I got that a lot.”

He certainly pushed the envelope with his avant-jazz ensemble Plunge. Melodies, especially familiar melodies, weren’t his priority.

But they are on his new CD, “Love, Time and Divination,” which is mostly devoted to Great American Songbook standards from the 1930s and ’40s, plus new compositions that are melodically similar.

He intended the album as a gift for his parents, Joe and Toni McGrain, who are now in their 90s. Their wedding photo adorns the cover.

One song in particular is especially familiar to Joe McGrain: the trombone/piano version of “I Can’t Get Started,” a 1938 hit for Bunny Berigan. Joe McGrain carried a 78 rpm recording of “I Can’t Get Started” in his footlocker during his service as a bombardier and navigator in the European theater during World War II.

“It was a real nice surprise to spring that on him,” McGrain said of his take on “I Can’t Get Started,” which concludes “Love, Time and Divination.” “I’m glad he’s able to hear it.”

McGrain will celebrate the release of “Love, Time and Divination” with two sets at Snug Harbor on Thursday. He’ll be backed by pianist Matt Lemmler, bassist James Singleton and guitarist Todd Duke.

A native of Rochester, New York, McGrain worked as a music copyist in Hollywood before joining the faculty of the Berklee College of Music in Boston. At Berklee for more than a decade, he mostly taught commercial arranging and jazz composition. Along the way he wrote a textbook, “Music Notation,” but didn’t play much music of his own.

Following a brief, unhappy detour to make corporate videos, he arrived in New Orleans in 1995 and refocused on being a trombone player. Over the past two decades, he’s enjoyed lengthy associations with guitarist Anders Osborne, trumpeter Michael Ray, Cyril Neville’s R&B Revue, Kirk Joseph’s Backyard Groove and vocalist John Boutte. For a time, he and Radiators keyboardist/singer Ed Volker performed as a duo. There were numerous other experimental collaborations with Singleton, as well as four albums with Plunge.

McGrain, Boutte, Lemmler and Singleton recorded all of “Love, Time and Divination” at Esplanade Studios on Aug. 14, 2017.

The album opens with McGrain’s muted trombone and Lemmler’s New Orleans stride piano on the standard “As Time Goes By,” one of three trombone/piano duets.

Boutte is featured on three songs: a McGrain original composition, “It All Comes Down to Love,” the Mercer/Van Heusen standard “I Thought About You” and a McGrain-arranged cover of the latter-day Pink Floyd favorite “On the Turning Away,” which describes society’s reaction to homelessness.

McGrain shot a video for “On the Turning Away” one Sunday morning as his wife drove them by homeless encampments around downtown New Orleans. “It’s in the neighborhood,” he said. “It wasn’t hard to find.”

McGrain wrote the salsa “Hola Brah,” the instrumental rhumba title track, and the swinging post-pop instrumental “Blossom.” He set out to “explore harmonies and melodies that would fit in with the songs from the ’30s and ’40s.”

He considers himself to be less of a player than an arranger and composer. “To me, playing is spontaneous composition. How can I make solos that sound like a melody that was composed? That’s what I’m striving for.”

That said, revisiting familiar, decades-old standards “became a composing challenge and a playing challenge — they have lots of ‘wrong’ notes. It’s very challenging to play through these things."

Beyond the Berigan song, the new album connects to Joe McGrain’s history in another roundabout way. The senior McGrain is huge fan of Pete Fountain, the late New Orleans clarinet legend; whenever he’d travel to New Orleans on business, he’d go hear Fountain. Lemmler, who is featured throughout "Love, Time and Divination," was Fountain’s pianist late in the legend’s career.

McGrain's parents, he’s happy to report, are big fans of their son's new album. At 63, he finally made an album on which he tried to color inside, rather than outside, the lines.

“In performing the songs on trombone, I’m trying to be as vocal as I can for the melodies, and to be more instrumental for the solos.

“As a player, it’s almost like a thesis. This whole project is about unabashedly beautiful music. I was just trying to make beautiful music.”

Follow Keith Spera on Twitter, @KeithSpera.

Keith Spera writes about music, culture and his kids.