New Orleans drummer Derrick Freeman and saxophonist James Martin first joined forces by chance. They formed a sax-drums-tuba power trio because a piano player missed his flight. They staffed a fictional brass band for a music video that, to their surprise, morphed into a real band.

All of it was accidental.

Their new joint album, by contrast, was a deliberate effort, made with very specific intentions about what it is and is not.

“Derrick Freeman and James Martin Present SOUL,” as the new CD is titled, features the duo’s Soul Brass Band on two songs; various band members appear on other tracks. The Soul Brass Band will perform at Thursday’s celebration of the new CD at d.b.a. Show time is 10 p.m.; admission is $5.

But the album is most definitely not a Soul Brass Band album. “Derrick Freeman and James Martin Present SOUL” is intended as a sort of summation of their artistic collaboration to date, one that includes their short-lived power trio MFG, Martin’s eponymous band, Freeman’s Smoker’s World, and the Soul Brass Band.

“We’re in the Soul Brass Band, but this is not a brass band record,” Freeman said recently. “But we do play five of the eight songs with the Soul Brass Band, even though these are not brass band versions on the record.”

In the summer of 2015, Freeman, then a few months removed from a multiyear hitch with Kermit Ruffins’ Barbecue Swingers, and Martin, a veteran of Trombone Shorty’s Orleans Avenue, were recruited to back trombonist Glen David Andrews on a tour. The band also included tuba player Julius McKee and a keyboardist.

But the keyboardist missed the flight to the tour’s first stop, so Freeman, Martin and McKee performed as a trio behind Andrews. Freeman and Martin liked the sound of it and decided to form a trio of their own with Kirk Joseph on tuba. They named it MFG — in one interpretation, that’s short for “Martin-Freeman-Genius.” They started recording an album.

But in the middle of the recording, Freeman was hired to assemble a brass band for a CeeLo Green music video being shot in New Orleans. He stocked this fictional band, dubbed the Soul Brass Band, with A-list musicians, including Martin.

As pictures of the musicians wearing their prop caps emblazoned with “Soul” circulated on social media, Freeman started getting offers for the band to play. The fictional Soul Brass Band quickly turned into a real, working brass band.

It took off so fast that the MFG project and its half-finished recording was shelved. But by necessity, the Soul Brass Band’s repertoire, at least early on, consisted mostly of MFG material. At the time, Freeman said, “we had more gigs than we had songs.”

More than two years later, Freeman and Martin revisited the MFG recordings. They didn’t want them to go to waste and soon realized that those recordings could be the foundation of a hybrid album documenting their collaboration's evolution. And releasing it would give them something to sell without having to rush out a Soul Brass Band album before they’d written more original material for it.

Other practical considerations also factored into the album's genesis. Licensing songs for television and movies has replaced actual CD sales as a source of income for musicians. Freeman and Martin have already placed at least one song with “NCIS: New Orleans”; they hope the new “Soul” record leads to more such windfalls.

“At this point in our careers,” Freeman said, “we’re trying to make songs that can be licensed.”

“Derrick Freeman and James Martin Present SOUL” contains several options. Martin contributed two songs from his 2017 solo album “Something’s Gotta Give,” including the title track and “Maintain Composure.” On Martin’s album, “Maintain Composure” is an instrumental; Freeman wrote lyrics for the version on the new album.

The Soul Brass Band blazes through a cover of Tower of Power’s “Soul With a Capital S” and a mash-up of the “Family Feud” and “The Price Is Right” theme songs.

A cover of Nirvana’s “In Bloom” started off as an MFG trio recording. They stripped out Martin’s saxophone solos, replacing them with Danny Abel’s guitar solos, and added more horns, a tricky process that required the musicians to precisely match the tempo and feel of the original tracks.

“It’s mostly impossible to do that, but it worked out,” Freeman said. “I still don’t know how we pulled it off.”

Follow Keith Spera on Twitter, @KeithSpera.

Keith Spera writes about music, culture and his kids.