With “Breathless” (Blue Note), Terence Blanchard is taking firm steps into R&B-based instrumental music that is a departure from the jazz and other improvisational music he is best known for.

“This is just the beginning,” he said of his new group, the E-Collective, which he debuts on the new album and at his Saturday set at the New Orleans Jazz and Heritage Festival presented by Shell.

Blanchard, 53, has always traversed musical borders, although his roots are in jazz. As a onetime member of Art Blakey’s Jazz Messengers, with a solo career featuring collaborations with people as divergent as saxophonist Donald Harrison and Latin jazz percussionist Poncho Sanchez, the New Orleans trumpeter-composer has always pursued music that tells stories through melody.

His compositions, including his Grammy-winning “A Tale of God’s Will (A Requiem for Katrina)” from 2007, which he will perform periodically this year in accordance to the storm’s 10th anniversary, and his work on Spike Lee films (he has scored all of them since 1991) also reflect a restless spirit that is not bound by expectations.

“Breathless” is connected to the hybrid soul-jazz-funk efforts by D’Angelo, Prince and late-era Miles Davis.

P.J. Morton and JRei Oliver contribute some vocals and spoken word, respectively, but the largely instrumental album takes flight through the high emphasis on melody. The songs developed from improvisational experiments during the quintet’s road dates last fall that culminated in recording sessions in December. On the album, the songs follow a journey from meditative grooves to hard-rock riffing.

The few cover songs are equally transformational: “I Ain’t Got Nothin’ But Time,” a country shuffle by Hank Williams from 1947, is unrecognizable in its remake, now existing as a late-night slow jam.

Blanchard said the sessions were brief to make sure the music stayed fresh. One goal? “I wanted it to be funky,” he said.

The fusion of genres provides dramatic climaxes and a swirling of emotional tension, much like a film score. Blanchard said his scoring work for Lee — he is about to start on “Chiraq,” Lee’s forthcoming film about Chicago’s South Side — helped push him in this direction.

Music, for him, is inherently visual and becomes more so in two songs on the album, “See Me As I Am” and “Breathless,” that were inspired by recent police killings of unarmed black men.

The first is an instrumental and features Blanchard’s trumpet sailing over a mid-tempo drumbeat, pausing for spacious interplay between the synthesizers and guitar.

“Whenever I play that, I envision young African-American men pleading to be seen as anything else but hoodlums and gangsters. They’re human beings,” he said. “As I’m playing the music, that started to resonate for me.”

The title song features spoken-word lyrics from Oliver, who quotes Eric Garner, the black man who died last year in New York City after police officers put him into a chokehold. Protesters from around the U.S. borrowed his final words, “I can’t breathe,” to galvanize their efforts for police reform, and those words become a chilling refrain in Blanchard’s song.

Blanchard, who grew up in New Orleans, said he often experiences discrimination because of the color of his skin, whether it is being ignored by clerks when shopping near his home or the unwarranted suspicion he encounters from strangers during everyday interactions.

“There is something going on, and it’s not just the police; it’s the perception of African-American males that people have in this country. That’s the issue.

“Stop seeing me as something you see on Fox News — that’s not who we are. Yet people like to put those images up. I don’t know reason for it because it only instills fear in people,” he said.

Blanchard said he is hopeful when he encounters young people who are colorblind, particularly those at the New Orleans Center for Creative Arts who have no perceived hang-ups about race or sexual identity. Polarization, he said, is responsible for the continuing tension.

“When you don’t see people as human, man, that’s an issue. That’s why we’re out here playing this music and trying to talk about these issues because people are sick and tired of it,” he said.

The E-Collective, featuring bassist Donald Ramsey, drummer Oscar Seaton, guitarist Charles Altura and keyboardist Fabian Almazan, will make its Jazz Fest debut Saturday. He said the festival represents a “homecoming” for him each year.

Not only did he first play there while a teenager, it is also the place where he said seminal musical moments of his past took place: From opening up for Sonny Rollins while a NOCCA student to a conversation with Wayne Shorter that changed the way he looked at music to learning that Stevie Wonder paused during his set so he could hear Blanchard’s trumpet play segments of his Katrina score from the nearby tent.

Impromptu moments like those also included the first time he played the festival following Hurricane Katrina.

“I was shocked at how emotional I was. When I stood on the stage and saw all of those people there, I just lost it. Because I knew those people were feeling it, too.

“It’s more than a jazz fest. It’s an event that people share.”

The Terence Blanchard E-Collective performs from 5:45 p.m. to 7 p.m. Saturday at the Zatarain’s/WWOZ Jazz Tent. The band also performs 9 p.m. Saturday at Le Petit Theatre, 616 St. Peter St.