It’s not such a surprise that the first album on Branford Marsalis’s new label, Marsalis Music, would be by Branford himself. What better way to set an agenda? Neither is it surprising that the CD, Footsteps of Our Fathers, pays tributes to the jazz tradition with "covers" of rarely performed pieces by jazz masters — a move that would be just as appropriate an extreme as Marsalis’s deciding to premiere a major original work for saxophone and symphony orchestra. What is odd is Marsalis’s choice of material. Ornette Coleman’s "Giggin’ " and John Lewis’s "Concorde," yes. But Sonny Rollins’s "The Freedom Suite" and John Coltrane’s "A Love Supreme"? Say what?

Both pieces were originally released as major statements. Rollins’s 1958 recording — with bassist Oscar Pettiford and drummer Max Roach — was intended as an explicit statement about civil rights at an early point in that movement’s modern struggle. Coltrane’s piece — with his "classic quartet" of McCoy Tyner, Jimmy Garrison, and Elvin Jones — was an equally cataclysmic statement of personal religious faith and spirituality. But the pieces also present a kind of formal challenge that leaves Marsalis exposed as an artist in a way that "Giggin’ " and "Concorde" don’t — they’re extended suites, long works (Rollins’s original is 19:35 and Coltrane’s is 33 minutes). Despite a clearly composed overall architecture, both pieces call for extended group improvisations on the original themes; as such, both are generally seen as inseparable from their original recorded performances.

In other words, with a performer takes on "Giggin’" and "Concorde" — or for that matter Charlie Parker’s "Scrapple from the Apple" or Thelonious Monk’s "Evidence" — he’s pitting himself against the piece. With these two signature works, Marsalis is pitting himself against a particular performance and begging comparison with the original player — who’s better, Branford or Trane, Branford or Sonny?

"I know what you’re saying," he concedes when I raise the point over the phone. "It’s like with ‘A Love Supreme,’ there’s a certain level of understanding of the blues that you have to have. Whereas with songs like ‘Countdown’ and ‘Giant Steps,’ you don’t really have to have an understanding of the blues at all. You just have to have phenomenal technique and a basic understanding of harmony, and you can rip through them. Which is why when you listen to people who play Coltrane songs, they’re usually ‘Countdown’ or ‘Giant Steps,’ songs that allow you to play a series of scales against a series of chords. And the faster it is, the better it sounds.

"Whereas ‘A Love Supreme,’ the first movement is basically the old ‘Seventh Son’ bass line. That’s all ‘A Love Supreme’ is. I mean, that’s just as basic in the blues form as you can get. One chord . . . it’s real hard to play on one chord."

Marsalis’s versions of the pieces clock in close to the originals — "A Love Supreme" just a few seconds shorter, "The Freedom Suite" a few minutes longer. Beyond that, comparisons become meaningless. Jazz lives not on score paper but in performance, so textual analysis will get you only so far, especially in such long stretches of improvised soloing. After all, how do you transcribe the attack and release of a given note, its particular timbre? Suffice to say that Marsalis burrows into the workings of each piece. In each, he follows his mentors in building expansive statements from short motivic "cells," melodic and rhythmic. In Rollins he finds the definitive wit of fearsome articulation at fast tempos, and in Coltrane he finds varying patterns over that "one chord" that build to ecstatic release in the Trane-like upward cries. But they are his own patterns, emerging from the ensemble interaction fostered by his superb band (pianist Joey Calderazzo, bassist Eric Revis, and drummer Jeff "Tain" Watts).

One of the pleasures of Footsteps of Our Fathers is its sequencing — the album itself is a suite, bookended with two concise elegant classics, the folkloric Coleman, and Lewis’s fugue-like riff tune. At its center is the release from the "hard" blues of Rollins to the prayerful "Acknowledgement" section of "A Love Supreme" (not, by the way, Coltrane’s fluttering arpeggios but Marsalis’s own melodic variations). And what’s true here has been true over Marsalis’s past few albums: he reaches a level of intensity where you’re not necessarily thinking about Coltrane, or even about Branford. Instead, you’re thinking about the music that’s unfolding before your ears. Which is maybe the point.

Branford Marsalis plays the Berklee Performance Center on November 20. Call (617) 876-7777.