There needs to be a term for the sphere of artists who succeed the first wave of innovators in a field and build substantively and distinctively on their work. We have avant-garde—fittingly, vaguely pretentiously derived from the French—to identify composers like John Cage and Ornette Coleman, who lead the advance guard on a creative battlefield. So why not call the body of artists who follow them something parallel—say, garde secondaire? It should be no slight to acknowledge that someone came second in line to a set of aesthetic principles if that person employed them meaningfully and perhaps advanced them a bit further. The chronology of creative influence carries with it no requirement of decay in artistic value.

The Other Side of Air, the wholly superb recent album by the pianist/composer Myra Melford and her small ensemble Snowy Egret, is shimmering, pulsing proof of this. The project, the 27th album that Melford has released as a bandleader or co-leader over the past three decades, is a musical achievement of a high order. It’s an impeccably accomplished and deeply satisfying collection of jazzy new-music pieces created largely (though not entirely) through free improvisation on melodic, thematic, structural, or attitudinal ideas that Melford provided or suggested to her bandmates. It’s not often clear which elements of the music were composed in advance and which took form spontaneously in the studio, through the interplay of seasoned improvisers skilled at listening to one another and responding imaginatively on the spot. But there’s no harm in that: All the music sounds intuitive and dynamic, openly expressive—alive.

Melford isn’t the inventor of this approach to music-making, of course, and doesn’t claim to be. Living as a young woman in Olympia, Washington, where she moved from her native Illinois for college in the mid-1970s, Melford was first exposed to experimental musicians like the multi-instrumentalists Anthony Braxton and Oliver Lake, important masters in the generation of “free jazz” improvisation that preceded Melford and her peers. Relocating to New York in the early 1980s, she studied under the composer/saxophonist Henry Threadgill, who was in the process of devising idiosyncratic new systems for composing. Melford began playing publicly in groups led by Threadgill and his contemporaries in the “downtown” New York vanguard, including the orchestra leader/conductor Butch Morris and the composer/violinist Leroy Jenkins. By 1990, she was performing and recording music of her own—inspired by her predecessors, as nearly all artists are, but not beholden to none any one of them.

For The Other Side of Air, Melford is again leading her quintet Snowy Egret, which first came together for live performances in 2012 and made its recording debut with a self-titled release three years later. Apart from Melford, the group includes the trumpeter and cornetist Ron Miles, a dependably unpredictable player perhaps best known for his frequent collaborations with guitarist Bill Frisell; Liberty Ellman, a virtuosic guitarist who has worked with hip-hop acts and also produced and played on Threadgill’s Pulitzer Prize–winning 2016 album In for a Penny, In for a Pound; the acoustic-bass player Stomu Takeishi, the premier artist on his instrument today; and the drummer Tyshawn Sorey, a 2017 MacArthur fellow and celebrated composer and bandleader in his own right. A few decades from now, the fact that these five people all once played in the same band may be as hard to imagine as the fact that, in 1953, there was a jazz quintet featuring Charlie Parker, Dizzy Gillespie, Bud Powell, Charles Mingus, and Max Roach.

Ornithologists teach us that the snowy egret, an American species of heron, often feeds while moving—walking, racing, or hopping on its spindly feet. I don’t know if Melford had this factoid in mind when naming the group, but the band nourishes itself on the move, too, creating its repertoire in the act of performance. The Other Side of Air captures nine compositions made this way, including the two-part title piece. They vary greatly, from the wistful, quiet “Turn & Coda” to the angular “Dried Print on Cardboard” to the cacophonous “Living Music,” on which Takeishi and Sorey seem to be competing to sound the least like they’re playing their actual instruments. Every tune has an interesting musical idea or two, or five—one from each musician, exchanged in an atmosphere of prodding, trusting openness.

Discussing Snowy Egret, Melford has said, “I really feel like it’s the vehicle that expresses where I am as a composer, performer, and bandleader.” If so, The Other Side of Air proves how successful Melford has been at rising to what, in my judgment, is one of the most daunting challenges in all the arts: honoring an established tradition—in this case, the tradition of improvisational liberty, defying the formal conventions of jazz harmony, form, and style—to make high-quality music, rich with original ideas. Her work is important not because it’s radically new but because it’s powerful and compelling. Newness, after all, isn’t really a measure of value; it’s a term of category. The term for Myra Melford’s work is, simply, “fine music.”