It gets more serious.

On his previous album, Jazz String Quintet, saxophonist Jim Gailloreto unveiled his beguiling collaboration with the HAWK Quartet, a Chicago-based stand-alone chamber ensemble. This partnership has not only inspired exacting, intimate, and especially powerful solo work from Gailloreto, the veteran Chicago reedman; it has also prompted the most accomplished writing under his name. In a handful of original works, surrounded by revelatory arrangements of jazz standards – and garnished by a mystical setting for poetry sung by Kurt Elling – Jazz String Quintet offered a redefinition of the jazz-and-strings concept.

So what does he do for an encore? He takes that concept still further, and even deeper, in the creation of the symphonic-length work that gives this album its title; he balances it with several even more inventive retellings of classic songs from the jazz repertoire; and he presents two new pieces, composed (at his request) and performed by Chicago’s doyenne of cool, Patricia Barber. American Complex proves that the previous album was no fluke, no one-off, no impulsive urge that has run its course. No, Gailloreto’s eidetic fusion of classical string writing and jazz improvisation has plenty of life; borrowing from a complex American of a past century, “it contains multitudes.”

Much of that has to do with Gailloreto’s cohorts; as he explains, this album is “half about the writing and half about the playing,” and in both realms of his creative process, the HAWK looms large. Gailloreto doesn’t simply write for string quartet: he writes specifically for this string quartet, tailoring his arrangements to the individual strengths of its members. “I have to give a shout-out to the group,” he says. “The thing that makes this writing so successful is the people I’m writing for: I know what they all can do.” That can extend even to the instruments they play; in the case of Jill Kaeding (Gailloreto’s wife), the acquisition of a new cello led him to write certain low-note passages that would not have carried as well on her previous instrument.

On the other hand, what Gailloreto writes for these string players has a direct impact on what he improvises – over, under, and even within the arrangements. The lack of a traditional jazz rhythm section provides a certain freedom from jazz conventions; at the same time, the string quartet replaces those conventions with structure less familiar and less flexible. And yet these arrangements, as played by non-improvisers, taps unexplored regions of the improviser’s imagination. When you add in Gailloreto’s sound on the soprano – rounded yet plaintive, without the reedy nasality you often find among jazz players – you have an instrumental texture that’s versatile and unique. In his words, “I don’t think anybody else plays soprano like this. But the way I’m playing is because I’m playing with a string quartet.

“With all my music,” he continues, “I want to improvise with the strings. I want the strings to have a certain vibe. I don’t want to say ‘swing,’ because that’s really different – but when I’m improvising with them, it’s got have the right feel. So I look for how to write that ‘feel’ into the string parts. I swing; the strings don’t necessarily have to. For what I’m doing, I need classically trained musicians” – musicians whose authoritative interpretation of the written parts supplies a springboard for Gailloreto’s own playing. (There’s an inherent tension between the rhythmic formulations of HAWK and Gailloreto; it echoes the subtle friction of pulses that underlie the elusive quality of “swing” itself.)

On the opening track, a stately arrangement of the classic American song All The Things You Are, the listener gets a step-by-step introduction to the players. It begins with solo cello, eventually joined by the other strings, and finally the soprano, which enters as just another member of the ensemble; in this piece (and throughout his writing), Gailloreto folds the soprano so nimbly into the string harmonies that you might almost forget there’s a horn in there. Gailloreto then embarks on an arpeggiated solo that manages to show his admiration for both J.S. Bach and Philip Glass (two names not often found in the same paragraph).

Most of the other works on this album showcase Gailloreto’s most enduring musical relationships. Guitar poet John McLean has been making music with the saxophonist since the 1980s, and they have appeared together on several recordings and many more bandstands. “I just love working with him,” says Gailloreto; “we have this real rapport.” That friendship buttresses Gailloreto’s remarkable arrangement of Well You Needn’t (one of two Thelonious Monk tunes on the album), which artfully reshapes bits and pieces of the original theme to strengthen the song’s already strong melodic bonds.

Meanwhile, the saxophonist engages two of the string players in that most open (and therefore riskiest) of settings, the duo. On one such pairing, Honeysuckle Rose, Gailloreto partners with his wife in a whirlwind of simpatico communication, augmented by Kaeding’s ferocious use of double stops and fortissimo bowing. “I think it’s my favorite performance on the record,” says Gailloreto. “I honestly didn’t think that would be the case, but the piece just grew on me over the years, and the way Jill and I play it, it sounds like more than two people – sometimes it sounds like a huge ensemble.” The other duet – Round Midnight, with violinist Katherine Hughes – may sound like “only” two people, but it also exploits the virtuoso technique of a highly trained classicist. (“And I’m really proud of that one, too,” adds Gailloreto.)

Gailloreto has often guested on Patricia Barber’s Monday-night residency at Chicago’s legendary Green Mill, a relationship that led to his participation in her critically lauded Blue Note album Mythologies. In fact, it was at the Mill that Gailloreto first heard Spring Song, which he recorded from the stage and proceeded to arrange for this project. “But it was all rubato, and I’ve never written anything that was all rubato, so I had to figure out how to translate that for the group. When I’m arranging other people’s music, I put myself in their place and try to figure out what’s needed to make this sound like their music. In other words, how do I be true to what they are – and still be creative?

“In this case, I finished the arrangement, and then I had a few phone meetings and e-mails with Patty, and then I realized: ‘I have to start all over.’ Because I wrote too much. I can write a lot of notes, but it wasn’t something I should do in this case. I literally took away 80 percent of what I’d written – and it sounded great. And that was a way for me to mature as a writer: ‘I’m doing it this way, because this fills Patty’s musical needs.’ ” On both this piece and Barber’s Wind Song, the blend of her crystalline voice and Gailloreto’s translucent writing shows each of them in a new light.

Sterling as they may be individually, these tracks also support the two larger works composed by Gailloreto: the title suite and Bad Clowns, a deceptive masterpiece arranged from a decades-old composition. The opening two minutes boast a panoply of musical devices: pedal tone, call and response, canonic writing, full-throated unisons, pizzicato darts and accents, and several more – all of which serve the extended development of the simple, sing-song melody that make its first full appearance at 00:43. (In keeping with the title, it’s even got a touch of slapstick.) Bad Clowns shows a composer in full command of his technique, using every trick he knows to turn the simplest phrase into a compelling novella.

At the other end of the spectrum stands American Complex, which Gailloreto calls “the cornerstone” of this album – a composition in which the composer measures and mutes his technique to convey moods of unexpected depth. Each of its four movements refers to an expression of the human voice: “Soliloquy, Incantation – I love what language does,” Gailloreto says. “When I’m writing music, I’m always thinking of the syntax, how a good melody line moves and then it stops – like a sentence.” Still, any literal connection between the titles and the music itself might lead you astray:

“I’ll admit, when I’m writing, I just write; the titles come later. My son asked me what I meant by American Complex” [a good question, in that a “complex” could be a mental illness, a collection of buildings, a knotty problem, and so on]. And I still don’t know. I’m sure that all the bullshit that happens in this country weighs on me – a lot. I just don’t care to figure it out; I write the music.” Whatever their derivation, the piece’s four movements encompass a grand swath of Americana, from the Shaker simplicity and Copland-esque chords of Soliloquy to the ethereal soprano soloing on Sermon, which showers the prairie theme with incisive torrents. Incantation has elements of a New England reel, but something else, a little misterioso – it’s a barn door you’re not sure you should open. And Lullaby is anything but: a motile, propulsive theme guaranteed to keep you awake, which in Gailloreto’s words “just unfolds and unfolds, and then comes back. I had no idea it would turn out to be that long. In fact, when I started writing it, I had no idea the piece would even be four movements; it could have been ten short movements, or three really long movements. I start writing and I see what happens.”

That combination of honest confusion and boundless confidence is the mark of a continually evolving artist: it allows one to start anywhere, in the middle of anything, but unafraid to traverse the imagination and see where it leads. “Even though there are plenty of standards on this disc, like the previous one, and really only two pieces that I composed, it still feels to me that it’s more about the writing. It got more serious for me.” The rest of us can take great pleasure that it did.

NEIL TESSER