It’s possible to imagine that T.S. Eliot had Maria Schneider in mind when he wrote (in “Four Quartets”) “ ... and the end of all our exploring will be to arrive where we started and know the place for the first time.”

Schneider, perhaps the most admired big-band jazz leader and composer of our time, has lived and worked in New York City since the late ’80s. But she derives much of her inspiration from her experiences growing up in Windom, Minn.

The title piece from her 1996 album, “Coming About,” evokes summer days sailing on a lake near Windom as a child.

Her largest effort in this vein, “The Thompson Fields,” a record that earned Schneider a Grammy last year for Best Large Jazz Ensemble, is a series of reminiscences about a neighbor’s farm, a work of quiet but striking beauty that recalls images of the prairie, of milkweed, of birds and, in one instance, a tornado she watched with her mother. It is surely Schneider’s masterpiece.

Excerpts from “The Thompson Fields” were the centerpiece — and the heart — of Schneider’s concert with her 18-piece band at the O’Shaughnessy on Thursday night. It was the start of a tour that will finish with several concerts in California.

Schneider opened her 95-minute set with an especially beguiling number from that disc, “A Potter’s Song,” a tribute to the late Laurie Frink, who played trumpet in the band and was an expert potter. As on the record, accordionist Gary Versace played the wistful opening passages. The number built to a majestic climax, then faded away gently as Versace brought back the opening theme.

Marshall Gilkes on trombone and Greg Gisbert on fluegelhorn took deft solos in “The Monarch and the Milkweed.” Later, two impressive veterans of this band, Donny McCaslin on tenor saxophone and Scott Robinson on baritone sax, played wailing solos on “Arbiters of Evolution,” then joined for an explosive duet. Trumpeter Mike Rodriguez proved to be a master of stratospheric high notes during “Data Lords,” an exciting new Schneider composition propelled by fierce, staccato punctuation from the brass section.

With each record and each all-too-rare concert, Schneider adds new colors and new visions to her artistry. Her ever-evolving style and her use of a through-composed format rather than the older theme-solo-theme structure of the swing bands give her music a compositional depth and a freshness that continue to surprise. Even the daunting economics of keeping a big band together hasn’t defeated her. (Schneider will return on her own April 8 as guest artist of the JazzMN Orchestra in a concert at Hopkins High School.)

Beyond the impressive music-making, this was, of course, a homecoming for Schneider. The concert had a party atmosphere. Half the population of Windom seemed to be on hand. One of them was Doris Schneider, Maria’s mother, who said after the concert that, yes, she’s a jazz fan.

Michael Anthony is a classical music critic.