The Flatlanders are a country-folk supergroup in reverse.

When the legendary group from Lubbock, Texas, formed to record one stunning album in 1972, few music fans had heard of its members: Joe Ely, Jimmie Dale Gilmore and Butch Hancock.

But after the group disbanded, each member went on to make a name for himself with a distinguished solo career: Ely for his dark, muscular country and Tex-Mex rockers, Gilmore for his delicate Zen ballad singing and Hancock for his wise, clever songwriting.

Every so often, the paths of these three musicians intersect, for a play, an art exhibition or a concert. On Saturday afternoon, the three reunited for a show at the Central Park Summerstage. First Hancock, the brains, performed; then Gilmore, the heart, played; next Ely, the muscle, took the stage. And, finally, brains, heart and muscle came together to create the precious, beautiful body that is the Flatlanders. The three performed "Dallas," their famous love-hate song to a city they compare to a "rich man with a death wish in his eye"; "West Texas Waltz," their carnal, upbeat and very funny national anthem of sorts, and "If You Were a Bluebird," an unrequited-love song told in metaphors. "If you were a hotel," Ely sang in the song, "I'd lean on your doorbell, and I'd call you my home."

That lyric was written by Hancock, one of the great unrecognized songwriters of the South but an inconsistent performer. In his set (which followed an opening set by another Texas songwriter, Jimmy LaFave), Hancock delivered the great turns of phrase, alliterations and hard-won truths that are his specialty in a gruff, laughing voice, interjecting Dylanesque harmonica solos here and there.

Gilmore followed by apologizing for opening the set with his own songs instead of Hancock's. Tall, reedy, pale and delicate with a long flowing mane of unkempt gray hair, he resembled a dandelion stalk whose seeds, with one puff, could be scattered to the wind. His voice resembled a plucked, trembling high-tension wire, his guitar picking was light and tentative, and his stage patter was full of endearing, unsure self-analysis. But though this sensitivity may seem like weakness on the surface, it became powerful when Gilmore applied it to songs that search for the dividing line between, to quote his lyric, "the being and the seeming."

The most popular of the three, Ely played dark, minor-key, finger-picked songs that made Gilmore's mental dividing line physical. He set his near the Tex-Mex border and explored characters trying to determine which side of the line they should call home. Ely ended his set with a tribute to the unofficial fourth Flatlander, a slightly older muse of sorts to the three named Terry Allen. He played Allen's "Gimme a Ride to Heaven Boy," in which a young man driving down the highway pulls over for a most unusual hitchhiker named Jesus Christ, who, in a cosmic joke befitting of these songwriters, ends up drinking his beer and stealing his car.