Schimmel, 61, has succeeded in restoring “cool” to a somewhat clunky instrument without removing its outsider appeal. But he was hardly aware of the accordion’s declining status in the mid-1950s when, as a 10-year-old in Philadelphia, he threatened dire consequences if he didn’t receive one for Christmas. All he knew was that the pat on the head he earned for his piano recitals didn’t begin to compare with the revelry that erupted when his uncles arrived at the house and took out their accordions.

By the time Schimmel auditioned for composition studies at Juilliard, his training at the Neupauer Conservatory in Philadelphia (where his uncles had gone) qualified him for advanced placement in nearly everything. Though Schimmel says he “did not walk into Juilliard wearing an accordion,” word got around: an accordion piece written by his roommate that Schimmel presented in Stanley Wolfe’s class led to a teaching fellowship, and he was tapped by Berio (“my first union gig!” he recalls) for a recording of Kurt Weill songs that Berio arranged for Cathy Berberian. Schimmel also earned money turning out two pop songs a week with a lyricist (“one of the last Tin Pan Alley gigs,” he points out) for Mercury records—switching from his L&M teaching blazer into a fringed vest before heading downtown and earning a friendly ribbing (“You whore!”) from classmate Jimmy Conlon on his way out.

Connections made at Juilliard landed Schimmel a number of theatrical gigs after graduation—including the 1979 production of Aristophanes’ The Birds at La Mama, on which he wound up collaborating with a dancer he had met at Juilliard, Micki Goodman, whom he married (and has been collaborating with over the course of their 27-year marriage). A tango he wrote and performed with friends on a contemporary music concert the following year drew interest from Eric Salzman at Nonesuch records, who suggested a tango project for the label. “We laughed; we thought it was funny back then!” Schimmel recalls. But no one was laughing when the recording, released in 1981, climbed to No. 1 on the Billboard charts—and was cited by reviewers as sounding more authentic than Plácido Domingo’s simultaneously-released vocal recording with an Argentine orchestra.

How did three New York-based freelancers communicate the essence of the tango so perfectly? “At first we tried to imitate the original guys literally, which didn’t work so well,” Schimmel explains. “Then we basically started to create our own vernacular, really getting into enjoying the tango ... and surprisingly, our recordings ended up sounding very much like some of the authentic old recordings.”

The tango is but one of the instrument’s associations. “People often ask me when the accordion was invented,” says Schimmel, “and my answer is, ‘It was invented so many times, where do you want me to start?’ Each culture has its own version of it, and each accordion has its own genetic makeup.” The familiar piano-keyboard accordion was brought to America from Vienna by two Italians, the Deiro brothers, and popularized through vaudeville. Schimmel owns several instruments, including “an elegant Titano Emporer with a full orchestral range,” one that’s “a little raspier and in-your-face, for tangos and such,” a bass accordion that he could “do the unaccompanied cello suites on if I want,” a “funky little streety model that you can get a lot of Cajun-sounding things out of,” and “a vintage Excelsior from 1958 that everybody wants, so I have to lock it up.”

His career encompasses just as much variety: Schimmel has played rock ’n’ roll with Tom Waits; performed in the New York City Opera production of Barber’s Vanessa; composed a Tango Mass that has received several performances; conducts an annual weekend of master classes and concerts at the Tenri Cultural Institute; and writes extensively, including a blog and weekly newsletter. His seminar on the world being not “flat” (as Thomas Friedman asserts) but “bellows-pleated, full of ins and outs” resulted in an invitation to speak at Microsoft to executives interested in “new ways of right-brain thinking.”

The accordion’s “built-in ironic duality” is what Schimmel loves most: it’s “elegant and vulgar,” “hip and square,” “beautiful and ugly,” all at once. No matter how classical or abstract the music, the instrument “has a certain nostalgia—it sprays memories,” he says. That “rich, messy dimension”—what he calls “the ultimate fall from grace”—is where he happily resides.