It is not a new story, certainly. Music played an important part in the lives of Jewish immigrants, both in religion (the singing of the cantors) and in popular music (klezmer bands featuring rollicking clarinets). First- and second-generation musicians, like George Gershwin, became attracted to ragtime and jazz. The mix of the two revolutionized popular music in America.
What Rousso-Lenoir brings to the table is a fresh-eyed, and somewhat unfashionable, wonder at the birth of a musical idiom. She all but revels in the ''Jazz Singer" stories of how children of immigrants rebelled against their parents in order to embrace the opportunities they saw around them.
One of these rebels, Rousso-Lenoir tells us, was -- who knew? -- Betty Boop. In one of the many great film clips we see the animated Ms. B in trademark low-cut evening dress trying to fly the coop from her strict, religious Jewish parents. The Marx Brothers are here, too, as are moving historical clips from New York in the early 20th century, though the focus is musicians such as Gershwin, Goodman, Irving Berlin, Fanny Brice, Molly Picon, and Harold Arlen.
Just as these Jews tried to free themselves from their parents' dislike of mixing, Rousso-Lenoir isn't held back by ethnocentrism in contemporary American political thought. To her, this is a thoroughly joyful story of the American melting pot -- how American Jews and blacks came together, delighting in each other's music in pursuit of a magnificent new art form.
Louis Armstrong learns from the Jewish family that gave him his first trumpet, Gershwin is inspired by black jazz pianists, and on and on, culminating in the sensational, fully integrated Goodman quartet with Gene Krupa and African-Americans Lionel Hampton and Teddy Wilson.
When Al Jolson dons black face to sing ''My Mammy," he is, according to Rousso-Lenoir, not exploiting African-Americans but escaping Jewish taboos so he can free his art. ''He is neither Jew nor black" at that moment, says Harvey Fierstein, the narrator for the ''Great Performances" production.
''From Shtetl to Swing" makes assimilation a virtue rather than a sin. And it makes its point so melodically that it's hard to argue with Fierstein's summation: ''What's not to like?"
Ed Siegel can be reached at siegel@globe.com.