It has been a long journey from “Tradition” to “Tradición.”

A half-century ago, “Fiddler on the Roof” barreled onto Broadway with a now-famous opening song, “Tradition,” that helped theatergoing audiences relate to a story of particular significance to Jewish Americans.

This fall a new musical, “On Your Feet!,” arrives on Broadway with a parallel first act number, “Tradición,” that seeks to universalize the hardships and hopes of Latin American immigrants.

In the intervening years, America has become steadily more multiethnic, while Broadway, generally lagging behind both film and television, has followed suit in fits and starts. But the theatrical season now getting underway is noteworthy not just for the diversity of its casts — a dramatic change from the largely monochromatic season just ended — but also for the ambitious, and risky, effort by producers and writers to make big commercial musicals out of uncomfortable chapters of history.

There is a new musical, “Allegiance,” about the internment of Japanese-Americans during World War II, and a stripped-down revival, “The Color Purple,” about the difficulties of black women in rural Georgia of the 1930s. The season opened with “Amazing Grace,” which highlights the depravities of slavery as it tells the story of an early British abolitionist, and it will close with “Shuffle Along,” about an early jazz musical born of the black vaudeville circuit.