George Gershwin’s “Rhapsody in Blue” turns 90 years old this week, and is barely showing its age. It remains as appealing and as fresh as it did at its 1924 premier, when it helped earn jazz a new degree of respect from America’s music critics.

Jazz was still quite young that year. It had only just emerged in the previous decade as African American composers began blending blues, folk music, popular ballads, and ragtime into a new musical form. For several years, jazz incubated in the juke joints, saloons, and nightclubs of New Orleans, building a following among the working classes and black community. Finally, in 1917, the Victor Talking Machine Company issued a recording of “Livery Stable Blues.” It was, many will argue, the first recording of jazz. It was also one of the first records to sell one million copies.

Despite the popularity of this, and the hundreds of jazz records that followed, jazz drew nothing but scorn from the voices of America’s cultural establishment: music critics, composers, conductors, and self-appointed moral guardians. But jazz became increasingly hard to ignore as young Americans were captivated by its bright, energetic sound. An entire generation, it seemed, was learning to play the saxophone, and the omniscient strains of the “Charleston” and “Black Bottom” were heard from urban night clubs to college campuses as the country entered its “Jazz Age.”...