Martha Bayles holds out till page 20 before slyly sidling into pop culture’s all-purpose anthem: “At some point,” she writes, “every critic tries to unpack Ellington’s famous title, ‘It Don’t Mean a Thing If It Ain’t Got That Swing.’” No need to feel so sheepish. As a distillation of the key distinction between pop music and the conservatory crowd, it’s hard to beat. But is the title Ellington’s? He sure enough wrote the tune, but the lyric is credited to Irving Mills, Ellington’s (white) publisher, an old-school Alleyman with an eye to the main chance, who wasn’t above passing off staff lyricists’ work as his own and cutting himself in on the songwriting royalties.

I don’t suppose Miss Bayles is aware of Mills’s claim, but even if she were, who wouldn’t rather believe in Ellington? On the one hand, a cool cat doodling at the keyboard and intuitively hitting upon the definition of what he does; on the other hand, an opportunist Tin Pan Alley hack measuring out the syllables and contriving a hit title to fit. It’s no contest. But the likelihood is that the phrase is Mills’s. It is, after all, in the preferred form of his opening lines: “When my sugar walks down the street/ All the birdies go tweet-tweet-tweet” or his suggestion for a novelty song about the first woman to attempt transatlantic flight, “You took a notion/ To fly across the ocean.” (“Mr. Mills,” his trainee lyricist Dorothy Fields protested, “nobody takes a