Jazz musicians love puns. Here’s an example: “Just You, Just Me” was a song from a 1929 film called “Marianne,” which was adopted by musicians as a jazz standard and reinterpreted over the years. In the 1940s, pianist Thelonious Monk composed a song with harmonies adapted directly from “Just You, Just Me” but with a new melody, which he titled “Justice.” This kind of oblique reference between “Just Me” and “Just Us” and “Justice” is commonplace, but Monk went a step further when he later renamed his composition “Evidence.” Of course, if you knew the tune had been called “Justice” before, the punning logic would need no explanation. These sorts of stacked associations, though, lead to some of the most interesting puns.

There are different flavors of puns, but one of the most common in jazz is what might be called a “recursive pun,” which Wikipedia defines as “one in which the second aspect of a pun relies on the understanding of an element in the first.” This describes not only the multistep logic behind “Evidence,” but also the rationale for a host of other classic compositions titles: Charlie Parker’s “Confirmation” was followed by Sonny Rollins’s “I Know,” Miles Davis’s “Tune Up” preceded John Coltrane’s “Countdown,” “How High the Moon” was reimagined as Coltrane’s “Satellite,” and so forth.

The practice of writing a new melody over existing harmonies, as Monk did with “Evidence,” is generally acknowledged as a major innovation of the bebop era, which encompasses the music of Charlie Parker, Dizzy Gillespie, and others in the decade after WWII. In academic parlance, these compositions are known as “contrafacts.” The story goes that jazz musicians enjoyed using American pop songs of the time as improvisational vehicles—primarily for their harmonic frameworks—but sought to avoid raising performing and recording expenses with royalty payments. Instead, they managed to play these same songs by writing contrafacts. Punning titles weren’t just inside jokes for musicians, though; sometimes, as in “Evidence,” they referenced their antecedents to create a point of tangency between the older music and the newer.

Not all puns are created equal, though. To my mind, the subtle connection between “Evidence” and “Just You, Just Me” is a respectable example of jazz witticism, but there are also far more tasteless titles than musicians would probably care to think about. Case in point: more than a few years ago, the standard “I’m Getting Sentimental Over You” was appropriated for a contrafact entitled “I’m Getting Cement All Over Ewe.” Even more cringeworthy is the album cover, which features the composer pouring a grayish powder onto what appears to be a stuffed sheep.

That same album, however, does feature a more sophisticated type of jazz pun: the translation of a melody from one song onto the harmonic scheme of a completely distinct song. The example from this record is a mash-up of the harmony of “Stella by Starlight,” a lush ballad with elegantly dark harmonies from the 1944 film “The Uninvited,” and the melody of Charlie Parker’s “Donna Lee,” a romping, up-tempo bebop line peppered with rapid chromatic turns. It’s worth noting that “Donna Lee” itself is a contrafact of the 1917 Tin Pan Alley song “(Back Home Again in) Indiana.”

It might just be this uncanniness—the feeling of both vague familiarity and distinct unfamiliarity—that attracts jazz musicians to the pun. Familiar melodies and phrases translated to fit unexpected contexts don’t have to be simply amusing or clever; they can defamiliarize the musical terrain that jazz musicians work with repeatedly when improvising over tired standards.Musical punning should be understood as distinct from “quoting,” though, which is the practice of directly referencing other songs in a song being played—often to ironic or comedic effect.

Musical punning takes this a step further by applying phrases that are familiar and adjusting them melodically to fit somewhere unexpected. They sound similar to the original melodies but aren’t quite the same, and it’s not always clear whether the musician intended to make the pun; this ambiguity is essential.

All puns rely on the ambiguities of language: without ambiguity, or with fixed, singular meaning for words, puns wouldn’t work. The fact that both words and musical phrases can oscillate continuously between meanings based on the context is a testament to the possibilities of language, which can generate both arbitrary and unexpectedly meaningful connections between ideas. There may be a bit of cognitive dissonance involved, but it’s a pleasant kind of dissonance when taken in moderation.

I wouldn’t go so far to say that jazz is characterized by an aesthetic of ambiguity or something like that, but the looseness of the jazz language is something that should be valued. As long as musicians continue to explore new possibilities with the common lexicon and resist the petrifying canonization of the repertoire, jazz will avoid the way of Latin, Anglo-Saxon, and other dead languages of the musty past .

—Columnist Kevin Sun can be reached at ksun@college.harvard.edu.