When we think of counterpoint, we’re usually thinking of the imitative kind, where melodies (or bits of them) echo one another. This is certainly the kind most of us encounter first, when we learn as kids to sing “Row, Row, Row Your Boat” or “Frere Jacques” as a round. It’s also the kind we encounter most often–not infrequently on a cell phone, whose ring tone may well be the opening of Bach’s Two-Part Invention in F.
But there’s also a non-imitative sort of counterpoint, a kind where different (often very different) melodies are made to “fit” together. Maybe the most familiar example of this sort of counterpoint is also found in Bach: his setting of the “Wachet Auf” chorale, in which he overlays a stirring Lutheran hymn with an almost ostentatiously dissimilar melody–one of the all-time ear worms, as it happens–of his own invention. (Think this isn’t hard? You try writing one unforgettable tune that has to fit contrapuntally with another.)
I’ll never forget my first encounter with non-imitative counterpoint. (How could I, it being one of my signal musical experiences.) One day the director of our grade school chorus was teaching us a pretty little song called “Inch Worm.” (As a third grader at the time, I didn’t know, and couldn’t have cared less, that the song was written by the great Frank [Guys and Dolls] Loesser for the movie musical Hans Christian Andersen.) The key moment came when our director divided the chorus in half, and taught the half I was in the song’s haunting countermelody (with its chromatic touches of minor), which you hear first, sung by the class of children, in the clip: “Two and two are four…” etc.. The sinuous combination of this melody with the main (“Inch worm…”) melody (sung by Danny Kaye in the clip) still gives me the good kind of chills.
It was only many years later that I realized Loesser’s full brilliance in contriving this countermelody. The song is in 3/4 (i.e., waltz tempo), into which the main, “Inch worm, inch worm…” text fits perfectly. But the text of the counterline doesn’t fit into 3/4, at least not comfortably. The 3/4 meter leads to unnatural stresses in the line (“Two and two ARE four __ , four and four ARE eight __ , eight and eight ARE sixteen, sixteen and sixTEEN are thirty two…”). But the counterline works perfectly in 2/4 (alternating stressed with unstressed syllables: TWO and TWO are FOUR __ , FOUR and FOUR are EIGHT__ , EIGHT and EIGHT are SIXteen, SIXteen and SIXteen are THIRTY-two…) Which is to say that what we have in this seemingly innocent ditty is an example not merely of polyphony, but of polymetric polyphony. But here’s the kicker: what is the text of the (2/4) counterline talking about, if not measuring by multiples of two! The transcendent musico-verbal wit of this connection reduces one to saying of Mr. Loesser, as a certain Mr. Schumann said in announcing his first acquaintance with the music of a certain Mr. Chopin, “Hats off, gentlemen: a genius.” (As if we didn’t know this about Loesser already.)