Around the start of the seventeenth century, a new sense of the word “harmony” emerged. To that point, harmony in music had been produced by the pleasing opposition of two melodies according to the principles of counterpoint. In the 1600s, “harmony” began to denote the non-melodic accompaniment to a line of melody. This sense remains colloquial today. If I say, “Here is a melody, let’s add some harmony,” I mean that there is a tune and it is getting some additional, subordinate music to accompany it. It is basically synonymous with chords. We would describe Taylor Swift as the melody, and her back-up band—its guitars and piano and bass—as the harmony.
But what is “harmony” in the older sense of the word, captured particularly in Bach’s counterpoint? Counterpoint is the accumulation of multiple melodies. It is like Louis Armstrong playing an improvised tune on his trumpet at the same time as Ella Fitzgerald sings “La Vie en Rose”—two different melodies simultaneously. Neither is subordinate to the other, or, if there is subordination (perhaps we listen a little more to Ella’s voice than the trumpet), they are both melodies, a status that the piano, plunking out chords in the background, does not share. In true counterpoint, all the sound created is produced by people singing or playing melodies. If we lived several hundred years ago, we would say that “harmony” is what joins and holds together those melodies, their counterpoint, in a pleasing fashion.