Our life . . . is but the concurrence, renewed from moment to moment, of forces parting sooner or later on their ways.
We exist by tarrying together. A special significance flashes out in one dragonfly tailing another, one biker keeping up with another, two clouds scudding beside each other: this tarrying happens just for a while, we realize as we watch, and it sticks out to us as a model of the temporary loyalty that makes each piece of our reality.
The musical term for tarrying together is harmony, from Greek harmos for joint or shoulder, one of the Indo-European ar– words meaning to fit together in some way. Remember the word “shoulder.”
For music theorists, harmony is an orchestration of resonance, a selection made from all the possible tone relations to define a certain world “vertically,” that is, at one time. To harmonize a melody is to put a flavoring on it, sweet or sour, and to give it a more specified, more interesting and serious path to move along—a decorum. Thus harmony is both the immediate richness of a musical declamation and its full address in a complex world of actual and possible changes.
That’s harmony in a formal perspective. But it can also be an utterly contingent and individual event of companioning voices, a rendezvous (be it tryst or fight), and a preeminent hook—as when John Lennon joins Paul McCartney in an eventful harmony vocal on the third and fourth verses of The Beatles’ “Hey Jude.”
The ostensible theme of “Hey Jude” is Jude’s desire to start a relationship with a girl. “You have found her, now go and get her.” You can see a message about relationships in the text, of course, but the song’s really meaningful substance lies in its being sung, where there’s a a junction of the singer with Jude, hovering by Jude in solicitude, lending him strength by speaking of strength, companioning him. That’s the deep harmony that counts, the real personal happening.
And the harmony is enacted in the singing by John and Paul, whom we know. Their voices together make the sound of a benchmark friendship. John has come in with various touches earlier in the track but at the ripest moment, fourth time around, slips into harness and sings the whole verse.
He wraps around Paul’s notes with close intervals, giving the lines a gentle spring. Toward the end of the verse John and Paul’s partnership starts to fly apart backstage, as it were, in obscure ejaculations, possibly even expletives, around the 3:00 mark (there’s a debate about who says what). But right then the verse blossoms into Paul’s ecstatic shouting and four minutes of people’s-chorus coda, another of the great na na na nas.
And now for a bonus that comes with our deep harmony reading of “Hey Jude.” There’s a mysterious line in the song that Paul would have changed but the poetically more open-minded John made him keep: “The movement you need is on your shoulder.” A harmony, or a friendship, is an enabling hook-up and a fulcrum in power transmission, a harmos, a shoulder. Paul’s encouragement of Jude (originally “Jules,” John’s son Julian) is a shoulder; Paul’s implicit address of John is a shoulder; John’s hanging in with Paul (while he’s leaving Paul, in a sense, for Yoko Ono) is a shoulder. The song is a shoulder for all; indeed, no harmony keeps its resonance just to itself.
Postscript (1/2/11): In the instrumental division, I think one of the greatest harmony events is a mysterious added note underneath the primary melody note at around 1:41 and 1:52 in Santana’s “Samba Pa Ti” on Abraxas (1970).
It must have been dubbed in, because I can find no video evidence of Carlos Santana playing it in his lead, yet it sounds like he is contriving to do it live, arranging a beautiful meeting between his own ideas.
 Conclusion, “The Renaissance.”
 According to the American Heritage Dictionary.
 On the outbursts in the background see the Wikipedia entry on “Hey Jude.”
 On the lore of what went into the song, see William J. Dowlding, Beatlesongs (New York: Simon & Schuster, 1989), pp. 203-206. Compare how Paul comes in on harmony vocals in “The Ballad of John and Yoko” after John and Yoko were married.