Ross writes,

Early in “The Fellowship of the Ring,” the first film in Peter Jackson’s monumental “Lord of the Rings” trilogy, the wizard Gandalf finds himself alone in a room with the trinket that could end the world. It lies gleaming on the floor, and Gandalf regards it with an attitude of fascinated fear. The audience feels a chill that neither Jackson’s vertiginous camera angles nor Ian McKellen’s arching eyebrows can fully explain. The Ring of Power extends its grip through the medium of music, which is the work of the gifted film composer Howard Shore. In the preceding scenes, an overview of the habits of hobbits, Shore’s music had an English-pastoral, dance-around-the-Maypole air, but when the ring begins to do its work a Wagnerian tinge creeps in—fittingly, since “The Lord of the Rings” dwells in the shadow of Wagner’s even more monumental “Ring of the Nibelung.” J. R. R. Tolkien’s fans have long maintained a certain conspiracy of silence concerning Wagner, but there is no point in denying his influence, not when characters deliver lines like “Ride to ruin and the world’s ending!”—Brünnhilde condensed to seven words.

Shore manages the admirable feat of summoning up a Wagnerian atmosphere without copying the original. He knows the science of harmonic dread. First, he lets loose an army of minor triads, or three-note chords in the minor mode. They immediately cast a shadow over the major-key music of the happy hobbits. (A digression for those who skipped grade-school music class or never had one: Why does the minor chord make the heart hang heavy? First, you have to understand why the major triad, its fair-haired companion, sounds “bright.” It is based on the spectrum of notes that arise naturally from a vibrating string. If you pluck a C and then divide the string in half, in thirds, in fourths, and so on, you will hear one by one the clean notes that spell C major. Wagner’s “Ring” begins with a demonstration: from one deep note, wave upon wave of majestic harmony flows. The C-minor triad, however, has a more obscure connection to “natural” sound. The middle note comes from much higher in the overtone series. It sets up grim vibrations in the mind.)

The minor triad would not in itself be enough to suggest something as richly sinister as the Ring of Power. Here Wagner comes in handy. He famously abandoned the neat structures of classical harmony for brooding, meandering strings of chords. In the “Ring,” special importance attaches to the pairing of two minor triads separated by four half-steps—say, E minor and C minor. Conventional musical grammar says that these chords should keep their distance, but they make an eerie couple, having one note (G) in common. Wagner uses them to represent, among other things, the Tarnhelm, the ring’s companion device, which allows its user to assume any form. Tolkien’s ring, likewise, makes its bearer disappear, and Shore leans on those same spooky chords to suggest the shape-shifting process.

In “The Return of the King,” which opens this week, Shore’s music keeps pace with the burgeoning grandeur of the filmmaking. When the hobbits escape Mt. Doom, Renée Fleming sings, in Elvish. As the evil lord Sauron comes to grief, the dusky harmonies of the ring give way to their mirror image in the major key. There is an abrupt harmonic shift that has the effect of sun breaking through clouds. You would have thought that sometime between the birth of Stravinsky and the publication of “Alexander’s Ragtime Band” such echt-Wagnerian material would have gone out of fashion, but there is life in the fat lady yet.

OK. First of all, although Ross’ assertions are correct on a harmonic level, he is dead wrong about why Howard Shore’s score to LoTR is a descendant of Wagner’s operas.

On this point, Ross is right: the major third is lower down in the harmonic series of a vibrating string than is the minor third. Hence, it may be described as more “natural” sounding if you’d like. But to argue from that base that “natural” equals “happy” and “unnatural” leads to “grim vibrations in the mind” is so much handwaving. Music theory is as much a cultural construction as it is a matter of science. That’s the problem that the Greeks ran into, as well as the problem that Bach papered over with his “Well-Tempered Clavier.”

What that means is, although acoutistics and the properties of vibrating bodies are a matter of physics, how the ear interprets them is a matter of conditioning, context, and prior preparation more than anything else. Don’t believe me? Then you tell ME how “Boot Scootin’ Boogie” is as much a party song as Balinese gamelan music. What music-theoretical parallels can be drawn between the two to isolate the “happy sound”?

Within the boundaries I’ve just established, it’s perfectly OK to say that major is a happy sound. In European society, it surely is. And it’s even possible to theorize that it’s so because major keys resolve so neatly.

Why is this? Because the half-steps in the major scale come between the 3rd and 4th degrees and the 7th and 8th (or 1st) degrees of the scale. In the key of C, that would be between E and F, and between B and C. Because of other aspects of theory which I won’t bore you with, this means that these half-steps fall in harmonically crucial places. 

In conventional music theory, a “V-7” chord, or “dominant 7th” in the key of C is spelled G-B-D-F (a G major chord plus an F on top). Theory dictactes that, in the key of C, a G chord likes to resolve back to a C chord (C-E-G). With the addition of the F on top, that tendency becomes far more pronounced.

Why? Two reasons. First, the minor third (D-F) placed on top of the nice-sounding G triad pollutes the harmony. A string vibrating G will generally contain prominent overtones of B and D. Any guitarist can tell you this. So this triad is part of what occurs naturally (and audibly) in any vibrating body. But adding the F on top sets up a series of conflicts that add dissonance to the mix. Dissonance, to Western ears, likes to resolve to consonance.

Second, the chord G-B-D-F contains a “tritone,” or two notes separated by four whole steps. In music theory, the tritone is a black sheep, neither consonant nor particularly dissonant, and it is the only interval that does not naturally occur in the interaction of the root of a given major scale with the other elements of that scale. (That is, all the possible intervals between two notes, except the tritone, occur in the following two-note combinations: C-D C-E C-F C-G C-A C-B.)

Look at those notes F and B. Earlier I mentioned that the pairs E-F and B-C were special. Guess where this tritone of F and B contained in the G-B-D-F chord likes to resolve to? That’s right-- E and C. E and C are two notes in a C chord (C-E-G). Thus, adding F to the triad G-B-D sets up a harmonic situation that tends very strongly to resolve to C-E-G, a nice, square, clean C major chord.

Since our ears are trained from birth with fundamentally simple songs that rely on this very harmonic device, such a tension-release series is very satisfying to us. Hence major keys produce harmonically balanced sounds that could be considered ‘happy.’ I’m not claiming that these theoretical reasons are the only reasons why major keys sound so happy, but it’s a major part.

Minor keys, on the other hand, are a different story. The minor second intervals fall between the 2nd and 3rd degrees of the scale, and the 5th and 6th. In C minor, that would be between D and E-flat and G and A-flat. That means that the tritone in the scale exists not between F and B, which tends to resolve strongly to the home chord of the key, but between D and A-flat. The tendency is thus for the key to resolve to E-flat major (why? just bear with me). Therefore, minor keys are constantly fighting their own tendency to go elsewhere, and only frank harmonic trickery and exception-making causes minor-chord pieces to work out harmonically.

Since our ears, as I’ve asserted, are trained to hear the square, mathematically neat resolutions of major keys as deeply satisfying, minor keys sound by comparison unsettled and dissonant. The same goes to a certain degree with modal harmonies which are beyond the boundaries of this particular bit of wonkery.

So. All this crap is to say that Alex Ross is engaging in a lot of post-Romantic handwaving when he talks about “dark vibrations in the mind” (he is a Wagner fan, after all!) Tibetan throat singing sets up dark vibrations in my wife’s mind, and that’s neither major nor minor. The real feat is that, using the simplest of musical tools available in the Western tradition,Howard Shore’s score advances the state of the art of “Mickey Mousing” (that is, keying musical cues to onscreen action) for almost the first time since John Williams did “Jaws” and “Star Wars: A New Hope,” and comes close to the heft, grandeur, and complexity of Wagner’s most demanding moments. Theme is heaped upon theme, harmonic relations are handled with a loose and masterful hand, and the tension-release cycle is closely keyed to the action we are seeing on the screen. In this regard more than anything else, Howard Shore has come very close to the spirit of Wagner’s writing, as a thousand shitty books will tell you at great length.  Regardless of whether Tolkien disavowed his Wagnerian inspiration or not, Howard Shore has brought the spirit of Wagner’s operatic scoring to the big screen in high style.