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Holiday Harmony Assignment

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In tonal music (at least until Debussy) there are basically two kinds of harmony: dominant harmony, and everything else. Dominant harmony is what we develop a feeling for when we consider harmonic motion: dominant progresses to tonic, V goes to I. The most obvious strong harmonic progression is dominant-to-tonic at the end of a phrase, and the strongest version of this is called “perfect authentic cadence.” Theorists cherish this as a PAC rather than as a Political Action Committee.

We hear the “most perfect” form of this in root position, with the leading tone (LT, or ^7) in the upper voice, rising to the tonic degree. Almost as “perfect,” the ^2-^1 in the upper voice places the leading-tone in an inner voice. Imperfect authentic cadences still resolve dominant-to-tonic, but can include inversions (not in root position), e.g. V6-I, with the leading-tone in the bass.

In the half cadence, the phrase ends on V, however approached. But the strongest form of a half cadence precedes the dominant with its own dominant, called V of V. (Some books abbreviate this to V/V.) If you imagine, for instance, in the key of C, a phrase ending on a G major chord and preceded by a D major chord, that relationship is just like V-I in G major, but because it’s a momentary thing and we’re still in C major, we say V of V going to V, using a secondary dominant. That means using a chromatic tone — a tone from outside the seven degrees of the major scale. When you see an accidental sign in a short tonal piece, that is a signal that most likely a secondary dominant is being used.

Earlier on we saw some simple hymns like St. Anne and Ellers. Maybe now we can revisit St. Anne and put some roman numerals underneath — analyzing the root functions of the chords (upper-case roman numerals are major; lower-case, minor).

This harmonization treats the melody like a cantus firmus: one change of harmony per note of the melody. Bach would have done it that way in his chorale style, albeit with more counterpoint — melodic motion in the other parts, but still one syllable of text per change of harmony.

The harmony assists the melody in pointing to a tonal goal: a cadence on the dominant. Harmonic motion towards the dominant at the end of the phrase is one of the most frequent phenomena in all tonal music. Look for it in Sleepers, Wake or Ellers. In Sleepers, Wake it occurs at the end of the first phrase, which is repeated; in Ellers, it ends the second phrase, right in the middle of the hymn.

Having identified V of V, we may look at some other secondary dominants. The beloved Navy hymn, Melita, offers some nice illustrations. Composed by The Rev. John Bacchus Dykes (1823-1876), canon precentor at Durham Cathedral, it offers further evidence that such a high percentage of good hymns originated with the Anglicans. (As a former choirboy in the Episcopal Church, who once earned $.25 a service, I confirm that we had much of the best music and still do. It was a good thing that Mendelssohn made so many regular trips to England, adding materially to the Oratorio Society tradition.)

Melita is slightly longer than St. Anne — three longer phrases instead of two — and thus has an opportunity for a wider-ranging tonality. (I left out some root analyses just to save time and space.) Where St. Anne has one strong secondary function (the theory professors, remembering Schenker, speak of “tonicization” — I accept that term, but Piston told me that it was too wissenschaftlich for his taste), Melita shows secondary dominants of ii, iii, IV and V. You’ll notice that the third chord in bar 6 (“deep”) is really V of V, so “ocean,” properly speaking, ought to be called V of V of V; V of V and ii have the same root, D, and the functional relationship of the preceding dominant (root A) is the same for both. For the ear, it’s a slight surprise, and we might wonder whether this phrase, cadencing on E minor, is really still in C major — should we say there has been a drift into E minor instead, a modulation? (After all, “Its own appointed limits keep” is half of an entire phrase in E minor.) That’s possible; the question could be regarded as ambiguous, and the ambiguity remains apparent to the ear in the context of  the entire hymn; but it’s probably not important whether you decide one way or the other, unless you practice Musikwissenschaft..

Here’s another example of skillful and rich use of secondary dominants, from Schubert’s waltzes, which we have recently been talking about. (To save space we omit first 8 bars and slightly simplify the notation. Bars 9-12 are identical to bars 1-4.)

The secondary dominants include the seventh of the chord, like the G sharp in bar 15. The seventh of bar 17 (C sharp) is suspended into bar 18 and resolves to B; similarly, the B in the next bar; bars 17-20 are part of a sequence. Bar 21 is a diminished seventh chord, used as a dominant of C sharp. You’ll notice that in these scant 16 bars, Schubert uses every note of the chromatic scale, though with his well-expanded, harmonically rich tonality, he never leaves B major.

Don’t worry if the mixture of Roman and Arabic numerals is confusing right now; the Roman ones identify the roots of the chords, so look for those. (When we talk about melody, as in the second ¶ of this article, we refer to scale degrees, e.g. ^1 is the first scale degree, the tonic; ^5 is the dominant, and so forth.) And if you are interested in attempting an assignment during the holidays, take a look at Praetorius’s “Lo, how a rose e’er blooming,” and locate its two secondary dominants. In this beautiful carol dating from about 1608, the very beginning of the era of tonal harmony, the secondary dominants expand the tonality just as they reinforce it.

Mark DeVoto, musicologist and composer, is an expert on the music of Alban Berg, Debussy, and other early 20th-century composers. A graduate of Harvard College (1961) and Princeton (Ph.D., 1967), he has published on many music subjects, and edited the revised fourth (1978) and fifth (1987) editions of Harmony by his teacher Walter Piston.

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