78: Secondary Harmony

 Two articles ago, we looked at functional harmony; the idea that certain chords that aren’t necessarily the tonic or dominant can “act” as if they were, and that certain chords are “pre-dominant,” that is, they exist to come before—to “prepare” the dominant. Last time, we looked at tonicization specifically looking at a harmonization of Jakob Hintze’s “Salzburg” hymn tune (used in English-language hymnody most often with “At the Lamb’s High Feast We Sing”) by Bach, in his chorale BWV 262 “Alle Menschen müssen sterben.”


Today, we’re going to look at something very closely related to both of those concepts, so be sure to read the articles mentioned above—in order—before continuing on with this one. We’re going to look at secondary harmony. 


Go back to the Hintze score, and you’ll see, in clear-as-day D major, that, briefly, there is an E major chord. That, of course, doesn’t happen diatonically in D, since the ii chord is minor. E-G-B, of course, is different from E-G#-B. But because of where it occurs, it doesn’t feel out of place at all, and any reading of the rules will find no qualms with the fact that the chord appears when and where it does. 


It occurs in a phrase where we’re tonicizing A; the melody is F#-F#-B-A-A-G#-A. Anyone who saw that phrase in isolation would have no qualms putting an E major chord in to harmonize the G# since it fits with the melody note and is the dominant of the key right before the end of a phrase, that is, in a spot where a perfect authentic cadence would be (pardon the pun) perfect. We need a chord with dominant function, so we get one: E. End of story. 


Now, let’s go put that into the broader Hintze context. The whole chorale is in D, but I don’t see how anyone could reasonably dispute that this particular phrase (“praise we Him whose love divine”, etc.) is in A, and, that A is the dominant of D. Therefore, since we’re tonicizing A, we need its dominant to get involved at “praise we Him whose love divine”, and, given the relationship between D and A, and the relationship between A and E, thanks to a sort of transitivity, E major (briefly) fits in perfectly well in technically-written-as D major. 

It’s this very notion of transitivity that we need to discuss. This is the key to secondary harmony. “X is the [scale degree] of Y” is quite an easy relationship to understand, one that was probably established for the first time 60 articles ago, if not longer. We are not replacing that now, merely extending it recursively by applying the same rule, to get relationships like “dominant of the dominant” or “submediant of the supertonic” and so on.

It’s thanks to relationships like this, for instance, that you see and hear what may at first appear to be a “II” chord, but very rarely is, on paper, anyway, and it won’ be weird. (Much more often, what looks like a “major II” chord is in fact a “V/V” chord—the dominant chord of the dominant, as was the case with that E chord in the chorale in D.)


We write this relationship with a slash and read it is “[roman numeral] of [roman numeral]”—in words, “the five of five” or “the four of seven” and so on. 


There is one real stipulation with these chords: if you, for example, analyze something intending it to be “IV/ii,” then the next chord that follows this supposed subdominant-function chord had better be the ii chord, or one of two people (or perhaps both) has made a grave error: the analyst or the composer. If you can’t prove that the next chord after the “[X chord] of [Y chord]” is Y, then “X of Y” is not correct.


Quite often, you’ll see composers simply walk across the circle of fifths in one direction. When they do this, implicitly, they’re acknowledging another fundamental truth about this kind of relationships; the slash chains can be as long as one wants, as long as the previous rule about what the next chord is must be respected. 


For example, you could totally get to C from F# (keys which are literally as far apart from one another as possible) by

F# (V/V/V/V/V/V)

B (V/V/V/V/V)

E (V/V/V/V)

A (V/V/V)

D (V/V)

G (V)

C (I)


As long as you don’t skips steps, such a walk around the circle is perfectly legal. Would you ever see a chain of “dominant of the dominant of the dominant of the dominant of the dominant of the dominant” unwinding itself in the real world in the Baroque era? Almost certainly not. But, entirely within the rules, could you, and, by the time we start encountering especially masters of the piano like Chopin and Debussy, would you be quite likely to, actually? Yes!


Knowing how to use these chains of secondary harmony can really broaden your harmonic horizons and allow you to explore new colors you would never have otherwise been able to reach. 



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