[Smt-talk] "Neighboring" 6/4 Chords

[Olli Väisälä]

Dmitri wrote:

> I know Donna wasn't directly meaning to engage my ideas, but I just  
> wanted to clarify that I am motivated by a different view.  For me,  
> the notion of embellishment plays no obvious, first-order role in  
> explaining why certain 6/4 formations are used.
>
> Here's a simple way to understand the point:
>
> 	1. Ask yourself which root progressions X-Y-X are common in  
> ordinary tonal harmony, where Y is a fourth above X.
>
> 	2. Ask yourself which "neighboring 6/4 progressions" are common:  
> A5/3->B6/4->A5/3, where A and B share the same bass.
>
> The answer to question #1 is "I->IV->I and V->I->V".
>
> The answer to question #2 is "I->IV6/4->I and V->I6/4->V."
>
> I am struck by the similarity between the two answers, which I take  
> to imply that the explanation for these common "neighboring 6/4"  
> formations is harmonic rather than contrapuntal.  Roughly speaking:  
> these 6/4 formations are common because the underlying progressions  
> are themselves very common.  Certainly, it does not seem like the  
> contrapuntal "neighboring" (or "embellishing") role over-rides the  
> pre-existing harmonic constraints, otherwise we could expect  
> progressions like ii->V6/4->ii.  These are vanishingly rare in the  
> literature.

But what, exactly, do you mean by stating that the explanation is  
"harmonic rather than contrapuntal"? Certainly there are crucial  
contrapuntal constraints for the use of 6/4 chords, the essential  
reason for which is the dissonance of the fourth. Obviously we cannot  
just take any common harmonic progression and arbitrarily invert  
chords to 6/4s (like I–VI6/4–IV6/4–V–I6/4). The use of the fourth in  
6/4 chords is regulated by similar voice-leading principles than  
dissonances in general. In my view, the labels "neighboring" and  
"passing" are indispensible for describing these principles, both in  
scholarly discussion and elementary instruction.

It would be more plausible to state that we need both harmonic and  
contrapuntal principles for explaining the use of 6/4 chords. The  
dissonant fourth has to be treated according to the general norms of  
dissonance treatment, that is, as a passing or neighboring tone if it  
is in an unaccented position. However, as Dmitri points out, not all  
6/4 progressions permitted by this principle are common in practice,  
and it is plausible to propose that the explanation for this lies in  
harmonic relationships. Typically, the explanation of musical  
practices requires allowing for several complementary principles, and  
it is often meaningless to argue which is primary or "pre- 
existing" (which, of course, you did not mean in the historical  
sense). In the present case, however, I would suggest a simple  
thought experiment. Suppose we encountered an instance of the rarer  
neighboring-6/4 formations such as II–V6/4–II or VI–II6/4–VI (in  
major). While we might recognize its rarity, we would have no  
difficulty in grasping its syntactic organization. On the other hand,  
a formation such as I–VI6/4–IV6/4–V–I6/4 would sound simply  
incoherent or incorrect syntactically. For those who share these  
intuitions about syntactic coherence, there is some reason to  
emphasize the contrapuntal (dissonance treatment) factor in  
explaining the use of 6/4 chords.

Whether the commonness [is there such a word?] of I–IV6/4–I and V– 
I6/4–V and the rarity of II–V6/4–II etc. should be explained on the  
basis of harmonic relationships is another question. At least, other  
factors also seem to be involved. First of all, the tonic and the  
dominant are, in general, the most significant and most commonly  
embellished harmonies, which suffices to explain that I–IV6/4–I and V– 
I6/4–V, and the corresponding root-position progressions, occur more  
frequently than other similar neighboring progressions. Second, all  
these progressions involve at least one half-step neighboring motion,  
which makes voice leading more effective than in II–V6/4–II or II–V– 
II (which is only possible in major in the first place). Hence the  
"the similarity between the two answers" to Dmitri's questions by no  
means necessarily points to a purely harmonic explanation, but is  
partly explained by a common underlying factor (the general  
significance of I and V) and partly, it would seem, also by voice- 
leading preferences.

What is written above does not help much to explain the original  
question in this thread. Why does I–V6/4–I occur so rarely, even  
though the progression would seem correct in both harmonic and  
contrapuntal terms? The previous mails contain several valuable  
points, the multitude of which helps to remind us that for questions  
about compositional practice we should not expect to find simple  
explanations, based on a single factor alone, since successful  
compositional solutions usually combine several desirable features.  
For what it's worth, however, here is a summary of the factors that I  
find most crucial in this case: First, passing motion is a more  
effective and fundamental way of dissonance treatment than  
neighboring motion; therefore I–V6/4–I6 arises more readily than I– 
V6/4–I. Second, for a bass line ^1–^2–^1 there is a very effective  
harmonization in I–V4/3–I (or I–VII6–I) involving parallel tenths;  
hence no need to use a neighboring V6/4 easily arises. Third,  
neighboring chords involving only upper-voice motions are much less  
weighty in character than those involving the bass; therefore I–IV6/4– 
I arises more readily than I–V6/4–I.

Olli Väisälä
Sibelius Academy
ovaisala at siba.fi