There is a bit of folklore out there (hopefully apocryphal) about a disagreement between two college-level Music Theory teachers that turned into a fist fight. No, no one insulted anyone’s wife or ancestral homeland. The stakes were way higher than that: it was about what’s the correct way to notate the Cadential 6/4 chord. One adamantly believed it should be notated as I 6/4 (obviously with the 6 vertically stacked above the 4) and the other insisted it should be V 6/4.
Who Was Right?
I know better than to go near that question, but let’s take a look at what this chord is and why it’s controversial. It’s the chord that often precedes the final Dominant leading up to a full cadence in Common Practice harmony. The bass is the Dominant, effectively a common tone with the V chord that follows, and the other tones are those of a tonic triad. So, presented with no context it looks like this:
I was always taught that it’s a I6/4, simply because this arrangement of notes taken out of context is a I chord in the second inversion. But this chord really has more going on than that than that, and in context it is not a tonic chord and should not have a I on it. The upper voices — the “6” and “4” — each resolve down to “5” and “3”, respectively, resulting in a nice, root position V chord. In other words, this chord can’t be taken out of context. It is part of a process of moving toward the cadence.
Some harmony books teach us to call this V 6/4 instead of I 6/4. I certainly understand the temptation to use V here, and in terms of understanding what’s going on here functionally, it is definitely closer to expressing it than I6/4. This value of this notation is that it forces the student to pay attention to the role voice leading plays in the process, and that indeed the Cadential 6/4 and the V are both part of one thing. It also highlights the fact that this chord is more precisely analyzed as an unstable V chord where two of the upper voices are accented non-chord tones on their way to resolution.
But here’s the problem. In our Roman Numeral notation for harmonic function, the Roman Numeral corresponds to the root of the given chord. So, even if the function here smells more like V, it’s best not to use that here, if for no other reason than to avoid confusion.
Roman Numeral notation is already confusing. When we use those little vertically stacked numbers with Roman Numerals to describe inversions (and melodic structures like passing tones or suspensions), we’re borrowing notation from Figured Bass, which is an entirely different discipline. A good way to think about it is that Roman Numerals describe theory and Figured Bass informs practice. In both cases, the numbers refer to intervals measured against the bass. A Roman Numeral alone tells you nothing more than what the root is, and added figured bass numbers tell you something about the upper voices. One has to extrapolate from that whether it’s an inversion. Figured Bass tells you only what the upper voices should be doing relative to the bass, and nothing about the function.
Using V for the Cadential 6/4 conflates the meaning of the Roman Numeral with Figured Bass. It correctly describes the function and treats the chord as an unstable V chord with accented non-chord tones, but the use of the “6/4” here is not consistent with Roman Numeral notation. This is very confusing to students, because they’re taught to expect a V chord in the second inversion if they see V6/4, and that is not what this is. To depart from the “usual” meaning just for the Cadential 6/4 scenario is a pedagogically terrible idea.
Part of our job as Music Theory teachers has to be not confusing our students. If we’re teaching them that the Roman Numeral corresponds to the root of the given chord, we need to be consistent. So, sadly, while I do prefer the V6/4–5/3 notation for its attempt to illuminate the voice leading and the unstable nature of the 6/4, I can’t accept it as a useful notation for students.
So, Who Was Right?
The mistake both of these guys were making was to believe that either of them had the right answer, which means the whole Music Theory world is without a good answer, or at least I’m not aware of any other mainstream way to do it.
I’m not 100% on board with I6/4 either, even though that’s what I was taught as a student. Putting a Roman Numeral I on it should imply that it’s a tonic chord (and I’ve seen it referred to as the “cadential tonic 6/4”, which I really don’t buy). It is categorically not a tonic chord. If anything, it is an unstable dominant chord.
I propose that we just call it “Cadential 6/4” and use only the Roman Numeral V grouping the Figured Bass numbers above it with a bracket. The two chords, after all, are functionally the same and should only be treated with one Roman Numeral.
I am not an academic and may be unaware of everything that exists out there that addresses this problem. I would love to know what others think. Please comment nicely.