Diminished seventh cadence, is this an IAC or a PAC?

Question

I have seen a few cadences where the only dominant function chord used cadentially is a diminished seventh, mainly resolving to root position tonic, though I have seen a few resolve to an inverted tonic. So I might see a cadence like this:

iv vii°65 i

Most commonly, I see this vii°7 I cadence occuring in minor keys, thus the minor key roman numerals in the quote above. That's not to say that I don't see diminished sevenths in cadences in major keys, but usually in a major key, it is extending an already present dominant function, not acting as a dominant substitute, like it often does in minor keys. So whether or not the cadence is a PAC (Perfect Auhentic Cadence) when there is not only the dominant but also the diminished seventh is determined by the V I motion when the diminished seventh is taken out of the cadential equation.

Now I know that if it resolves to an inverted tonic and that inverted tonic feels like a point of rest, the cadence is automatically an IAC (Imperfect Authentic Cadence), because a PAC requires the root to be in the bass.

According to most sources, this is what defines a PAC:

1. The cadence goes from V to I or V7 to I
2. Both chords are in root position
3. Highest note of the tonic chord is also the root

And generally speaking I see IAC being defined as any V I cadence that either has the tonic inverted or the tonic is in root position but the highest note is the third or fifth. I don't really see the possibility of a vii°7 I cadence mentioned much, let alone how it fits into the PAC IAC split. And I have seen vii°7 I cadences that check all criteria for a PAC except V I motion, which makes me wonder, are all vii°7 I cadences IACs, no matter how close it is to a PAC?

My gut instinct tells me that a vii°7 I cadence would be considered to be an IAC regardless. But on the other hand, I have seen some vii°7 I cadences that are so close to being a PAC that if the dominant seventh was put in place of the diminished seventh, it would no doubt be a PAC. Those cadences make me question the vii°7 I cadence = IAC that is in my gut instinct.

So, are there any cases where a vii°7 I cadence is considered to be a PAC? Or is a vii°7 I cadence always considered to be an IAC, no matter how close it gets to filling the criteria for a PAC?

Answer 1

It’s an IAC simply because the dominant function chord isn’t V. The PAC is the most strictly defined cadence, and I agree with the definition you’ve quoted. It explicitly defines a PAC as being from V to I.

It’s pretty common to define at least three different flavors of IAC:

• root-position IAC. The first two conditions of your definition are met, but the soprano voice ends on the third or fifth scale degree rather than the tonic. This is the strongest of the IACs.
• inverted IAC. The first condition of your definition is met, but one or both of the chords is inverted. How the soprano voice behaves is not generally significant to this definition.
• leading-tone IAC. The first condition in your definition is violated, which is to say that the dominant function chord is not V (and thus is very likely to be vii°). The definition doesn’t care about whether the chords are inverted or what the soprano voice does. In the common-practice era, this was considered to be the weakest possible IAC.

Obviously, there’s all kinds of nuance that these basic definitions don’t cover, and it’s certainly possible to write a relatively weak PAC or a relatively strong leading-tone IAC. They’re just the defaults.

Answer 2

It really just depends on your definition. The history of the term perfect cadence is that it originally required the so-called clausula vera, whereby a sixth interval between two voices moves outward to an octave. (The sixth was also generally preceded by a suspension.) In some older sense, your proposed cadence might be considered a "perfect cadence," though modern textbooks wouldn't tend to call it thus.

Meanwhile, the term authentic cadence tends to refer to the descending fifth root progression motion apparent in the harmonic progression V-I. It is most frequently seen in root position for both chords, thus having a 5-1 bass leap.

A perfect authentic cadence should thus have both characteristics -- the clausula vera and the descending fifth progression. However, at some point in the 1800s around the time when PAC became a common term, the clausula vera was deemphasized, and our only remnant of it is the requirement that the top voice generally moves stepwise to tonic in a PAC.

Anyhow, that's the history of why modern textbooks don't generally refer to a vii^o-I as a PAC, though cadential nomenclature over the centuries often varied a lot from source to source. The term authentic comes directly from the sense of a falling fifth (as at the bottom of the octave species that authentic modes had, in contrast to plagal). As a vii^o-I cadence lacks a falling fifth both in the bass and in the root motion, it makes little sense to think of it as an authentic cadence.

On the other hand, if we treat the vii^o chord as an incomplete V⁷ or V⁹ chord, then there is an analogy to be made with the concept of an authentic cadence. Effectively, following Rameau, we treat the vii^o chord as having a "missing root," and imagine the 5-1 root motion is still implied, if not literally in the music.

Hence, I suppose this is the source of the terminology in some modern textbooks adding this progression to the list of possible Imperfect Authentic Cadences. By historical definitions, it would make more sense to call it a perfect inauthentic cadence (as long as it contained the traditional clausula vera motion), but that would likely just confuse everyone. Consistency in nomenclature isn't always the priority in music theory.

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But then one also needs to consider the reason for this distinction in the first place. What exactly are we trying to label? In renaissance music, a vii^o-I motion could potentially occur to create something that was viewed as a "cadence" by theorists at the time. In late baroque and classical periods, such a progression would likely not have been thought of as a "cadence" most of the time at all. Their versions of "imperfect" V-I cadences would almost always still involve root position motion, merely with a change in soprano voice. Occasionally, inverted chords might function in places where a "cadence" was necessary at the end of a significant phrase, but they were uncommon. (In most cases involving inversions in the baroque and classical period, these motions are often better thought of as evaded cadences, rather than true cadences.) But then in the romantic period the inversions came to be more commonly used in cadential points in phrases, and sometimes even the vii^o-I motion.

So, to ask whether one should consider the vii^o-I as within the group of "authentic cadences" is more a question of: "What music are you analyzing? How did composers of that time/style/genre view cadences? Would they have considered the particular chord progression you're analyzing in that particular piece a 'cadence' or not?" It's fine to have theoretical arguments about what to include or exclude, but such arguments are generally only informative if they revolve around particular musical practice.

In any case, except if one is analyzing music written prior to the year 1500, it's doubtful to see cases where a vii^o-I cadence would be viewed as having the same strength as a root position V-I cadence. Hence, in modern terms, it may make sense to call it an IAC, but it really doesn't have the same force as a PAC, based on the harmonic patterns that have dominated western culture for the past 500 years or so.

Similarly, if one is just discussing compositional theory today, what exactly are you trying to group and why? To my ear, the different flavors of "imperfect authentic cadence" according to modern textbooks already have grossly varying strength. A V6/4-I motion likely won't sound cadential at all, while a V6/5-I or a V4/2-I6 will at least have the strength of a tendency tone resolution in the bass. By that standard, a vii^o-I might be "stronger" in a feeling of resolution than a V6/4-I, so why should the latter be "cadence" but not the former? To me, it's less about theoretical consistency than it is about what precisely you're trying to identify in your distinctions. Personally, I'd consider a root position V7-I with scale degree 3 in the soprano to be a "stronger" cadence than a vii^o-I in almost all situations. If the former isn't a PAC, why should we consider a vii^o-I to be a PAC? Now, you add the seventh to the vii^o. That perhaps makes the sense of resolution stronger, but now you're comparing two different "imperfections" -- is bass motion more important or soprano motion? Why?

Welcome to the arbitrary divisions of music theory. If you want to move beyond arbitrary textbook definitions, you get to decide your own priorities.

Answer 3

Yes, vii°7-I is as functionally close to V7(♭9)-I as makes no difference. It deserves to be classed as what I've always known as a Perfect Cadence, but I see is now sometimes labelled an Authentic Cadence.

But if you're going to define different flavours of Authentic Cadence, and if the definition of a Perfect Authentic Cadence is one with 5-1 in the bass and 7-8 on top, then vii°7-I isn't one!

Answer 4

The vii° -> I cadence is at best an IAC because the roots are not 5 -> 1.