Rootless chords in Beethoven sonata?

Question

Okay, I came across a bit of a wrinkle in the paper as I analyzed the third movement of Beethoven's Sonata Pathetique. It has to do with this passage in the C section(which is in Ab major):

For those of you wanting bar numbers, those are bars 92-94 of the third movement

The previous passage which had suspensions was very easy for me to analyze. Here is how I analyzed that passage:

Again, for those wanting bar numbers, those are bars 88-90 of the third movement.

Now, it looks as though those harmonies are repeated in bars 92-94. Problem is, in bars 92-94, I see no roots except for the first harmony which is Ab major. This leads to a bit of a paradox. It looks like the harmonies are repeated, but there are no roots which means that it can't be the same harmonies, because there is no such thing as a chord without a root.

Okay, so what if I do analyze it differently? Here is what I get:

As you can see, the first 2 chords are conventional. But then there is a progression from the minor dominant of the mediant to the mediant. Now that is weird, even for Beethoven. I have seen the minor dominant being used a few times in the sonata, but that's just it, the minor dominant of the tonic, not the minor dominant of the mediant. I have even seen Beethoven use this minor dominant when he is in a major key. But it is still unusual to have the minor dominant of the mediant appear right after the subdominant of the tonic.

That is, if I analyze it differently to avoid the root paradox. What if I don't do that and I take it head on? Here is what it would be analyzed as if I took the root paradox head on:

Now that looks just like the previous suspension passage. But I don't see a Bb to confirm ii, an Eb to confirm V, or worse yet, an Ab to confirm I in the last harmony. The Bb, Eb, and Ab are the roots of their respective harmonies and not having the root leads to the paradox of looking like the same harmony, but impossible to be the same harmony.

So how should I analyze this passage? Should I take the root paradox head on and just ignore the missing root notes? Or should I go with the unconventional v/iii to iii motion? Or should I do neither? If neither, what should I do? Beethoven is really confusing me here.

Answer 1

These two passages are exactly the same harmony, but with different displacements in RH and LH rhythms. Perhaps a triad does not exist without a root, but a chord can have no "root."

This is the problem with analysis. I am pretty confident that Beethoven wasn't sitting around deciding what the chord progression was going to be. Instead, he got clever and said "hey, I know how I can use the exact same notes but switch up the octave and change the beat which they come on and it will sound really cool and different!"

There is a lot more interesting stuff going on in here, like how the RH and upper LH notes are echoing octaves. Just because they are moving in contrary motion doesn't make it conventional. (It is also interesting where the notes in the RH are doubled, since leaving it undoubled would draw the ear to a parallel movement.)

In analysis, one is trying to wedge a piece of art into a system. That's not how art works. Instead of trying to label it, I would just describe what he does and leave it at that.

Answer 2

I-IV-viii-iii... This is just your run-of-the-mill circle-of-fifths progression, with a bit of extra suspension, and missing the fifths of the chords.