What's going on in measures 11 - 16 of Beethoven's Sonata Appasionata?

Question

I'm studying the Neapolitan Chord and the textbook includes the following excerpt to analyze. Up until measure 10 I understand what's happening, but I have no clue how to interpret measure 11 and onwards.

What I have so far:

• Measure 1 to 4 is the Tonic (f minor) plus a short section with the Dominant, the dominant is slightly extended here with a second inversion vii° chord.
• The end of measure 5 initiates the bII chord, which is tonicized up to measure 8, where it ends on its Dominant. Measure 7 contains a short extension of bII's Dominant using a second inversion vii° chord.
• Measure 9 is the Dominant of the Tonic again, C major. It's extended for 2 measures.
• The above creates Tonic - PreDominant - Dominant (I-bII-V), an almost complete phrase

But then measure 11 comes in and I feel lost. I see the following chords: - diminished natural e7 - minor b flat - C major (in the next measure) And after that, there's a longer passage with diminished natural e7 before we reach the end with a first inversion Db followed by a first inversion C.

I have no idea what's going on there. The e and b flat minor don't really work together as a Tonic-Dominant, which was what I first tried. I've tried seeing this as follows:

• e natural as some sort of tonicization of C major. But this doesn't work because it would be a iii° 7th, which is not a harmony I've seen in a major scale so far.
• e natural as vii°7. This was my best shot but that would go back to f. There is no f chord anywhere in the rest of the excerpt. It also doesn't work with the b flat minor 7th chord.
• tonicization of e natural. Given how e natural is also used in measures 14 and 15, this seemed like a good option but I also can't make it work because of its diminished nature. Its 7th prevents me from thinking of it as a potential tonic. Plus the b flat chord doesn't work because a) it's flat and it would push towards e flat, not e natural, and b) it's minor and lacks the push of a major Dominant chord.
• Assumed that the e natural moving to F in measure 11 could simply be a chromatic accent, and in turn make this be a G major 7th chord. Basically a V/V for the tonic (f). But the chord would be g minor, not G Major and again it kinda loses its quality as Dominant for C Major.

I just don't know anymore and I've wasted a couple of hours on it. Feel free to school me on this!

Answer 1

This is a notoriously difficult sonata to analyze, but I recommend keeping two things in mind when considering mm. 11ff:

1. Most importantly, you're correct that m. 9 begins a dominant prolongation. In fact, check out the bass pitches in mm. 10, 12, and 13: the D♭ to C in the bass really continues that dominant prolongation, doesn't it? As does the C7 arpeggiation that starts in m. 14. In my ears, mm. 11 and 12 are just a part of this larger dominant prolongation. In fact, you could view the e°7 of m. 11 as an upper part of a C7♭9.

2. As for that odd B♭m7, note the sequential ascend that begins in m. 3, continues in m. 7, and returns in m. 11. In other words, this B♭m7 harmony is just as much a product of the sequential ascent as it is its own bona fide chord. Understood in this way, I think it's less important to label this chord, and instead to recognize it as a product of the pattern that Beethoven has set up. Even though it doesn't make perfect sense functionally, we know how that middle chord functioned in its earlier instances, and we imbue that middle chord with the same function when it returns. In other words, the B♭m7 just embellishes the more important e°7, which itself embellishes the more important C7.

Answer 2

We can always find interesting examples in Beethoven's works :)

At a high level, I consider the entire section of m.9-16 as a prolonged dominant section (Beethoven loves to extend V). In terms of Roman Numerals, it's like the following.

i - V - [I - V]/bII - D - VI6 - V6 - i

We could listen to m.10-13 and consider those e° or e°7 chords as extensions on the emphasized C (as Richard♦ mentioned). So they form a big long V7b9 chord. But they can also simply be explained as vii° and vii°7 of F minor. V or vii have the same function here so it's not really important how we interpret them.

Then the last part in m15-16 is a deceptive cadence and finally resolves to i.

The only question is what on earth is that B-flat chord in m10. You can think of it as a voice-leading pattern (as Richard♦ mentioned, it's well established). You can also view it as the SAME vii°7 chord, if you treat that B-flat as a neighbor tone in the baseline, and the F natural as a neighbor tone in the melody, and the F natural later as a passing tone. Then the entire m.11 (and until the bending of m.12) is simply a vii°65 chord with some non-chord tones.