Analysis of Pathetique Sonata, Is it accurate?

I have fully analyzed both the form and harmony of the Pathetique Sonata(yes, all three movements of it). Even though I didn't include this in my analysis for the sake of space, here is what I feel as the sonata progresses expressed in the form of a story:

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A person is in such bad pain that he doesn't want to move from his spot.(Start of the Grave) However, this threat comes upon him(Second part of the Grave(where it goes fortissimo)). The person eventually realizes he isn't safe and has to move despite the pain(virtuosic passages in the Grave) and engages the fight or flight response(First theme of exposition). He is outrunning the threat(Second and Third themes of the exposition) but it eventually catches up to him(Codetta) and he is out of energy(Grave section repeat). He gains back his energy and prepares once again for the fight or flight response(exposition repeat). Immediate threat is far away now, but the pain is even worse(Second Grave section). He knows however, that he can't stay for long, and so ignores his pain and starts running away from the threat(Development). The threat now knows this and takes a shortcut. By the time that he thinks he is safe, he actually is in grave danger(Recapitulation First Theme). For a short amount of time, he is safe(F minor section of Second Theme). But the threat catches up and it is life or death(C minor section of Second Theme). He once again runs out of energy and is in severe pain(Third and final Grave section). But he is so close to safety, that he runs to safety(Final Allegro of the Coda)

He is now safe and is recovering from his pain and regaining his energy(ABA of second movement). The threat tries to get him(C section of second movement) but the people guarding him successfully defend him as he recovers(A section again). His pain is gone eventually and he feels ready to defend himself(Coda of second movement)

The threat once again puts him in grave danger, but he is more prepared(Main theme). He stops the threat in its tracks(First episode) only for it to threaten him again(Main theme). This time he gets closer to defeating the threat(Second episode), but it is still threatening him(Main theme). Third time, he gets so close that he thinks he has finally defeated the threat(Third episode in C major). But that thought gets crushed(retransition to Main theme). So he goes to defeat it once more. But this time he is successful(Ab major in the Coda). However, he has suffered severe injuries(C minor ending of the Coda). Hopefully it doesn't happen again.

As you can probably tell, it is very dramatic. Most of Beethoven's C minor pieces are very dramatic. So much so, that C minor is sometimes called Beethoven's key. Anyway, there are a few things that struck me as odd. Here they are:

Tertiary Applied Chords

By this, I mean something like V7/IV/IV. There were a few chords in the sonata that I just could not seem to simplify to being secondary, so I had to notate it as tertiary.

Minor Dominant in a Major Key

Yeah, believe it or not, there are instances in this sonata where Beethoven is in a major key and uses the minor dominant. Usually in this case, the bass line is descending, which is a common place to see the minor dominant, but only in a minor key. The minor dominant being used in a major key just struck me as odd.

Ab Minor

Just the appearance of this key struck me as odd. Usually such a rare key as Ab minor is associated more with Jazz than Classical. I know how Beethoven is using this key. He is using it as the parallel minor. He seems to love his parallel key relations. But even taking this into consideration, it is still a key that startled me a little when it appeared, unlike say the C major - C minor parallel that Beethoven uses so frequently.

Here is my harmonic and formal analysis of the sonata. What do you think? Yes, I know, I didn't notate the inversions in the third movement, but besides that, what do you think? How accurate is it? Do I have too many modulations? Too few? Any other mistakes besides not showing the inversions for the third movement?

"Tertiary applied chords" are only useful if you have some sort of cyclic motion going on, and even then I don't think they're very useful. It's better to just call it a secondary dominant chain and call it a day. Sure knowing what the chords are is helpful, but when a chain's function is just to be a chain, it's better to call it what it is rather than try to force something it's not into them. When you use them in this analysis, they rarely have this function as it is, as they're more deceptively resolved normal applied chords. 
For this reason, I think you could stand to use more modulations in your piece. Recall the III as a very common modulation point in minor in this period, as opposed to being a prolongation of the tonic in some way.

43 minutes ago, Monarcheon said:

"Tertiary applied chords" are only useful if you have some sort of cyclic motion going on, and even then I don't think they're very useful. It's better to just call it a secondary dominant chain and call it a day. Sure knowing what the chords are is helpful, but when a chain's function is just to be a chain, it's better to call it what it is rather than try to force something it's not into them. When you use them in this analysis, they rarely have this function as it is, as they're more deceptively resolved normal applied chords. 
For this reason, I think you could stand to use more modulations in your piece. Recall the III as a very common modulation point in minor in this period, as opposed to being a prolongation of the tonic in some way.

 

Yeah, but the instances of Eb major in the Grave just don't sound convincing enough to me to be truly a modulation to Eb major as quite a few analysts suggest it is. I mean for one thing, the very first instance of it leads right to vii°7 of C minor. If I were to analyze it as being in Eb major, I would have to analyze that diminished seventh as vii°7/vi, which as far as I know, is not all that common, especially compared to vii°7 and vii°7/V. And while yes, it would get rid of the tertiary applied chords in the Grave, analyzing it as being in Eb major rather than C minor, the cadence to Eb major that is proposed by the Bb7 in the Grave, never actually happens until the exposition. And in most cases, a cadence to the new key is required to really make it sound like a modulation has happened. Here, Beethoven evades that cadence by going first to a D major chord(and here, it actually does sound like a cadence to D major) and then from there, going to C minor via a diminished seventh chord. The fact that Beethoven is evading a cadence in Eb is why I stayed conservative as far as keys and analyzed the entire Grave introduction as being in C minor.

Not a bad reading, but I'd encourage you to look further back and start your modulation there instead. A cadence in a new key does not necessarily mean it starts there, in fact it could have started quite a ways back, like the first E major cadence in the Moonlight Sonata.

2 minutes ago, Monarcheon said:

Not a bad reading, but I'd encourage you to look further back and start your modulation there instead. A cadence in a new key does not necessarily mean it starts there, in fact it could have started quite a ways back, like the first E major cadence in the Moonlight Sonata.

 

So, you're saying that in measure 4, that Bb bass under the virtuosic melody while it could be viewed as a non-chord tone in an F minor harmony(which is what I did in my analysis), it could also be viewed as being the point where it modulates to Eb, even though the would be chordal seventh is part of the virtuosic melody and isn't really there long enough to confirm the movement to Eb major in the next measure and thus doesn't sound strongly like a cadence to Eb? If that is the case, then the cadence to the D major chord that Beethoven does after the Bb7 chord could be viewed as another modulation, this time to D major. And the D major chord itself could be the pivot back to C minor before the Allegro starts, being the dominant of the dominant.

So in other words this as far as modulations in the Grave:

• Measures 1-4: C minor
• Measures 4-6 starting at the Bb bass: Eb major
• Measures 6-7 starting at the evaded cadence: D major
• Measures 7-10: Back to C minor to start the exposition

Sorry if it sounds like I'm trying to suggest a specific reading, I'm actually trying to do the opposite. When I say more modulations can be used, what I really mean is that there are so many options with all the diminished harmonies to be considered pivot chords than there's no need to try to keep it so rigidly in C minor.

For my personal quick look over the score, I would say the F minor in m. 4 is the pivot ii chord in E-flat major. That D major you're referencing, I definitely view more as a V/V in C minor, signaling that that chord or a chord just before it is the true pivot back to Cm. 

But like I said, don't trust me; you've definitely looked at it more closely than I, I'm just suggesting another way of looking at it.