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Looking at a chord towards the end of the development in measure 169, beat 2, spelled C♯-E-A♭ over the G pedal.

enter image description here

How would you analyze this in the context of the harmonic progression at that point?

The best I can come up with is that the C♯/E is a non-harmonic tone leading up to D-F-A♭, a diminished chord with subdominant function. So the core of the progression is then V-ii(dim)-♭VI-V.

What I'm wondering about is whether the C♯/E/A♭ has a function of its own in the progression. I might call it a ♭ii(dim) but that doesn't quite feel right.

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Can you provide an excerpt of that section with a measure before and after this? – Dom Feb 13 at 14:18
    
Relevant section is at the 6 minute point in this video: youtube.com/watch?v=zh6O5vwouXY (the progression gets repeated quite a few times, so there's little chance of missing it) – Caleb Hines Feb 13 at 14:27
up vote 4 down vote accepted

The whole passage is essentially a linear elaboration of V♭9. Let's "de-broken-chord" it: it fairly leaps to the eye what Beethoven is doing here when you see the voices.

enter image description here

Note that we're getting a big A♭-G appoggiatura in the top voice, but the inner voices are marching up and down in minor thirds between the chord tones of the dominant (marked "+") in such a way as to sort of tonally center on G: passing tones E/C♯ to suggest an approach from the dominant's dominant, E♭/C to suggest the tonic minor.

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The best way to look at it is as you stated as the C♯ and E as non harmonic tones leading to the D and the F respectively. It could be looked at as a variation of a Neapolitan 6th where the 3rd is minor instead of major that goes to the iio instead of V especially since if you look at it as different enharmonic equivalents of D♭, F♭, and A♭ which make D♭m. While this is a possibility keeping the C♯ and E as non-harmonic tones that lead to iio makes more sense, but you can see where the idea for this harmony comes from.

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