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How does one analyse the progression in bar 81 of this Mozart piano sonata?

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This is a tricky one since there are only two voices. Ultimately, we as analysts have to determine what pitches are implied to create these chords. The intuition needed to figure out these missing pitches just comes from a lot of experience with tonal music and learning what the common patterns are.

As it turns out, this is an example of what we call the lament bass progression, where the bass moves down by semitone to help create a set of chromatic harmonies.

enter image description here

Some comments:

  • The fourth eighth note of m. 81 is what we call an applied, or secondary, dominant. If we imagine we're briefly in the key of IV (E♭), we have a V42 of that E♭ that then leads to an E♭ chord (IV) in first inversion.
  • The It+6 could be either a French or German; I just put Italian for simplicity. In any event, it's definitely intended to be an augmented-sixth chord.
  • The final two chords might be the trickiest. Ultimately, the music ends on IV (E♭), but it gets there in a roundabout way. One way we can understand these last two chords is by saying that they both temporarily occur in the relative minor of G minor. As such, these last two chords create a simple V–VI deceptive progression in that key. Note that I'm not suggesting it modulates to Gm; the subsequent music clearly stays in B♭. But we can understood this pattern as V–VI in Gm that basically serves as a chromatic way to get to E♭, which is the IV of the overall B♭.
  • How are you calling that last chord a VI with an E-flat in the bass? – MarkM Dec 20 '18 at 17:20
  • Because it's understood as being in the relative key of G minor, and E♭ is VI of G minor. – Richard Dec 20 '18 at 17:21
  • Oh, I see what you did -- missed that you switched to g minor for the roman numerals. I can see how you came up with that. Sure doesn't sound like g minor to my ear — just sounds like passing tones leading to IV. – MarkM Dec 20 '18 at 17:23
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    Yes, that's the edit I'm making now, having seen the subsequent music in my own score. – Richard Dec 20 '18 at 17:23
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    Isn't this overcomplicated? In the second bar, does it make sense to think of every note as a different chord, instead of "chromatic stuff in Bb"? Those last to bars feel very much like V I. – coconochao Dec 20 '18 at 18:23
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This is my take on it...

enter image description here

...basically I consider those chromatically inflected contrary lines to be embellishment of the tonic chord then it does a converging cadence. Why consider it to be embellishment? The basic harmonic rhythm is around 1 or 2 chords per measure. Treating m. 81 as a single I chord fits the basic harmonic rhythm nicely. Also, I thought it was important to continue with the measure after m.81 to show the cadence. The E chord functions as a subdominant beginning the final cadence of the movement. The simplest way to get from m.81 to an E chord is just I|IV... (The little numbers with carets above them are the scale degree numbers.)

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This is the end of the last movement of k.570. In the context of the piece I would analyze this in the key of B-flat, but the excerpt here, out of context, looks like a cadential formula in E-flat.

In E-flat the first measure is basically a dominant of V. You might say

M1: vii dim7/V - V/V (65)
M2: V
M3: I

Of course in B-flat, this all gets transposed to be a cadential formula landing on IV, which in the piece quickly moves to V and then finishes.

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