5

Everything makes sense until mm. 5. It looks like it moves from c minor to Eb major.

Suppose we're in Eb major starting at mm. 5

From the end of mm. 5 to the very beginning of mm. 6, it's a vii°7/vi in Eb. It cannot be vii°7 because the root is B. It can't be CT°7 of the next chord because the root of the next chord is not in it.

Then it moves to the V7 chord. But it's not used functionally because it never resolves.

Next, it becomes even more interesting. It goes to vii°42/D and V42/D. And it resolves to D6 in mm. 7.

Finally, it goes to vii and V of c minor in mm. 8-9 (simplified a bit here).

mm. 5 is probably never in Eb

That D chord in mm. 7 is probably not in Eb major. It makes more sense to be a V/V in c minor.

If we work backward, that vii°7/vi in Eb should be vii°7 in c. It came from iv42 in c (instead of ii42 in Eb). Beethoven just used that long dominant chord in mm. 4 to tonicize to III of c minor.

But what is that unresolved dominant in mm. 6?

It probably makes sense in the context of a sequence. The voice leading takes precedence of its function. And it sounds surprising. I guess there can be a better explanation here. I'm curious to hear what people think.

Beethoven Piano Sonata in C minor, Op. 13, mvmt. 1, mm. 1–10

Conclusion

Thanks @Aaron for the response. I think everything makes more sense taking into account the enharmonic spelling. So this is what I have. Everything is in c minor.

measure 5

It starts on III of c minor. Goes to iv42 on beat 3.

On beat 4, it moves from CT°7 -> iv64 -> vii°7/III.

measure 6

It moves from vii°7/III to V7/III on beat 2.

In the rest of the measure, instead of resolving the V7, it moves on from vii°42/V/V -> V42/V/V -> vii°43/V/V.

measure 7-8

It resolves that vii°43/V/V to V6/V.

Starting from beat 3 until the end of beat 2 on measure 8, it goes through inversions of vii°42 and lands on V7 in beat 3.

Finally, it moves from V7 -> iv7 -> V7.

At a high level

If we ignore those fancy applied chords (vii -> V on those tonicized centers), this is what happens from measure 5-8 (ignoring the inversions).

III -> iv -> V/III (or VII, unresolved) -> V/V -> V -> iv -> V -> i

I still find that unresolved dominant in measure 6 very interesting. It's Beethoven telling you "Hey, think I'll resolve to Eb? Guess where I go next!". In terms of listening, it creates a strong sense of searching.

Another interpretation

I originally tried to find a linear progression here but I couldn't because I was trying to find one that connects the entire passage.

If we only look at measure 5 beat 3 until measure 6 beat 3, it is a linear progression connecting iv42 and vii°42/V/V.

I also found https://www.harmony.org.uk/book/linear_progressions.htm, which has a Mozart example with a similarly unresolved V chord in the progression.

Some people believe that Beethoven was inspired by this Mozart sonata. I think that makes sense. There are many similarities between the two and Beethoven just takes it to the next level.

2
  • I learned the concept of linear progression back in school, but I'm not sure that I can find the two functional chords that it's connecting. And it still doesn't explain that unresolved major-minor 7th chord. I guess nobody made the rule that it has to be resolved, but I find it really interesting.
    – lbbl59
    Nov 26, 2021 at 14:27
  • @Aaron. Oh. My bad. I meant Eb. I'll edit the post
    – lbbl59
    Nov 26, 2021 at 16:26

1 Answer 1

1

TL;DR

Beethoven is using a combination of common-tone and enharmonic modulation. Common-tone diminished chords are discussed in various posts here; a list can be found here. Enharmonic modulation, as used in mm. 5–8, is where a diminished chord is reinterpreted according to an enharmonically equivalent diminished chord.


Analysis

measure 5

Begins in III (E♭), moving to ii[4-2]/III (Fm7/Eb) on beat 3.

The chord on beat 4 is spelled as viio[6-5] (Bdim/D), but interpretively, it's rooted on F: a common-tone chord, which undergoes a voice exchange by passing through an apparent ii[6-4]/III, but which is best considered as "just a passing chord".

The Bdim spelling is to help clarify the descending motion of the bass: Eb-D-C-B-Bb across m. 5 into m. 6.

  • Functionally, the second half of measure 5 is ii/III, the harmony being prolonged via a common-tone diminished chord and voice exchange within that chord.
  • Contrapuntally, the diminished chord serves to bridge the ii[4-2]/III chord with the upcoming V7/III chord in m. 6 beat 2.

measure 6

The common-tone diminished chord proved to be a contrapuntal, passing chord connecting measure 5's ii/III with V/III on beat 2.

Beat 3 immediately employs another common-tone diminished chord, this time Bbdim, but spelled as C#dim (viio[4-2]/V/V) to hint at the arrival on D major (V/V) in m. 7.

Beats 3 and 4 comprise a contrapuntal expansion of the diminished chord, again via voice exchange, which conveniently places the "passing" V/V/V (A major) on beat 4 — a strong rhythmic position compared to the diminished chord on the &-of-3 and &-of-4.

measures 7 and 8

After an initial arrival on V/V (D major), beat 3 sees the arrival of another common-tone diminished chord: Ddim spelled as Bdim to reflect the larger context of C minor.

This time, instead of voice exchange, Beethoven takes the diminished chord through its various inversions, all of which serve as an extended chromatic passing chord between V/V in measure 7 with V7 in measure 8.

Finally, V7 is expanded by briefly visiting iv6 (Fmin/Ab) on beat 4.

4
  • Thanks for the detailed analysis! Based on what I've learned, the root of the resolution of a CT-dimished chord must appear in the CT chord. But this never happens in the score. However, I think your interpretation of the enharmonic spelling makes sense (though I'm not really sure what the problem is to change B natural to C-flat at the end of mm. 5 and the beginning of mm. 6).
    – lbbl59
    Nov 27, 2021 at 10:11
  • (Don't know how to put new lines in a comment. Let me edit my post instead) So mm. 5 beat 4 and mm. 6 beat 1-2 are simply [vii -> V] of Eb major (III). Then this V is never resolved and moves to [vii -> V] of D (V/V) in mm. 6 beat 3-4 and mm. 7 beat 1-2. Everything after until mm. 9 is [vii -> V -> iv -> V] of c minor. If we treat those [vii -> V]'s as voice leading additions, the entire passage is basically [III -> iv -> V/III (or VII, unresolved) -> V/V -> V -> iv -> V -> i] of c minor. The unresolved V is still very interesting.
    – lbbl59
    Nov 27, 2021 at 10:14
  • @lbbl59 - I'll note that your "V -> iv" is actually V -> iv6, which, according to my Royal Conservatory of Music-approved textbook, actually is a permitted chord progression in common practice period harmony due to its strong resemblance to a V -> VI deceptive cadence.
    – Dekkadeci
    Nov 27, 2021 at 14:33
  • @Dekkadeci, I ignored the inversions and showed only the functions. I thought that sounds smooth because of the voice leading but I think the textbook is right that it sounds like V->VI. Similar to how an N chord sounds like IV.
    – lbbl59
    Nov 27, 2021 at 21:56

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