Harmonic analysis of J.S. Bach's Prelude in Cm (BWV 847)

Question

I sometimes try to analyze the harmony of a Bach prelude to understand how chords change, and how he manages to shift from one key to another. Here is the prelude in Cm BWV 847 (source image, MP3 here):

Here is what I understand:

BAR    CHORD  DEGREE / KEY
              [Cm key]     [Gm key]      [Fm key]
1      Cm     I
2      Fm     IV
3      G      V 
4      Cm     I
5      Ab     VI    =      IIb ?
6      D                   V
7      Gm                  I
8      C7                  IV      =     V
9      Fm                                I  

Would you have a similar analysis or are the key changes on bars 5 and 8 incorrect?

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Notes: I'm using capital letters for every degree, I don't write I for major and i for minor, I hope it's understandable. Also I haven't written the chords "with bass", for example bar 5 it should Ab/C for Ab major chord with bass C.

Answer 1

First of all, I suggest you study chords in BWV 846 which contains much to indicate why your strict harmony approach is limited.

Let me just remark on a few things. In Bach's music, as in much of that time, melodies can force the music to go in a different direction from where the harmony wants to go. So you need to look at melodic lines here.

To me the sequence of measures starting at 5 is a two interlinked chains of tension-release. In the melody there are the pairs Eb-D, D-C, C-Bb &c, with in the bass C-Bb Bb-Ab Ab-G. (In the left hand there is a middle voice going A-Bb G-Ab along with the bass.)

Yes, that is a sequence of II-V but that alone does not explain the overall structure. For instance, the transition measure 4->5->6 to me is driven by the G->Ab->A melodic motion. Chromatic up means increasing tension, so that gives you the starting point for the sequence of II-V resolutions.

Answer 2

As a starting point, I disagree with the analysis of m. 3, which I see as B diminished seventh over a C pedal tone. I hear the left-hand Ab as the structural pitch and G as the decorative one.

I agree with m. 5. It's a pivot chord, serving as VI in the original key of C minor and bII in the upcoming (tonicized) G minor.

Bar 8 partially matches my analysis. I consider it a direct modulation (tonicization). That is, it's V the following F chord, but does not function in the key of G minor. To be a G minor chord, it would need to include Eb rather than E-natural. (Although the E natural could, perhaps, be attributed to melodic minor, the expectation would be that it move to F#, which it does not.)