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?
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.