Beethoven's 32 Variations in C minor for piano (composed in 1806, LISTEN HERE) use as its theme practically the same bass line as the 'Crucifixus' from J.S. Bach's Mass in B minor, composed in the 1740s but based on the same composer's 1714 cantata 'Weinen, Sorgen, Klagen, Zagen' (LISTEN HERE).
This is harmonised in a different, more tonally-driven way than Bach's version. You may notice that the harmonic analysis here uses both figured bass and Roman numerals, referring to the root-position chords built on each degree of the scale of C minor.
As is typical in Classical-era pieces, the beginning outlines the key by using only its three main chordal functions, namely the tonic (chord i), dominant (V) and subdominant (iv or IV), as well as two secondary dominants (in round brackets). These secondary dominants are the dominant (chord V) of the chord that follows (so the root is a fifth higher).
The chord in bar 5 is especially interesting as it is a type of augmented 6th chord (the interval between Ab and F# forms an augmented 6th), traditionally and rather randomly called ‘German sixth’ chord, but perhaps better described with the more neutral ‘augmented six-five chord’. This dominant of the dominant resolves, as expected, to the (simple) dominant (chord V), but the dominant here has a 6/4 suspension, making it look like a tonic chord (i) in second inversion. However, this is not how it is perceived. The 6/4 suspension, perhaps confusingly, is resolved only after an inserted chord iv, and the sudden change to unisono writing may make one forget that chord as still implied.
Incidentally, the rhythmic-melodic profile of the theme – along with its bass line – suggests a strong kinship with the Baroque chaconne or passacaglia, which is rather unusual for Beethoven's time and may have to do with his fascination with the music of George Frideric Handel.
Feel free to leave any comments below and sign up to the newsletter if you'd like to receive updates on new blog posts! If you are interested in more pieces using this bass line, why not listen to some works by the following composers or bands? Cavalli, Lully, Purcell, Rameau, Led Zeppelin (1), Led Zeppelin (2).