Chord progressions in the Bach Chaconne

Posted byEthan

Recently I have been digging deep into the Bach Chaconne. Since I’m a poor music reader, I’ve been using Ableton Live to remix, loop, and analyze the piece, both in audio and MIDI form. It’s working! The structure of the Chaconne makes sense to me now when I hear it, and I’m learning to play sections of it (slowly and haltingly) on the guitar. I’m supposedly doing this because the piece is a useful teaching example for minor-key harmony. Really, though, I just enjoy listening to it and thinking about it, and I’m lucky enough to have a job where I can use some of that thinking later.

You’re supposed to analyze classical harmony by annotating the score with Roman numerals and figured bass. I come from jazz, though, and while we like Roman numerals in jazz, we don’t do figured bass. I did learn figured bass well enough to get through grad school, but I would rather write and think about modern chord symbols. Also, I’d much rather analyze by ear than on the page. So I went through the MIDI file of the Bach Chaconne and segmented it out whenever I heard a chord change. Then I labeled the chords, through a combination of looking at their constituent pitches and my subjective sense of the chords that those pitches imply.

Here’s a complete chord chart for the piece. Click to see it bigger.

I made a flowchart of all of these chords and the sequences they appear in.

The chords in blue are from D minor and its related flat side keys. The chords in green are from D major and its related sharp side keys. The purple chords are dominants in both D minor and D major. Smaller chords occur less frequently. Here are the flat-side chords only:

And here are the sharp-side chords only:

I created these diagrams using OmniGraffle. I used the invaluable force-directed graph layout tool. From there, I moved things around by hand to optimize the layout for a balance of compactness and legibility. Optimizing the planarity of a network graph is one of the most relaxing and enjoyable activities I know of.

So, aside from the visual pleasure of the flowcharts, what can we learn from these things? For one thing, you can use them to generate your own chord progressions with Bach-like flavor – just pick a chord and follow the arrows. For another thing, you might notice that there’s more harmonic diversity on the sharp side than on the flat side. This is surprising, because only a third of the piece is in D major. There’s plenty of excitement in the D minor sections, but apparently it’s more melodic than harmonic.

Most of the chords in here follow the conventions of Western tonality, but every so often Bach throws a curveball. The strangest part of the piece harmonically is measures 81-83.

I couldn’t make sense of this chord progression at all. I asked Musicology Twitter what they thought. Garrett Schuman responded:

https://twitter.com/garrt/status/1209334764500586496

https://twitter.com/garrt/status/1209335383848345600

In other words, Bach was more concerned about the shape of the simultaneous melodic lines he was writing, and less concerned with what chords those melodies happened to spell out among each other. Jason Martineau analyzes it a bit differently:

Jack Dubowsky speaks for most of the musicologists when he says:

This is unsatisfying, though. Bach wasn’t just throwing notes around at random when he wrote counterpoint. He had to have been at least somewhat aware of what the vertical relationships of all those chromatic pitches was going to be, right? Why else would he have used the specific ones that he used?

I was admonished by Schenkerians in the Facebook Music Theory group that I shouldn’t be considering any harmony in a Bach piece out of its broader context, that the mystery chords make perfect sense as a prolongation of simple underlying cadences. But what is the fun in that? The mystery chords sound amazing looped out of context:

Musicology Twitter gave me some other examples from the 18th century canonical repertoire where composers used chromatic sequences to push their chords outside of their typical tonal function. But to find chords as weird as the ones Bach used, you have to go earlier, to the Renaissance, when functional harmony was a new idea and composers were pretty much groping around in the dark. When I asked Musicology Twitter for examples of “naive” Renaissance contrapuntal harmony, Garrett Schumann pointed me to Vicente Lusitano’s Heu Me Domine:

Arrestingly weird though this is, I like Bach better. His melody is smoother and more logical-sounding, and it’s pushing against a stable D minor framework. Far-out harmony makes more sense when it’s an audible deviation from conventional harmony. Anyway, I’m not sure how I’m going to present all this to my Fundamentals of Western Music students next semester, but I’m sure I’ll enjoy figuring it out.

See also: a deep dive into the Chaconne