Art of Fugue – Contrapunctus VIII

In this post, I’m digging deeper into Bach’s The Art of Fugue with Contrapunctus VIII. It’s way more complex and intense than Contrapunctus I. I used Ableton Live to line up a MIDI file of the piece with Angela Hewitt’s recording, and then color-coded and annotated it to show the structure, the harmony, the subjects and so on.

Angela Hewitt says that she had to overcome some reluctance before learning The Art of Fugue.

I had heard extracts over the years, performed by various soloists and ensembles, but the work itself never seemed to grab me in the same way as the rest of Bach’s music does, on first hearing. Could it be that, at the end of his life, Bach had finally written something boring? It was hard to believe. I was determined to apply everything I had learned about Bach to see how I could make the work come alive.

It’s true that this music doesn’t grab you on first listen the way Bach’s catchier material does. Like, for example, the E major violin partita jumps right out at you. My kids were walking around singing it for months after I started practicing it. The Art of Fugue is not like that. But it pays back your effort and then some.

Here’s how Contrapunctus VIII sounds on a (super goth-looking) harpsichord.

I have a special fondness for this recording by Edgar Meyer, Béla Fleck and Mike Marshall on bass, banjo and mandolin respectively. (It’s annoyingly mislabeled as “Contrapunctus XIII.”)

The Emerson String Quartet plays it too fast for my tastes, but they are still awesome.

Contrapunctus VIII has three subjects. I wrote them out below, with an added kick drum underneath to clarify the meter, which is easy to lose track of in music like this:

Some detail on the subjects:

  • Subject 1 (blue in the video) is more hip and chromatic than the theme from the first seven Art of Fugue entries. Its metrical placement is weird and (to my ears) counterintuitive.
  • Subject 2 (pink in the video) is chromatic too, and it starts with a nifty syncopation. The motive at the end of subject 2 (orange in the video) might also be considered its own mini-subject; it appears before the first entrance of subject 2 itself, and is interwoven all throughout the piece.
  • Subject 3 (green in the video) is an inverted and rhythmically abstracted version of the main Art of Fugue theme.

Fun fact: Contrapunctus XI uses these same three subjects, plus their inversions. To dig deeper, check out Teoria’s tours of Contrapunctus VIII and Contrapunctus XI, both of which include lots of helpful audio examples.

My analysis is informed by this dense but illuminating article by Denis Collins in Music Theory Online. He explains fugue structure like so:

A fugue begins with an exposition, which comprises a statement of a subject in each of the voices in succession. A triple fugue may contain more than one exposition; that is, there may be a new exposition for each subject. This is the case with both Contrapunctus 8 and 11. Some expositions may use the subject of a previous exposition as a countersubject to the newly presented subject. Episodes refer to passages based on independent material or on short motives derived from a subject or countersubject already presented. Episodes normally do not involve any complete statement of a subject. A middle entry involves at least one statement of a subject in complete form and it is based on a subject heard in one of the preceding expositions, not in a following exposition. A middle entry is usually preceded and followed by an episode.

A few points of interest from Collins’ paper:

  • Starting in measure 52, there’s a nifty passage with the motive pinging around between the voices.
  • In measure 57, the motive plays in the top voice, harmonized by its own inversion in the bottom voice. It happens again in measure 141. When I think of counterpoint, this is what I think of.
  • In measure 82, subjects 1 and 2 play at the same time over a super hip descending chromatic bassline.
  • In measure 89, subject 2 plays against itself in the upper two voices while subject 1 becomes a chromatic bassline before jumping up a tritone and turning into a 32nd note run.
  • In measures 124-127, subject 2 plays on the bottom, then gets overlapped by itself on top, while subject 1 harmonizes with itself in thirds.

Here are few more spots that I think are especially interesting:

  • Bach uses the descending chromatic melody in subject 1 as the basis for longer and longer chains of descending chromatic harmony: in measures 22-23, measures 74-76, measures 80-83, measures 89-90, and most awesomely, in measures 114-118 over a long D pedal.
  • There are some nice crunchy major seconds in measure 63, measure 120, measure 121, measure 122, measure 154, and measure 184. When you loop these measures by themselves, they sound like Thelonious Monk.
  • In measure 76, there’s an Eb chord, which sounds both like the IV chord in Bb major and like an augmented 6th chord setting up the V7 in D minor.
  • Starting in about measure 163, there are more and more chromatic notes (notes from outside the local key that sound temporarily “wrong”), and while the underlying functional harmony is still there, Bach pushes it as hard as it was possible for a stodgy 18th century German composer to push.
  • The three subjects never play simultaneously until section 4. Then they play simultaneously several times in quick succession, with the subjects in different voices each time, in measures 148-150, measures 153-144, measures 159-161, measures 172-173, and finally (and most dramatically) in measures 183-185 to bring the piece to a close.

There are so many cool patterns, and patterns of patterns, and breaks in the patterns, and patterns of breaks in the patterns, and breaks in the patterns of breaks in the patterns, and verbal description is not really adequate to any of it. But those things are all audible in the music, and visible in the MIDI (and I guess in the score, if you’re a better music reader than I am.) I find I can hear the structure more clearly with a beat underneath:

So what, if anything, is this music “about”? Dylan Marney’s DMA thesis explains that it’s about the “conflict shown in the form of new contrasting themes, which combine with the main subject to reach an eventual conclusion… The inherent volatility of the new theme can be seen in these early measures as this fugue shows harmonic activity quite unlike anything seen in any of the prior fugues.” Marney hears lots of psychodrama: a story of “isolation” (subject 1), then “partial combination” (subjects 1 and 2), then “back to near isolation” (subject 3 and the tail end of subject 2), “returning to partial combination” (subjects 1 and 2), and, finally, “total integration” (all three subjects.) He hears the story of subject 1’s “independence”, subject 2’s “codependence”, and subject 3’s “resistance, as it strives for independence in this new setting before tensely combining with the new themes and falling into resignation.” That is a lot!

I hear this music as being about the limits of the human attention span. It’s too much information to absorb in real time. When I listen, I have to just pick a dimension and follow it, and screen everything else out. When I was looking through the MIDI for instances of the subjects and motifs, I had to ignore the vertical dimension completely, and when I was listening for chords and keys, I had to loop short sections and mostly ignore the horizontal dimension. I can usually only attend directly to one voice at a time, unless two voices are interacting in highly specific and formulaic ways (locked in rhythmically and harmonized in thirds, or doing exact imitation.) This feeling of being overwhelmed by information can be a pleasure, or it can just be off-putting. I do enjoy digging into the piece again and again, finding new patterns and structures and organization, but the pleasure comes after doing all this work, not before it. Angela Hewitt talks about how concert promoters are reluctant to book Art of Fugue performances, and I can see why.

There’s a puzzle game aspect to Bach’s fugues, both in the sense of Bach posing puzzles for himself to solve, and in the sense of music theorists trying to articulate his solutions. Composers and theorists have taken Bach’s unfinished Contrapunctus XIV an especially challenging puzzle to solve. Games have rules, and in this music, the rules may be complicated, but they’re also not hard to figure out if you listen enough times. There’s a lot of overheated rhetoric out there about how this music is universal and transcendent, and we should always be skeptical of that kind of thinking because it so quickly devolves into white nonsense. But it is true that Bach has stayed remarkably popular and influential far outside his original cultural context. I think it’s because this music was meant to be didactic, and as a result, it’s especially good at teaching itself to you.

The Online Etymology Dictionary says that the word “fugue” comes from the Italian fuga, meaning “flight.” That in turn comes from the Latin fuga, “a running away, act of fleeing,” the noun verb of fugere, “to flee.” It’s the same root as “fugitive.” I made a joke in my Contrapunctus I post about being in a fugue state. So far as I’m aware, musical fugues are not connected to psychological fugues except in terms of their sharing a Latin origin. Still, there is a shared sense of a flight from something. From reality? Bach must have been deep inside his head to sustain the concentration necessary to write music this complicated. Maybe it’s unhealthy to be that isolated! Bach must have thought it was a good thing, because it put him in touch with God. I don’t know what being so deep inside this music is putting me in touch with, other than Bach and his various interpreters. I don’t believe there’s anything supernatural going on here. But there’s plenty that’s natural (and cultural), and that is more than enough.