On Teaching

July 27, 2020

Gavin Black, director of the Princeton Early Keyboard Center, Princeton, New Jersey, is preparing performances on Bach’s The Art of the Fugue on both harpsichord and organ for the next two concert seasons.

The Art of the Fugue, part 8

In the last few columns, I have started writing and thought of a suitable and effective name for each column somewhere along the way, even at the end of the process. However, today I was able to start with the title, because it is time to get back to writing about Johann Sebastian Bach’s The Art of the Fugue!

This is still an uncertain time, no less so than a month ago. And it is still true that there are things that are unknown as I write this that will be known when you read it: will there be a Major League Baseball season? Who will be the Democratic nominee for vice president? Will there be a post-Memorial Day spike in COVID-19 cases? Will Broadway theaters really reopen on September 6? And there are things that are unknown now that will probably remain unknown, at least with any certainty by then: will there be a second wave of the virus? What will Advent and Christmas be like—for church musicians, for retailers, for families? Will the practice of going to the movies survive?

When I wrote my first Art of the Fugue column a year ago, I could not have imagined that over the succeeding year I would be unable to practice or perform the work, so this column really was my only study of the piece. I also could not have predicted what the content of the columns would actually be. I thought that I could, but it turned out to be very different from what I initially planned. But that is all eerily appropriate. When Bach first set out to compose the work he certainly did not know that he would be forced to leave it incomplete or that he would not see it published. Uncertainty has to be an underlying theme of The Art of the Fugue.

I strive to organize some of my thoughts about how the uncertainties surrounding the order of the movements interact with my thinking about the work in general. In my column from May 2020 I wrote of “the basic definition of counterpoint, namely two or more things that are different from one another happening at the same time.” The second consistent characteristic of counterpoint as we usually know it—for me, just below the level of “definition”—is that things that are the same happen at different times. Paradoxically this is perhaps even more important in shaping our range of reactions to counterpoint: esthetic, emotional, intellectual, etc. It is the source of our need, when we analyze pieces of this sort, to know about and recognize themes, subjects, countersubjects, motifs: anything that happens more than once. And this phenomenon is entirely dependent on memory. We know that a theme has recurred because we remember it from before. This is true immediately when a fugue subject appears for the second time. That part is relatively easy. (And it is assisted by expectation, if we have been told that what we are hearing is a “fugue” and we have just heard a theme in one voice unaccompanied.)

When a theme comes from elsewhere, as in a chorale prelude, for example, the process of recognizing that theme takes on another layer or two. I find it interesting that chorale-based pieces have a kind of double life. They come across differently to listeners who already know the tune and those who do not. Presumably most chorale-based pieces have been written in the first instance for listeners who knew the tunes extremely well—almost instinctively. In a multi-movement chorale-based work like Bach’s Canonic Variations on Vom Himmel hoch da komm’ ich her the recognizability of the chorale creates unity that perhaps makes the exact order of the movements function differently than it might in another situation. That is not to say that it is not important: it is manifestly a somewhat different piece with the movements in one order from another. It is interesting that Bach did indeed present the work in two different orders: first, in a published version, with the most complex and imposing of the five variations as the closing movement; later, in an autograph manuscript, with that variation in the exact middle. (This could be a rationale for considering it possible that the triple/quadruple fugue from The Art of the Fugue could function not as a culmination but as an interior building block, way station, or destination.)

When a theme has been altered, perhaps through augmentation, diminution, inversion, or something else well defined, perhaps by just a small change or two, recognizing it becomes more abstract and mediated by the subconscious. For many contrapuntal works this creates a kind of layered structure in which as elements recur in different ways, they evoke different kinds of memory. The development of the sense of “this is answering that” or “this edifice has that kind of shape or structure” is a multi-faceted, interlocking, overlapping experience.

In my December 2019 column, I wrote that “the subject or fundamental building block of The Art of the Fugue is not ‘the AOTF fugue subject’ but is ‘the very concept of the melodic interval.’” That column develops some of the reasons I believe that this is so, which I will not repeat here. If this is true, it sets up a condition in which the layers and facets of what we recognize as we listen, what we rely on to create structure in our minds, is infinitely complex and varied. The more the status of recognized themes or ideas is different (some more obvious, some more subliminal), the more complex that structure will be. 

I believe this relates to the question of the order of the movements. Since these connections are so numerous—effectively infinitely numerous, since there is very nearly nothing within the universe of the piece that does not connect to other things—and since the nature of those connections is so varied and fluid, convincing, engaging patterns will form themselves in the listener’s mind regardless of the order in which the components are encountered. The structure is then not “x follows y, which follows z” but “a, b, and c are all connected.”

So the nature of the opening theme and the ways in which it is developed in the first contrapunctus set up this focus on any and all melodic intervals, which in turn creates an infinitely fluid set of ways of hearing connections and perceiving or synthesizing shape. This explains why the piece can be effective almost regardless of the order in which the movements are heard. And it is not just that it is effective: it takes on a convincing overall shape, a strong sense of arc, direction, and structure. This does not mean that Bach did not have an order in mind. It just explains perhaps why the piece works so well even though we do not and very likely cannot know what that intended order was.

I say “almost” regardless. I believe, based on this analysis and intuition, that it is important for Contrapunctus I to be first, since it sets the stage for all that follows. I also think that not placing the triple/quadruple fugue at the end makes the biggest difference among all possible ordering choices. I am reluctant to say that it is “wrong” or would not work, but I know that it would be a big statement to place it elsewhere.

Conventional ordering of musical content

With certain sorts of pieces convention gives us an expectation as to how the ordering of types of musical content will create shape. This is true of suites, sonatas, symphonies, and other similar types of works. These conventions are not ever absolutely fixed, and they vary with time and place. But there is no convention as to the ordering of twenty or so contrapuncti. The content must create the possibility of shape and arc if there is going to be such a possibility.

This thought leads to an idea that I have held for a long time, have never been able to implement, and will likely never be able to implement. It would be a logistic tour de force and extraordinarily expensive as well. The analysis above helps to explain why I think that it could in theory work. Consider a performance of The Art of the Fugue by twenty different performers or performing ensembles, each playing one contrapunctus in a different room. Each movement in its room would be played over and over, and the listeners would be free to wander from one room to another. Each audience member would create their own path and could come and go from rooms at any time. Timing considerations would make it close to impossible to hear all of the movements in any order without also hearing fragments, since each movement in each room would be a different length from the others. The experience for any listener would not be that of “hearing the piece” exactly, but of getting absorbed in it. This is not a type of deconstruction that I would suggest for, for example, the Goldberg Variations or most other multi-movement works. But I think that it would work beautifully here.

Some of the observations that I have been trying to pull together in the last several months’ columns have led this thought to occur to me. The Art of the Fugue is a fully, rigorously contrapuntal work, and that is a large part of the lens through which we think about it. There is a body of music out there that is clearly imbued with counterpoint, but that is not fully contrapuntal. For me one quintessence of this sort of music is the keyboard music of William Byrd. There are passages that are fugal, there are passages that are chordal, and there are fugal bits in which the number of voices seems to fluctuate, or in which it is not always clear which notes belong to which voice. There is music by Mozart, Beethoven, and many subsequent composers that fits this profile. I have always had a nagging tendency to be uncomfortable with this: is it counterpoint or not? Fundamentally there is no reason to consider this anomalous or problematic, though some of us do. Looking at counterpoint as an analogy to the structure of the world or of the universe in the manner that I described in my previous column, and noticing that under some circumstances entities other than complete, defined subjects can be fodder for contrapuntal development, both tend to mediate between and reconcile contrapuntal and non-contrapuntal textures and make sense of the sorts of pieces that flow from one to the other.

Another less esoteric part of my recent Art of the Fugue experience has been that circumstances have led me to practice quite a bit on the piano. Using the piano in our home as a practice machine has been interesting. Vestigial memories of studying piano in my youth have come to the fore and have caused me to drift into doing things with volume that I am not very good at and that are not really relevant to this music.

But that raises a good question: does the “volume temptation” reveal things to me about the piece that are valid and that I can make use of, or is it just a distraction? Or is it actually misleading? These are not questions that I have never heard people ask. But they feel more vivid to me now as I have sat at the piano more in the last couple of months than I had in the previous many years. Many students do a fair amount of practicing on instruments other than the one on which a lesson or performance will take place: piano for harpsichord, piano for organ, electronic keyboard for either, or of course harpsichords and organs that are just very different from others. I have had too much tendency to see this as a necessary evil, to believe that ideally practicing on the exact right instrument is always better. I still believe that practicing on the performance instrument is better, more efficient, and that it should make up as significant a portion of practicing as possible. But since I am finding sitting at the piano to be enriching and interesting, I find myself rethinking all of this a bit. 

This is my twelfth consecutive column that is either about The Art of the Fugue or framed by my inability to write about The Art of the Fugue. It is my plan to put writing about the piece on the back burner, while getting back to actually working on the piece.

Just as I used the titling of this column as a boost of morale, I will reuse my mini-bio from 2019 below to express a bit of optimism about getting back to performance. It turned out not to be true then. Perhaps it will be now.

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