On Teaching: The Art of the Fugue, part 1

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.

Repetition II

During the week after I finished writing my previous column, I had several experiences, each of which had some bearing on what I wrote about, so I will describe these before continuing and expanding the discussion from last month. One of them was a delightfully well-timed refutation of something that I wrote last month, the others more in sync with my thoughts.

First, a student asked me to review some of the music of Johann Caspar Ferdinand Fischer with him. We started with the Musicalischer Parnassus, a collection of nine suites published in 1738. I was reminded by reading through the collection that the prelude to the first of those suites follows almost exactly the same harmonic progression as the first prelude from the Well-Tempered Clavier, and it is in triple time. Thus it sounds a lot like my tripled version of that passage from last month: probably more so than the Bruhns excerpt that came to my mind when I contemplated my altered version of the Bach. The relevant measures of the Fischer are found in Example 1.

It is widely accepted that Bach knew Fischer’s music and was influenced by him. Fischer, about whose life not much is known, was probably nearly thirty years Bach’s senior. However, the collection that contains this passage was not published until twenty years or so after Bach wrote the WTC prelude that seems to echo it. Did Bach know this piece in manuscript? Did Fischer know the WTC, which of course was not actually published until decades later? Probably not. This is probably coincidence, and this passage is possibly just another interesting example of the use of repetition to create an aesthetic effect.

Next, I was coaching some musicians on a chamber music project, and I was surprised to be told that they had decided to make cuts to one of the pieces they were to play at an upcoming concert. Specifically, they were going to leave a movement or two out of the very long piece. However, in the longest movement, they were snipping out bits: a few measures here, a few measures there, based on a sense that the movement was too long and repetitive. This caught my attention since I had just written in my February column that, “. . . we essentially never find ourselves wanting to omit any part of a piece that isn’t a repeat. I have never had a student ask me about a through-composed piece ‘should I or should I not play mm. 9–16?’ or anything like that.” And indeed I cannot remember any previous instance of this.

A hypothetical discussion of the ramifications of this choice by these musicians would probably start by invoking respect for the composer and go on to talk about the shape and arc of the piece. It might emphasize “right” and “wrong,” or just attempt to characterize the nature of the changes brought about by this sort of editing. Some people would say that if they didn’t like this piece as is, they should play something else. I did not engage in very much of that discussion with these performers, at least not then. The choices had been made, practiced, and rehearsed. And I am not sure what I would say, beyond just that I was surprised and that I tip my hat to the Fates for delivering this to me at that exact moment.

I have heard debate from time to time about whether or not a performer should take the repeat in the long first movement of Schubert’s Piano Sonata in B-flat Major. Performers and musicologists talk about the length and raise questions about balance. But since there is a fairly long first ending as part of the section that we either do or do not decide to repeat, part of the discussion is about the material in that first ending. I have heard people use it as a reason to take the repeat—so that one does not entirely omit material that the composer wrote. But I have also heard it given as a reason not to take the repeat—on the grounds that the first ending material is boring, not up to the standard of the rest of the piece. This again touches on the question of when we do and when we do not give ourselves permission to second-guess a composer.

Then a student of mine, a former player of a melody instrument, just now getting into keyboard playing, spontaneously asked why so much keyboard music has repeats: is it just because they want to make the pieces longer? I touched on that a bit in the February column as well. It is an idea that we tend to resist, since in a way it could be taken to be disparaging or belittling of the work of composers. That does not mean that it is not true. And whatever the intent, the effect of repeats on length is real. I found it interesting that the question came up naturally for someone whose take on this repertoire was fresh and unspoiled.

The last of these chance occurrences was about the Widor “Toccata” from Symphony V. I wonder how different this piece would seem if the first measure were repeated exactly as is before the (actual) second measure. That second measure starts out as a repeat of the first, but crucially changes on the final beat.

Further questions regarding repetition

One question that I find fascinating in repeat situations is whether the two instances of the same material, one after another, are a statement of something and then a restatement of it, or are a question and an answer. This question itself will not always or often have an answer. However, in some cases for us as players, and for our students, observing our own feelings about this, one case at a time, might be revealing.

It might seem counterintuitive that the exact same notes could be both the question and the answer. However, this is not impossible even with words:

“Really?”

“Really!”

or even more extended:

“Really?”

“Really.”

“For certain?”

“For certain.”

Each of these question and answer groups works. Furthermore, each word or phrase has its own particular feeling. The “really” answer in the second grouping feels different to me from that in the first, because it is not being asked to express finality.

In the realm of music without words, the question and answer attribute is more abstract, more elusive. Attributing this to a passage almost certainly cannot ever be right or wrong or subject to proof, or even perhaps to analysis. But because it cannot ever be wrong, it can always be potentially useful. If thinking of a repetition situation as a question and answer, or as a statement and restatement, perhaps in a different mood or by a different “person,” seems useful or seems to enliven the experience of playing the passage, then it is a fruitful and correct way of looking at it.

With words, the vast majority of attempts to use the same word or phrase as a question and its answer will fail:

“Would you like some toast?”

“Would you like some toast.”

and so on.

The possibility that a repeat will seem like a question and answer can never be subject to failure as such; it can just seem like an interesting idea or not. This brings us to one of the fascinating things about repetition, both signed repeats and the repetition or recurrence of any material, whatever the structure. The fact that we can accept the amount of repetition in music that we do accept invites us to think about the ways in which music resembles or does not resemble those forms of expression that use words or concrete visually based images.

In a work of theater—play, movie, television episode—if a structure in which something happened and then was literally repeated, then something else happened and was also literally repeated, and so on, were to be used, it would be at best some sort of special effect. It is not necessarily the case that this has never been done. But it is not routine or remotely common. It would be possible to go to dozens of plays and movies per year for a lifetime—and watch an almost infinite amount of television—without ever once encountering this form.

But in music it is routine. Why is this so? It should not be that the repetition is inoffensive—acceptable—because it is meaningless. If it were meaningless, then we would not have a vast repertoire in which a substantial amount of repetition has been perceived as valuable by a vast audience over many centuries. (At least that is a fair assumption or a reasonable hope.) But the meaningfulness is abstract, and that seems to be the big difference. The extent to which repetition in music engages our “why are they doing that again?” reflex is limited.

Perhaps because the repetition is abstract, it can also evoke a response to the very idea of repetition itself. That idea is powerful. As much as we like newness, we also like familiarity, and repetition gives a sense of connection to the past and future. It is possible that sometimes, at least when we hear the repeat of a passage, we react as we do when we see an old friend or go back to our favorite restaurant. Repetition may suggest something like resurrection or reincarnation, or hint at some of the things that we wonder about and crave having to do with eternity and infinity. This is especially true of recurrence in composition, as in rondo technique or recapitulation. Certainly these images are overblown and should not be taken too literally or even too seriously. But I am pretty sure that some of these sorts of feelings are there much of the time. It is part of the picture of what repetition can feel like or mean.

In music that has words and is in verses, we expect the music to repeat, but not the words. We can sing any number of verses in a row of a hymn and happily accept that the musical notes will be the same for every verse. However, if the words were exactly the same for each verse it would seem bizarre. A phrase in words might recur. But any sameness of that sort has to be dealt out very differently with words than with music.

The term “repetitive” is, in everyday usage, almost a synonym for “boring.” You never hear someone say “that was a wonderful book: really repetitive” or “that movie was the most repetitive I have seen in a long time. I loved it!” So that suggests that we need to feel a bit of caution about whether repetition, whatever its power, can lead to boredom. This is to some extent the domain of the composer. If we think that a composer’s use of repetition in a particular piece creates boredom, we might just not want to play that piece. But nonetheless as players, we need both to make sure that we do what is necessary to make repeated material interesting and to refrain from overreacting.

I believe that a lot of students tend to overreact to the fear that repeated or recurrent material will be boring. This can manifest itself in wanting to add ornamentation or change stops. There is a kind of fruitful paradox, that if you always change ornaments or change stops on repeats, that in itself becomes repetitive and potentially boring. So everyone should be motivated to limit those sorts of gestures or to think carefully and in an individually tailored manner about when they are the most valuable.

If a repeat—or material that comes back or resembles other material—seems intrinsically boring to you, is there a way of framing it aesthetically, philosophically, or through imagery, that brings it to life? Is there a way of playing it with more energy, or less energy, like a response, like an echo, like a reaffirmation, like something thoughtfully reconsidered? A serious engagement with ideas such as these should probably precede choices about out-and-out changes. Any changes in the notes (ornamentation) or the sound (registration) or performance values (articulation, phrasing, use of timing devices, rubato, and so on) will be based on taking the passage as seriously as it warrants, not on halfway giving up on it in advance.

A very practical though mysterious aspect of playing repeated passages or identical material is that the same exact notes can seem easier or more difficult to play depending on whether you are playing them for the first or second time. Sometimes, in a long piece in which something comes back after a long interval, this can be explained by stamina and concentration issues. This is something that I have to remember to think about consciously when I am playing the Bach Prelude and Fugue in E Minor, BWV 548, for example. In each movement there is an extended true da capo. And when the opening material comes back it manifestly does not feel the same. I need to remember consciously to give it an extra dose of concentration to compensate for the effects of playing non-stop for a long time. Also the return of familiar material in a case like that creates the danger of a letdown: “oh, it’s just that old passage again; I did that fine ten minutes ago.”

One way to avoid that letdown is to focus on the possible rhetorical differences alluded to above. Try to remember, whether it is an instant repeat or a return after a good deal of other musical wandering, that by virtue of its not being the initial statement it is a different thing that is going on and needs attention and interest. On a very practical note, if the fingering and pedaling of two passages that are identical in notes can also be identical, that should save time and work and lead to greater security. This is something that seems like it could go without saying, but that is also worth remembering consciously.As I said last month, a lot of this is speculation or ideas that I find interesting to try on for size. I would encourage students to think for themselves as much as possible about what it means to take an interesting and important musical idea and just plain do it again. The ways in which I have framed some of my thoughts about it might be useful to some people, but all the more so if they invite people to come up with their own.

The Art of the Fugue, part 6

I recently had a concert performance anxiety dream. This one was specifically about The Art of the Fugue, and it followed a common pattern: I was aware I was to perform the piece, and I sat down at the organ, but when I looked at the score, I realized that I had never seen the music before. I started to panic, but also to try to scheme: could I get away with sight-reading this? How slow could I play it without giving away what was going on? Could I leave out the hardest bits? I remember looking around hoping to see something happening that would force the concert to be abruptly canceled. The music on the page was not actually The Art of the Fugue. It was dense, chordal, and chromatic. The typeface looked like something French from the late nineteenth century. But within the dream I accepted that this was indeed the work that I was supposed to be playing. I had just somehow neglected to learn it.

I have this kind of dream once or twice a year, but I am pretty sure that these dreams usually involve playing at someone else’s behest, in chamber music or in a church service, not solo performance. My Art of the Fugue project is something that is being carried out only at my own behest. My decision to do it is a choice to focus on something that is specifically important to me and that I am utterly convinced I can only do well if I am very committed to doing it the way I want it to be done.

So why the dream? My only thought so far is that I am trying to remind myself that I should really learn the thing! There are always traps in any project, and maybe the trap with this one is that my sense of “ownership” over this work, my awareness that I have been studying it and interacting with it for nearly fifty years, my experience of being comfortable with it at a conceptual level will disguise how hard it is to play and lead me into complacency about the business of learning the notes. Maybe that is what the dream was about, or maybe not. Yet, any interpretation of a dream that reminds me to work as hard as I can to become as certain of the notes as possible is worth paying attention to!

Connections

The connection between the sense of understanding, inner commitment, ownership, and the nitty-gritty practical learning of a piece is a complicated one. At one level, there is the fact that, for almost everyone, focus and concentration are easier and more successful working on something we love than on something that we do not care about, or at least not very much. This is why I want students who endeavor to become more accomplished players to work on music they care about. The translation of time and effort into growth as a player is most efficient this way. Students do not know what music is out there as well as I do or another teacher does. The process of helping them to explore things that they do not know interacts in complicated ways with the goal of working on music they love.

Yet, I am wondering about something deeper. If one feels a deep bond with the music one is working on, what dangers does that invite? I believe there is a risk of assuming that the bond with a piece or a composer or a repertoire is in itself enough to make something come across to listeners. If I feel something while I am playing and listening, am I interpreting the music a certain way because of my love of the music? Is this hiding the necessity of doing something interpretively from me?

Overall structure of The Art of the Fugue

I now turn to some thoughts about the overall structure of The Art of the Fugue. There are two salient facts I would like to discuss. The first is that one of the movements is incomplete—the one that most of us take to be the final movement. Second, that there is some uncertainty as to the order in which Bach intended the movements to be played. There has been a lot of serious, thorough, and fascinating scholarship about both of these matters, each of which has a different set of interactions with performance. Regarding the final movement, there is the question of whether to play it as it has come down to us, breaking off abruptly, or to alter it in some way, either by completing it or by ending it at an earlier point than the break-off. As a set of choices this is probably more about philosophy than about scholarship or research. Scholarship, research, and analysis can, for those who wish to perform a completed version of the piece, elucidate different possibilities for that completion. There is also, however, the question of whether to play it at all. This is a matter that has to be addressed by a combination of scholarship and philosophy. It used to be fairly common for performers or scholars to entertain the possibility that this movement was actually never meant to be part of this work. I believe this is a rarely held view nowadays, and indeed the musical connections between this movement and the rest of the work are convincingly strong. To be fair, though, there are one or two quite recent recordings of the work that omit the long, unfinished fugue.

Anyone who sets out to perform The Art of the Fugue has perforce to end up making a decision about an order in which to play the pieces. And, speaking of recording, I have just completed a quick and random survey of a dozen or so CDs of the work, and no two recordings present the movements in the same order! This includes performances on organ, harpsichord, piano, and by chamber ensembles, such as saxophone ensembles, consorts of viols, and so on. These are mostly recent recordings, subsequent to the burgeoning of Art of the Fugue scholarship that we have seen over the last few decades.

(Further regarding recording: nowadays it is easy to set up a recording of the piece with each movement in a separate file, and with playing order to be determined by the listener. This could be as a set order or as a random “shuffle.” So I should say that any performance of The Art of the Fugue presupposes a choice by the performer about movement order. Only a live performance does so of necessity.)

There are two underlying causes of uncertainty about movement order. The first is there are two primary sources for the piece: a manuscript of most of the movements in Bach’s own hand from the mid-1740s, and the edition published in 1751 by Bach’s heirs. These sources have different numbers of movements and are presented in different order. The second source of uncertainty is we do not know how much input J. S. Bach himself had in the preparation of the printed edition. Therefore we do not know that he had signed off on the order represented there.

For example, it is possible for a performer to assume that, since the people who finished the preparation of the 1751 edition were close to J. S. Bach and worked with him directly on at least much of the project, the order that they created is probably the correct order. But this would be at best just an assumption, and there is a significant amount of scholarship to call it into question. A further complication is that the published edition contains elements that almost everyone agrees are not really part of The Art of the Fugue at all, at least not part of the integral structure of the work as a whole. For instance, there are alternate versions of two of the movements and a chorale prelude, the latter manifestly added to the end of the publication as a kind of compensation for its incompleteness and a memorial to the composer. I have never encountered or even heard rumored any performance of literally every note in that original edition in the order in which those notes are found there. So what were these early editors up to, and what did or didn’t they understand about the composer’s intentions?

You will probably not be surprised to read that we cannot answer that question. As I said, there is a lot of good scholarship on the matter, but that scholarship is often in disagreement. Every argument rests on assumptions, and while many of those assumptions seem sound, none of them seem rock-solid certain.

As a performer I must come up with an order. I notice, reading my 1985 program notes, that I then completely accepted the order that I had grown up with. This is the order that Helmut Walcha used in his recording, and I used the same order. This is almost the same as the order used by the early twentieth-century scholar Wolfgang Graeser, who is credited with rediscovering The Art of the Fugue, and whose edition was used as the basis for the first known public performance of the work, which took place in 1927. As best I remember, I did not particularly know at the time there were issues about movement order, since much of the scholarship on the matter has been carried out since then.

I found considerable structural logic in the shape of the piece with this order of movements. For example, I considered the placement of the group of four canons, with their two-voice and therefore relatively light texture right after the dense and complex Contrapunctus XI, to be aesthetically and structurally significant. However, the canons as a group are not placed after Contrapunctus XI in either original source, and they are differently placed in the two sources. Other performers find logic in spreading them out around the other mostly four-voice fugal contrapuncti. This uses the lighter texture to define groupings in the successive fugal pieces. Some performers place them after the long unfinished fugue, displacing it as the ending, and instead ending the work using the lighter textures to create a relaxed sort of coda.

I also found logic in the gradual introduction of the B-A-C-H motif, successively more open and clear in Contrapuncti IV, VIII, XI, and XVIII. Likewise, I find logic in the immediacy of the motion from the flourish ending Contrapunctus XVI—the four-voice mirror fugue—to the opening subject of Contrapunctus XVIII of which it is a very close pre-echo. This happens only if the appropriate section of Contrapunctus XVI is the last item before Contrapunctus XVIII. I also found the juxtaposition of Contrapunctus VIII—the first one whose subject opens with an interval smaller than a fourth—and Contrapunctus IX—the first one whose subject opens with an interval greater than a fifth—to be meaningful. This is only a juxtaposition if those two movements are indeed next to each other.

There are a number of questions that arise out of this complicated picture. If I see a convincing overall structure in this piece with a particular movement order, does that mean that this is likely to be the “correct” order, the order that the composer had in mind? (I will answer this one: no.) Or am I simply imposing that sense of structure because I am accustomed to that order and fondly want to believe the piece has a meaningful overarching shape? (Maybe.) Is it possible that if we really knew for sure what order Bach had in mind we would see that order gave to the work an even more compelling overall shape than we experience now?

Musical entities that are not just clearly one unit have a variety of shapes. To stick with Bach for the moment, The Well-Tempered Clavier is one thing (a collection of completely separate pieces, but ones constructed along similar lines to one another); a suite or partita is something else (a piece clearly intended to have an overall shape, but made up of movements that are in different forms from one another, each of which could stand as a piece in itself); The Goldberg Variations is something completely different yet a piece made up of clearly separate movements, but also with a clear unifying principal among the movements. Das Orgelbüchlein falls into the same category as the WTC. How about Clavierübung III? Unlike all of the above, it gets part of its unified or structured feeling externally, through the associations that we have with the hymns on which the pieces are based. It is also given a circular structure by the prelude at the beginning and the fugue at the end.

Which of all of these would seem very different if the order of the component parts were changed? It would probably depend on the specifics of the changes. For example, if in The Goldberg Variations, the return to the opening “Aria” were taken away from the end and placed somewhere in the middle, that would feel like a drastic change, probably a change for the worse. If the imposing “Variation 16” were moved away from the position that it occupies in the middle of the work that would probably seem odd and weaken the overall shape of the piece. Moving other movements around might make considerably less difference. In Clavierübung III, if the closing fugue were moved into second position right after the prelude, leaving the work to end with the four duets, the structure of the whole would seem radically different. If the four duets were distributed throughout the piece rather than placed in a group at the end that would seem like a real change as well.

In all of these cases we have reason to believe that we know what order Bach intended. With The Art of the Fugue we approach the same sorts of issues from a less anchored place.

I will continue this discussion next month, attempting to tie it in as closely as possible to some of the specific compositional details of The Art of the Fugue and, in turn, to performance as such.

To be continued.

The Art of the Fugue, part 5

This month I continue my discussion about the process of performing Johann Sebastian Bach’s The Art of the Fugue. The connection of all of this to teaching is tangential, perhaps, but very real. As part of the act of working on a project that is especially important and challenging to me, I find myself trying to delve more deeply, accurately, and honestly into understanding what is most important and meaningful to each student.

Yet it can be hard to figure out what is important to oneself and why. In my recent attempts to look closely at that, I have noticed that a majority of the artwork that I care about the most is either big in scale or possesses a convincing overall arc that gives it a spacious feeling regardless of the literal size or length. That arc is a significant part of what is artistically important about the work.

I recently made a list of the five specific artistic entities that mean the most to me or have meant the most to me over my life. This was not in connection with The Art of the Fugue project, though coincidentally, they all have this quality. Just for the record, the five entities are, in no particular order, as follows: The Art of the Fugue; Handel’s Messiah; Hamilton (the current Broadway musical); the Jethro Tull album-length song Thick as a Brick; and the off-Broadway immersive theater piece Sleep No More. All are in the category I have described. Each of you reading this could probably make such a list; it would surely be very different from mine. The same is true for each of our students. But I could also make a list of moments, bits of music or theater or other narrative, say no more than ten or fifteen seconds long, that are in themselves deeply important to me.

Presumably a work of art that moves through time, like music or a play, cannot have a convincing and important overall arc unless each constituent part of that arc is convincing in itself. Some of those constituent parts may be the ones that strike a given person as especially intense, important, or moving. Others may be just part of the moment-by-moment flow. Something about the relationships of those details to one another, ones that are adjacent in time and ones that have to rely on memory to be connected, has to be convincing in order for the overall arc to be convincing. Is it important to think, in shaping each detail, about how it relates to the overall arc? Or is it possible to trust that if each detail comes out the way that you want it to (on its own terms) the overall shape will take care of itself? Does this differ from one piece to another? Are there many possible ways of dealing with this effectively, and do these arise out of and then shape the interpretive stance of different performers? It seems that, among other things, it would have to vary from player to player, based on different fundamental feelings about the relative importance of overall arc and moment-by-moment experience.

Why is the overall arc so important? I do not have one specific answer, though I think there is value in asking the question. I believe that one answer that is highly personal and significant, but that also risks sounding cliché, is that it relates in part to the quest to understand what it means to experience the arc of a life, and thereby to come to terms with death. Of course, The Art of the Fugue has a special role in this regard due to its unfinished nature.

The longer a work of art is, and the more compelling its shape, the more it feels to me like a place—perhaps a place into which one can escape for a while. (That is significant even without anything from which to escape. The sense of being elsewhere for a while is enticing and refreshing in and of itself.) I grew up in New Haven, Connecticut, and spent a lot of time as a small child roaming around some of the buildings of Yale University. Many of these structures are maze-like and are imbued with a strong feeling of being places unto themselves, hidden and self-contained. This was perhaps especially so to a child for whom they are frighteningly big. This shaped some of my taste in architecture, but I believe it spilled over even more powerfully into my taste in music and in theater. It is relevant to all of the works of art I mentioned above, but most especially to Sleep No More. It is also a source of my love for golf, since a golf course is also this sort of place. (If you count the movements of The Art of the Fugue one particular way, the number comes out the same as the number of holes on a golf course.)

I am finding (or re-confirming for myself) that because of my propensity or craving for long structures, it actually is not a challenge for me to play from one end of The Art of the Fugue to the other. Encompassing the whole of it in my focus seems to be the aspect of working on it that comes the most naturally to me. The challenge—the part where I have to be honest with myself and not let myself indulge any laziness—is making sure that that overall shape is as convincing to audience members as it is to me. This is a place where the questions I posed above about details become critical.

To have an intermission or not: that is the question . . .

Here is a consideration that arises from the length of this work taken in conjunction with the desire to make the overall shape convincing and powerful: intermission. I do not yet know exactly how long my performance of The Art of the Fugue will be. I am sure that in my graduate school performance the music itself took about an hour and forty-five minutes, in addition to an intermission. Subsequent performances have varied in length. My recording on two harpsichords with George Hazelrigg used faster tempi still. It lasts about 78 minutes and just fits on one CD. I think that my planned solo harpsichord performances will be somewhere in between. It is rare for a classical concert lasting over an hour and a half to lack an intermission. On the other hand, an intermission interrupts the flow of the piece significantly. But so will listeners’ impatience and need for a physical and mental break. We go to movies that are longer then that, without needing to take a break. Plays lasting ninety minutes with no intermission have become more and more common. But as I ask people about this—concert patrons among my friends, students, etc.—I get a pretty strong consensus that an intermission is a necessity. I am very reluctant to go along with that, so I am conflicted. Perhaps some performances will include an intermission while some will not.

Playing a work as if improvising

I have written in previous columns that it can be useful to pretend that you are improvising the piece that you are performing. This is not a literal idea, since I am not a particularly adept improviser, yet it is an image or a way of mentally organizing the quest for spontaneity. How does that relate to The Art of the Fugue? After all, the piece is so complex contrapuntally, and we know that Bach worked on it over a long period, so we can safely assume it was not improvisatory in origin. Yet, it might be all the more necessary to try to have that improvisatory feeling as a corrective to the tendency to be over-awed by that structure, formality, and complexity.

It is a myth that improvisatory means unstructured, free, or rhapsodic. Improvisation can be of that sort, but it can also be highly structured, contrapuntal, well planned motivically or harmonically. A few times over the years I have heard an improvisation that was begun by a player who did not know how long the improvisation needed to be, but who ended up producing an experience that seemed to have a convincing overall shape. It seemed to me listening as if the expectations shaped by the beginning determined the rest, including the timing of the end. How is that even possible? Of course, I am only reporting my reaction, not anything scientific or measurable, and I do not have recordings of these moments to study objectively. But those experiences have always been in the back of my mind as a paradox that probably has something to say about musical shape. I will return to this next month in discussing the state of my thinking about the structure of The Art of the Fugue.

After practicing on different harpsichords recently I have noticed that in the four-voice mirror fugue there are passages in parallel tenths, a rarity in Bach and other Baroque keyboard music. However, these passages disappear when one voice is in the pedals, so their existence as an unavoidable technical matter is harpsichord-specific; and I can reach those notes on a harpsichord with a 61⁄4′′ octave, but not on one with a 61⁄2′′ octave! So as a very practical matter, this defines or limits what instruments I can successfully use for an Art of the Fugue performance on harpsichord. This is another example, specific to me, of the ways in which this work is playable, but just barely.

It’s all in the name.

There is no evidence that the name The Art of the Fugue or its original in German, Die Kunst der Fuge, came from J. S. Bach himself, or that he even encountered it. It is found on the title page of the first edition, published under the supervision of members of Bach’s innermost circle. It is entirely possible that the choice of that title reflected something that they knew about what J. S. Bach intended or wanted. But it is also possible that it did not: that he had not said anything about a title by the time he died, and that therefore they just had to come up with something.

I believe that the name has tended to move us toward thinking of the work as being more academic—more of a treatise or exposition about something—than the music itself gives us any reason to think that it is. In fact the younger generation circa 1750 might well have seen it as old-fashioned in a way that seemed to make it into something academic. C. P. E. Bach certainly seems to have revered his father. But he also lived surrounded by musical aesthetics that would have been foreign to his father. If J. S. Bach himself had meant to call this work something very different, say The Mysteries of Harmony or Grand Passacaglia in D Minor or The Strife of the Gods, would we see the piece differently? Would the tradition (quite weak now, but prevalent for many years) of thinking that this work was only suitable for study, not for performance, ever have formed?

We do not really know how much any child understands about the work or indeed the character of a parent. It is convenient to assume that what C. P. E. Bach says about J. S. Bach, or what he implied by engraving a certain title on a piece, is valid. No one would suggest that it be arbitrarily dismissed. But it is just not accurate or intellectually rigorous to assume that it is correct or that it could not be misleading. I know that when I myself try to understand the work or the intentions of anyone of an older generation whom I knew well, I am under very strong internally derived pressure to make the kind of narrative out of that story that I would like it to be or that I can in some way admire or relate to. I resist that, but I do not think that I can escape from it. A composer’s children and students belonged to a different generation from that composer and grew up with different artistic assumptions.

Talking about study

I have found myself slightly more inclined to look over The Art of the Fugue away from an instrument than I normally do with music that I am working on. All of the analytical work that I do with pieces is usually done at a keyboard, teasing out voices and actually playing them, looking at aspects of harmony, rhythm, melody, and so on, either while playing them or in a position to play on the spur of the moment any or all of what I am trying to analyze. Why am I spending time with my Art of the Fugue score in front of me at a table or seated in a comfy chair? I am not sure. Should I suspect myself of being subconsciously influenced by the age-old classification of the piece as one suitable for study? I do not quite think so. I believe it is two things: that I want or need to spend more time thinking about the piece than I can or should spend playing, and that I am just plain interested in it. I think that some of the time that I am spending reading The Art of the Fugue sitting in a chair is taking the place not of practicing it more, but of reading a novel or the newspaper! Needless to say, I am rethinking the ways I encourage my students to study away from the instrument!

Next month I will write more about the structure of The Art of the Fugue, in particular, the ways in which the overall shape makes sense even though the piece is incomplete and even though we are not certain about the order of the movements.

To be continued.

Repetition I

Recently I have been thinking about situations in which something in a piece of music happens more than once. This encompasses out-and-out repetition—which may be written out or may be indicated by repeat signs—true da capo, the structural element known in some circumstances as “recapitulation,” recurring sections in rondo forms, and any recurrence of a passage identically—even when it is not da capo. This also includes the ubiquitous practice of using recurring motifs—fugue subjects, other motifs treated contrapuntally, any sort of leitmotiv, the repeating bass line of a chaconne or passacaglia, and so on. I want to share some of these thoughts in this column and the next.

These columns will be filled with questions and speculation about a number of different aspects of repetition and how we come to expect it. I will also offer a few practical thoughts about what the concept of repetition and recurrence means for teaching, learning music, and performance. The value of this speculation for teaching lies mostly in the possibility that students may find it interesting, and perhaps it will lead them to further exploration. I also have thoughts about ways in which focusing on repetition and recurrence can help with the practicality of the learning process.

How many times shall we repeat?

Let’s begin with a curious example of repetition. Namely, why did Bach write the first Prelude of the Well-Tempered Clavier like the passage in Example 1 rather than like in Example 2 or Example 3?

In Bach’s composition, the first half of each measure is repeated exactly to form the second half of that measure. (It is so fully exact that he could have used repeat signs.) This pattern persists until the ending, where it is altered to lead to a satisfying cadence. We are deeply accustomed to the piece that is created by this patterning: it is one of the most familiar in the repertoire. But a piece on either of the other two models would have been a perfectly valid musical entity as well. If he had written it one of those ways, we would be deeply used to that.

Or would we? Maybe the “real” version is somehow actually better. I have played through the entire piece with both of these patterns, and it is my feeling that they work. Each one suggests something different about performance. The most striking of these differences is that the three-times-per-measure version feels to me like it should go a lot faster than the other two. It ends up reminding me of this passage from the longer Praeludium in E Minor of Bruhns, at measure 95 (see Example 4). If Bach had written version 3, we might speculate that it was influenced by this passage, which he may have known.

I tend to play the once-per-measure version slower and with more rhythmic freedom than either of the others. It is interesting that a mainstream analysis of the piece, which would be an analysis of harmony, since it is such a pure chord-based piece, would be essentially identical for each of these three very different pieces. I doubt that we can answer the question of why Bach wrote it one way rather than another, or indeed whether one way is better. It seems pretty clear that one repetition is very different both from no repetition and from two or more repetitions. Would writing the chord pattern four or five times in a row be as different from three as three is from two? At what point would it become ridiculous? If each chord pattern were repeated sixteen times, it would be a particular kind of extreme statement: outside the realm of Bachian music or most of what we ever encounter, but valid nonetheless.

So what about repeats as such? We accept it as normal that in many pieces of music, something—a definable passage that has a pretty clear beginning and an end, and not typically just a half-measure—will happen twice in a row. This is a defining trait of late Renaissance and Baroque dance forms: which usually consist of two sections, sometimes more, each repeated, like A-A-B-B. We accept that as routine, but, as with the Bach prelude, we would never expect each such section to be repeated more than once: A-A-A-A-etc.-B-B-B-B-etc. Same question, here applied to bigger increments of music: why not? I mean, why not in both directions? Why is twice in a row effective, and why would more than that not be? The same question applies to other places in common musical structures where repeats are routine, such as the first section (and sometimes other sections) of works in sonata-allegro form.

Tension and release

The most interesting effect and purpose of a repeat does not arise from or during the repeat itself, but rather at the moment when the repeat does not happen that second time. That is, the repeat sets up a tension (about whether it is indeed going to happen yet again, and whether it will end), and the motion to the next section relieves that tension. This tension is a fiction that we allow ourselves to experience, or that the music allows us to experience. After all, we know that the repeated material will not go on forever. We know this for certain if we know the piece, and we know it essentially for certain even if we do not. But there is something in listening to music that allows our reaction—our appreciation—to feel surprise even when listening to something that we know intimately.

I strongly suspect that this dynamic is one of the explanations for the persistent tendency for all of us to feel that “taking the repeats” is a different matter for the first section of a piece in binary form than for the second section. When we come to the end of the second section, first time, the suspense-and-relief scenario has just happened once, and our appetite for it is perhaps satisfied. Also, we know that when the second section gives way, whether after a repeat or not, it will give way to the silence following a cadence, and then perhaps another movement or another piece. That is a less compelling change of direction. This may also tend to explain the almost universal practice of not taking repeats in da capos of the sort represented by the return of the Aria at the end of the Goldberg Variations of Bach.

This may also tend to explain why repeats of sections happen only once (AABB). If part of the point is to set up the moment at which the repeat gives way to something new, it is important for the repeat not to wear out the listener’s interest. Once makes the point, more than once risks irrelevance.

I once heard an experienced concert pianist, playing from memory, repeat the opening section of the first movement of Beethoven’s Waldstein Sonata twice (that is, play the section three times). My impression was that he accidentally started the first ending after the second time through, and that led inevitably to replaying the whole section. I remember having the following reactions: first of all, that it was nice to hear the passage an extra time, just because it is wonderful music; but second to feel a little bit of panic that it would never end!

This experience makes me ponder, how does our enjoyment of a particular passage play a role in interpreting or perceiving repeats? Does this apply in particular to pieces that are short enough that repeats will not try anyone’s patience? In the Bach variation set on the chorale O Gott du frommer Gott the composer follows the structure of the chorale melody as far as repeats are concerned, repeating the first half of each variation, but not the second, at least in most variations. In Variation V and Variation VII he does indeed repeat the second half as well, violating the relationship between the chorale melody and the shape of the variation. Why? Well, I noticed practicing the piece that the opening measures of each of those second halves was especially charismatic, unusual in texture, and harmonically rich. These are moments that I would find myself practicing over and over again just because they are so cool to play and hear. I had to remind myself to practice other bits that needed practicing more. I noticed this before I stopped to think about those repeats. But I wonder whether Bach put in those extra, musicologically “wrong,” repeats just because he liked that bit of music! This is a kind of non-rigorous, taste-driven choice making that we do not associate with JSB. But perhaps we are wrong not to do so.

Do repeats generally have to do with symmetry or logic? I think that we often assume that they do or that they should. If the allemande of a given suite is A-A-B-B, then presumably the courante and the other movements will also be. Otherwise there would be an imbalance. When playing the above-mentioned Bach variations, I have been aware of a pull either to omit the extra repeats in the two variations that have them or to add repeats to all of the “B” sections. And this would be in apparent direct contravention of the wishes of the most august of composers. I once had a student who was working on the Goldberg Variations, and who proposed to omit almost all of the repeats, but to take one pair of repeats, namely in Variation VII. He had an interesting registration idea for that movement, which required four rather than two sections. I have to admit that this bothered me: no logic or symmetry, just going with an aesthetic choice. It is just an interesting light on what I (we?) sometimes want out of repeats.

To play the repeat or not, that is the question.

This brings us to something pretty concrete and specific: “should I take the repeats?” Essentially we never find ourselves wanting to omit any part of a piece that is not a repeat. I have never had a student ask me about a through-composed piece, “should I or should I not play measures 9–16?” or anything like that. Even though we accept repeats, we clearly do not quite accept them. That is, we do not accord the notes indicated by repeat signs absolutely all of the status that we give to other notes. We give this higher status to passages that are a lot like, or exactly like, earlier passages, including actual da capos. Only when a few measures of material are repeated right away, and with such exactness that it can be notated by a repeat sign, do we consider it an issue whether to play those notes or not. In fact, we likely think that way only if the repeat is actually notated by a repeat sign. Once in a while a repeated passage, a literal, full repeat, is written out. In such a case I do not often hear a student, or anyone, suggesting cutting out the similar bits.

For an interesting side note, in his notes for his 1950s recording of Scarlatti sonatas for Columbia, Ralph Kirkpatrick said of his not taking the repeats in the pieces, almost all of them in binary form with repeats indicated, that if listeners wanted to hear them again, they could play them again on the record! This probably indicates as much about his skeptical attitude towards recording as it does anything about his approach to repeats.

As for myself, I recognize a strong tendency to want to take all repeats, in whatever way they are indicated by the composer. I think that this has to do in part with my having spent my life absorbing the ethos of “the composer is always right.” That ethos has grown pretty steadily over the last couple of centuries and has found one expression in certain aspects of the early music movement. And I believe there is a certain logic to that. If a composer put in repeats, why shouldn’t it just be routine to play them? I have this stubborn feeling that there really is not any reason to single those notes out for omission. I also recognize that this could be a different story for pieces that were written in a style that made repeats a matter of routine—early dance movements, say—than for pieces written with no assumptions about repeats—nineteenth-century sonatas, for example—as to which composers made choices about repeats on a custom basis.

I also notice that, of course, repeats make a piece longer. That may seem trivially obvious, but the magnitude of a piece in time is a valid part of its aesthetic. The difference in length between a Haydn or Mozart symphony and a Mahler or Bruckner symphony is of course not even close to the whole difference. But it is not meaningless or insignificant either. If you take no repeats in one of the Bach French suites, it becomes a short piece. There is at least one recording of all six of those pieces, by Thurston Dart from 1961, that managed to fit the whole collection onto one LP. Independent of anything about the playing or the instrument (clavichord) or the recorded sound, that presentation of the whole collection as being that short feels different from a recording twice as long that would have had to occupy at least two LPs. (I say at least because it was a rather long LP.)

Making a piece long by repeating each of its parts is not the same thing as making a piece long by composing a longer amount of new material. And one thread over the long arc of western classical music has been to look for ways to create bigger structures without literal repetition. But in making a choice about whether to take repeats or not, the effect on overall length is part of the equation.

In keeping with some of my thoughts above, I do suspect that when I hear a performance of a piece that features repeats as part of the structure, but are ignored, I usually feel disappointed by the time the second section appears. If the suspense created by the repetition has not been allowed to build, then the resolution of that suspense through moving on to something new cannot have the power that it was meant to have.

To be continued.

The Art of the Fugue, part 7

I begin this column with an account of something that happened in a recent lesson, something surprisingly germane, by complete coincidence, to what I had already been planning to write about this month. I notice recently that between when I finish one column and when I am due to start writing the next, something often crosses my path, completely by chance, that is relevant to what is coming next in the column. Sometimes it provides an example, other times an interesting sidelight. Often it essentially ratifies and strengthens what I had been planning to write; yet sometimes it suggests a bit of a change.

Before I get to my story, it occurs to me that the fact that I encounter these coincidences as often as I do is itself a commentary on the philosophy and purpose of the column. My hypothesis is that everything is relevant to performing music and to teaching others about music and performance. I believe everything we encounter in life might be potentially fruitful for our music and our teaching.

This series of columns on The Art of the Fugue is meant to be an account of my working process. Part of that working process is to be aware of anything that might lead to an interesting thought about the piece or the performance. If we notice things and assume that they will be interesting and relevant, we cannot lose. If they are relevant, the gain from having noticed them is clear and describable; if they are not, the thought process sparked by noticing them is still rewarding.

The teacher-student experience

A week or so ago a harpsichord student of mine brought up The Goldberg Variations, partly as a step in thinking about whether to work on the piece, partly to ask a few questions. What is the overall structure of the piece? Did the composer write the movements in the order in which we see them? Does the order matter in performance? If so, why? Is it about individual transitions or something else? We talked about all of this a bit, mentioning “official” sources of structure and continuity. These start with the basic fact that each variation shares some version of the same underlying harmonic pattern and includes the phenomenon of every third variation’s being a canon. We talked about the formal layout of the canons, in which each one is a canon at a one-greater interval—Variation 3 a canon at the unison, Variation 6 at the second, Variation 9 at the third, and so on, up to Variation 27, which is a canon at the interval of a ninth. We discussed, but did not resolve the question of whether this formal layout is palpably meaningful to a listener, or is just meaningful as a formality.

Then we tried a live-action version of something similar to an experiment I described in a recent column, about electronic listening. I played a movement, or the last few lines of one, and my student turned some pages at random. I then started the movement on the new page, randomly chosen, after the one that I had just completed. We did not go through the whole piece in this fashion—not enough time, and other things to do. But we got a good sample of what it felt like to move from one variation to another when that transition is neither what the composer had in mind nor what we are used to.

The result was that each transition sounded fine (“worked”, nothing jarring) but also sounded odd. The oddness came from the confounding of fixed expectations, fixed by years (or for me, decades) of listening. It is hard or impossible to sort out what each of those transitions would have sounded like to someone who had never heard the piece before. I strongly suspect that they would each have been just fine, but I cannot be sure of that. This was a reminder that structure comes in part from expectation. The kind of expectation that comes simply from having heard the work before can be very powerful. But I assume (or perhaps I hope) that expectations created intrinsically by the music are even more powerful.

Sources of overall structure in The Art of the Fugue

It is my working hypothesis that in The Art of the Fugue there are two main sources of overall structure. The first is the nature of the theme itself and the way that it sets up other themes and musical gestures to be meaningful. The second is the recurrence of specific themes. I mentioned both of these in my 1985 program notes that were reprinted here in two recent columns. But I want to delve into both of them in more detail in this column and in next month’s. Of these two ideas, the recurrence of specific themes is, perhaps, the more clear-cut. It is not remotely unusual to include as a source of continuity and of structure. This includes all of the uses of the main theme and its variants: the top level of what we get by contrapuntal analysis. But there is also more below the surface.

My thoughts about the nature of The Art of the Fugue theme are perhaps more speculative. That theme starts on a note, goes up a perfect fifth, goes down a major third, then down a minor third, then down a semitone. After that it goes up by that same semitone, and up and down by step until it ends. Every musical theme, of course, has some pattern of intervals that I or anyone could describe in words. What is striking to me about this theme is how comprehensively, systematically, almost encyclopedically, it lays out all of the intervals that define tonal music. They occur in what could plausibly be considered their order of importance, there is essentially no redundancy: almost no interval is repeated until each interval has been heard (the exception is the semitone), and the inversions of intervals are assumed rather than stated.

My own experience as a listener has been that throughout the piece I hear any interval as a reference to this theme. This starts right away, as soon as there is anything to hear other then the theme itself. The scale notes that make up the counterpoint to the second entry of the theme at measure 5 fill in the opening interval of the theme itself (Example 1).

Does a listener hear it this way? Does a listener spontaneously think, “that is that same theme” or “that is a reference to that same theme?” I believe I do, and that I began to do so after repeated listening years ago, before I thought that I might have any idea why.

The chromatic countersubject in Contrapunctus III seems to arise out of that original semitone that is the interval from the fourth note to the fifth note of the opening theme. The leaping thirds that are one of the characteristic gestures of Contrapunctus IV seem to answer the thirds that make up measure 2 of the theme. Contrapunctus V plays around further with the idea of the third. First of all, when the theme comes in the second time, it is a third away from the note that accompanies it. (In Contrapuncti I–IV, this has always been the interval of a fifth.) Second, this movement contains a pervasive gesture that is the interval of a third filled in by step, and there are also a lot of parallel thirds!

The thirty-second-note flourish that pervades Contrapunctus VI, and that is a principal justification of the heading of this movement as being “in French Style,” sounds like a reference to the last four notes of the opening theme. The mordent-like figure that enters Contrapunctus VII in measure 3 is related to the semitone-based gesture in the opening theme going (in Contrapunctus I) from the end of measure 2 into measure 3. For me, the nature of the opening theme itself turns the whole piece into a tapestry of familiar, known, referential themes and gestures.

A complement to this is the gradual introduction of the octave into the picture. The opening subject, while displaying all of the discrete intervals of its tonal language, almost pointedly fails to encompass an octave. However, the first thing that happens after the filled-in reference to the opening interval that I pointed out in Example 1 is a drop of an octave: the first octave in the piece. When the second voice to enter (the soprano voice) finishes its statement of the fugue subject, it immediately makes an octave leap: one not in any way required by the counterpoint or harmony (Example 2).

Then, later on, whereas each of the first seven contrapuncti begins with the interval of either a fifth or a fourth, Contrapunctus VIII beings with a step, a very striking change. While the compass of the theme of each of the first seven movements has been never more than a sixth, the compass of the opening subject of Contrapunctus VII is a tenth, but one that could also be seen as outlining an octave. (The first and last notes of the subject are an octave apart, and the note that creates the tenth is off the beat and somewhat ornamental.) Then Contrapunctus IX begins with the brand-new gesture of a leap of an octave. The compass of this subject is a ninth, and that of the next movement a tenth, so that we are in a region of expanded compass of themes.

All of this is enough to make me feel that it makes sense to say that the subject or fundamental building block of The Art of the Fugue is not “the AOTF fugue subject” but the very concept of the melodic interval. This in itself does not create structure in the sense of linear shape. But it establishes the conditions for the creation of that structure.

The repetition, recurrence, and referencing of identifiable individual themes is the foundation of counterpoint, and probably the major defined source of contrapuntal structure. At the level of “this theme is the inversion of that theme” or “this theme is the same as that theme, but with altered rhythm,” this is fundamental and definitional. And there is an abundance of that sort of correspondence in The Art of the Fugue. What interests me beyond that is the more fleeting or hidden thematic connections. There are quite a few of these in the piece. The phenomenon that I have tried to describe above (the tendency of this piece to permit any interval, even in an isolated occurrence, to seem meaningfully thematic) is a background against which it becomes clear, I think, that small, individual thematic connections are meaningful to a listener and almost certainly intentional on the part of the composer. Some of the ones that stand out to me are as follows:

This seems to be an isolated event in the bass line in measure 35 of Contrapunctus IV. The notes seem like a filler in a kind of quasi-cadence (Example 3).

All of the eighth-note motion in the movement prior to this has been by step, as is almost all of it after. This is then picked up in Contrapunctus X (Example 4). The figure that enters in the tenor voice at the beginning of this example is passed back and forth among all of the voices and then culminates in an exact statement (at a different pitch level) of the theme from Contrapunctus IV cited above.

The beginning of the main theme of Contrapunctus X (Example 5) is referenced in passing in the bass voice near the end of Contrapunctus XI (Example 6) and again in the middle of the final movement (Example 7).

That latter one is an “answer” rather than a literal quoting of the motif. Are these parallels valid? It could certainly be argued that the fragments of themes that I am pointing to here are just routine cadential figures or other tropes that are too non-specific to be meaningful. I do not hear them that way. Again, I think that the structure of The Art of the Fugue subject itself predisposes any motivic entity to be significant, and the ways in which some of these fleeting motifs are deployed seems too systematic to be non-intentional.

As I said above, I think that there is more to be gained by assuming that correspondences are real than by resisting hearing them that way. Next month I will bring forward several more examples—perhaps even more important to the actual overall structure of the work as a whole—and talk more expressly about that structure.

To be continued.