On Teaching: The Art of the Fugue, part 8

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.

Stories and conversation

In mid-March, when I last sat down to write a column, the current health crisis was at a relatively early and very uncertain stage. I wrote that I hoped that by the time that column appeared in The Diapason things would be much better. I sit here writing now a week or two after that last column appeared, and this one will not be read for nearly another six weeks. It seems accurate to say that the situation remains dire and that the sense of uncertainty remains as high as it was then. While society is slowly starting to reopen, we will not know the effects of this action for quite some time. This very morning there are hopeful headlines about a vaccine, but we have no idea whether that hope will pan out or, if so, what sort of timeframe this will take.

I still cannot consider it prudent to schedule concerts. I wrote in my March column (written in mid-January) that I did not have any concerts scheduled at all, a first in nearly thirty-five years. I stated that that was “odd: simultaneously peaceful and eerie.” Today it feels more eerie than peaceful: the latter has been partially replaced by impatience and the fear that it will never seem right to schedule events. Looking back, as of a couple of weeks ago I have not played in public for over a year. That arises out of a chain of mostly unrelated circumstances: first I kept my schedule clear for several months so that I could practice for planned performances of J. S. Bach’s The Art of the Fugue; then I had to deal with my shoulder surgery and recovery; then the current phase in the history of the world set in. The last time that I went more than a year without playing in public was prior to 1980. 

Over the last several weeks there has been a lot of discussion, much of it deeply anguished, about choirs and choral singing. This does not affect me directly at this point in my life except as a listener, though I know it is deeply affecting many of my friends and colleagues. In fact, it may be two years before widespread choral singing will be possible again. I hope very much that by the time you are reading this that hypothesis will have turned out to be overly pessimistic.

There is a lot of variation in how people react to this uncertainty when it comes to the parts of their lives and daily activities that are subject to discretion. Some colleagues are using their extra free time to learn new music or new skills—the technique required to work on new and unfamiliar repertoire or even a new instrument. Some are taking up new activities or hobbies—perhaps ones that they have always meant to pursue. So far, I have done none of the above. My reaction to the situation has been to put much of my motivation to tackling preexisting projects. I mentioned in my previous column that I needed “to take a deep breath.” At that point, early in this whole scenario, I felt that my students needed that as well, and that it was a good thing for all of us. Shortly after writing that, I did start to offer various forms of remote lessons or consultations to my students. However, I have not felt my own motivation returning, either to plunge back into practicing or to explore anything new. Most of what I have been doing has been “comfort food,” as we have been baking a fair amount of bread and cooking a bit more elaborately.

I am not certain why this is. It may be partly a direct reaction to the sadness and difficulty of what is happening. If so, it is not necessarily entirely a depressive reaction or a reaction of feeling indifferent. I suspect that in the face of so much tragedy right around me I am afraid that I will find the music that I might normally be playing too intense. That has been my reaction to the little bits of playing that I have done and also to much of the music that I have heard. Also, I have always had better practice habits when I have performances coming up. That impetus is gone for now. I do feel certain that the motivation will come back. But the main point is this: that any such reaction is okay. I am overjoyed that so many of my colleagues are, for example, posting videos of performances from their homes. That is generous and helpful. I have been an avid viewer and listener, and that is helping me get through certain days. However, I believe it is important that no one feels pressure to cope in ways that are unnatural. In general getting a lot done is more admired in society than not getting anything done. And I am confessing to embracing the latter, though just for now, and claiming that I am within my rights to do so. 

But if it is self-serving, it is not selfish since I hope very much to help persuade everyone to give themselves the same leeway, as much as they need. Doing the things that we have to do is enough as far as fulfilling obligations is concerned. 

At the same time, I have been thinking about counterpoint and The Art of the Fugue. It feels like the odd times in which we live are encouraging me to engage in ever more speculative thinking. Rather than indulging in the technical aspects of counterpoint, I have been pondering more about images and ideas around the concept of counterpoint. Ideally the images and ideas will inform the way that I think about the technicalities. 

One very powerful idea about counterpoint is that it is related to conversation. If two musical entities are engaged with one another, doing different things at the same time, it is natural for us to hear what is happening as analogous to human verbal conversation. This is not an idea of mine, but has been the subject of articles and books as well as informal discussion. It is intuitively convincing. When counterpoint is being produced by separate instruments the conversational aspect is enhanced by the visual and the conceptual: we see and are aware of a different source for each musical line, just as we see and are aware of each different speaker in a conversation. In vocal counterpoint, we see and hear something that is remarkably similar to conversation, down to the humanity of the sources of the sound and the expressions and gestures. At a keyboard instrument the conversational aspect is something that presumably arises solely from the sound. Visually, and often spatially, everything comes from pretty much the same place. The extent to which it is up to the performer and to performance choices to make the conversational aspect of the music convincing is not necessarily very different from the parallel concerns with ensemble counterpoint.

For the performer, one of the great strengths of conceptualizing counterpoint as conversation is that it brings home the need to make each line in and of itself an effective piece of communication—something that has “meaning” though not dictionary or visual-image based meaning. At a minimum this is psychologically helpful, even inspiring, for many performers. For me it serves as a reminder to behave as if every note matters. In conversation every word matters, in that it can be heard by someone and may affect that person. That does not mean that every word is serious, solemn, or weighty. Some are funny, light-hearted, rhetorical rather than meaning-laden. But they are all there and all have an effect.

I have a few caveats about counterpoint as conversation. For one thing, it seems important to me to remember that, as I just mentioned, music in itself does not have dictionary meaning, semantic, idea-based meaning, and that it does not mean anything that can be encapsulated in a visual image. It is liberating and powerful to accept that Example 1 means exactly what it says and nothing else. This freedom from word-like meaning gives a line of music the ability to do things that words cannot do and the flexibility to be used in ways that words are not used. 

Related to that is the first major difference between verbal conversation and musical contrapuntal conversation. In the latter, we not only allow but expect material to be used multiple times. Although the essence of counterpoint is found in two different things happening at the same time, it is habitual for identical or similar things to happen at different times. This can be recurrence, repetition, echoing, answering, returning, and so on. But all of these techniques play a minor role in anything like normal conversation and a limited though sometimes important role in poetry, drama, and literary narrative. They are pervasive and important in music.

In verbal conversation, we do not expect many voices to be sounding at the same time. We expect them to take turns and occasionally overlap, which is fascinating in verbal conversation. Sometimes, it functions to create continuity and an overall arc. At times it is an interruption, which can be a sign of enthusiasm and can constitute rudeness. It is common and normal for interruption to take the form of one person’s finishing another’s thought—not necessarily in the way that the first speaker would have finished it. It is not normal for two or more people simply to talk steadily at the same time as one another for a substantial amount of time. This would cease to be conversation. But it is the norm for musical contrapuntal conversation. 

With words, we do not expect to be able to follow even two let alone three or more lines of thought at the same time. With counterpoint, that is exactly what we expect to do: it is a major concept of the exercise. It is not necessarily easy, and it is not necessarily something at which we always fully succeed. It is almost certainly both common and unproblematic for some of that following to be subconscious or subliminal. People differ in the extent to which they are consciously, specifically aware of following and really parsing the separate lines of counterpoint as it goes by. And, of course, different performances of the same piece or passage can seem to make it easier or harder to follow in that way. (And interestingly different performances can seem different in that respect to different listeners.) I think that it is a pitfall of the counterpoint-as-conversation idea that it can tempt us to try to make the analogy fit even more closely than it naturally does. This might involve downplaying the significance of the simultaneity of lines or even denying that following multiple lines at once is possible. I have heard people suggest that the way we listen to counterpoint should fundamentally involve switching focus from one line to another, as we would presumably have to do if we were trying to listen to two or more people talk at the very same time. 

Questions of how many lines we can listen to simultaneously are complex. Does it vary from one person to another? If so, is that somehow intrinsic—or of life-long standing—or does it arise specifically from music-based training? Can almost everyone follow two voices? Can anyone really follow six? eight? forty? Do people mainly listen to or notice the beginnings of notes, or are the sustained portions of notes important as well? In counterpoint is one line ever more “important” than another, and, if so, what does that mean and what should a performer do about it? Whatever these questions are, I believe it is important not to let the speech analogy influence our answers to them, or how we frame them, more than it should.

Another concern about the conversation analogy is that musical conversational counterpoint is mostly experienced by listeners, whereas verbal conversation is fundamentally experienced by those who participate in it. We who love counterpoint love playing it. It is interesting to contemplate how much we function as listeners while we play and how much of our experience is the pure experience of playing. But the vast majority of music listening is done by listeners. Listening to a spoken conversation in which you have no part happens and is perfectly normal, but not the most usual or common.

The completely different model of counterpoint that has come to interest or even preoccupy me over the last few years is one that is harder to encapsulate in words: counterpoint in music is a model for the whole phenomenon of the existence of the universe. This model was suggested to me by some of my experience as a theater attendee.

Over the last several years I have attended quite a few theater events that are organized in what amounts to contrapuntal layers: different parts of the story going on in different or overlapping spaces, perhaps threads sometimes coming together in one space or passing near one another, sometimes remaining separate. Together they all add up to the complete story. Some such pieces that I have experienced are Sleep No More, Then She Fell, The Grand Paradise, Ghost Light, Here, Seeing You, and versions of Hamlet and A Midsummer Night’s Dream. 

I was initially puzzled by why I found this sort of story-telling so powerful. Events of this sort seem very much like closed worlds: nothing from the outside gets in or interferes. This helps the audience to concentrate and stay committed. It also means that the world built up inside the walls of the event has the chance to feel complete—it is temporarily defined as being all that there is, and it is structured according to its own content.

I realized after a while that the structure always felt, through a number of different styles and each time with a different story, like an analogy to the “real” world: layered and complex enough for that analogy to seem valid and emotionally convincing. 

At some point I realized that the experience of being at this sort of show reminded me strongly of closing my eyes and becoming totally absorbed in a piece of contrapuntal music. In such a piece of music there might be only three or four component lines; in a show such as the ones that I am talking about there might be any number of component storylines weaving their ways around one another. In the universe as a whole there are infinite numbers. But the analogy still seems to hold.

This image neither contradicts nor directly complements the conversation analogy. It is simply another angle and one that I along with some of my students have found particularly interesting and powerful.

It is my intention—uncertainties aside, for the moment—to return next month to some nitty-gritty motivic analysis of The Art of the Fugue, not without some speculation about the role of memory in creating structure.

The Art of the Fugue, Part 1

Before delving into the principal topic of this column, I must first briefly revisit the subject of the last two columns, which dealt with aspects of the practice of listening to music. Shortly after I finished the May column, I was in New York City for the day, and I happened to notice, walking along one of the avenues, some bins of used LPs outside an antique store. I had a few minutes to spare, so I started leafing through the boxes. Midway through I saw a record of Brahms’s First Symphony. This is a favorite piece of mine, and part of my program for that day was to hear a concert performance of it at Lincoln Center. I pulled it out to take a look, as I wanted to know who recorded it. But there was nothing: no orchestra name, no conductor, no date, no recording venue, no clues.

I had just written of my experience noticing that students and other listeners have a habit of seeking out recordings online and listening to them without noticing anything about who the performers are. I presented this as being a characteristic of the structure of modern listening technology and a strong and well-accepted modern ethos. But it is interesting to be reminded that it also is not a new concept. This Brahms LP, monaural as far as I could tell, is an artifact reflecting the view that it is perfectly acceptable to listen to a performance not only without noticing who is playing, but also without having any way to find out.

Some of the implications of this would be fascinating to explore at greater length, and I will write more about it at some point. When we listen to a performance, especially when we listen to the same one repeatedly, what do we feel about letting that particular way of performing the piece shape our way of defining it? Do we think about this consciously and give the performance permission consciously and deliberately to affect us in certain ways? The history of this has been more complicated than I was remembering when I touched on it before. That in turn ties in with questions of authenticity, which we tend to think of as being about composers, and authority, which can come from any number of places—writings, performances, teachers—and which can influence us with or without our being aware of it.

Questions concerning Bach’s The Art of the Fugue

For this month’s discussion, I turn to Johann Sebastian Bach’s The Art of the Fugue, BWV 1080. There are a myriad of issues surrounding this monumental opus that open windows into our thinking about authenticity and authority in particular, as well as many different aspects and dimensions of what we do as performers, listeners, students, and teachers. With its length, complexity, and importance in the arc of the work and career of Bach, crucial questions about the work are unanswered and perhaps unanswerable.

So, what is The Art of the Fugue?

It is a work written by Bach over the last decade or so of his life, consisting of many movements—about twenty, but that is one of the areas that can be looked at a number of different ways—each constructed contrapuntally, some as fugues and some as canons. The movements are all based to some extent and in some way on a particular theme. The piece was published shortly after Bach’s death in an engraved edition, and while Bach certainly composed the bulk of the music, the work was completed by others. There are also surviving earlier manuscripts of some but not all of the work.

The theme mentioned above is found in Example 1. The theme in this form opens the first movement, which is a four-voice fugue on this subject. The first movement is the only one to open with a simple statement of the theme in exactly this form and the only one that is based primarily on this form of the theme. The variants of the theme that form the basis of the other movements include inversions, diminutions and augmentations, rhythmic variations, and versions with added passing tones.

One question that intrigues me, and that I will broach here and come back to in the course of these articles about The Art of the Fugue, is, why this theme? One answer could be, why not? After all, Bach wrote fugues on a large number of different subjects and must have improvised fugues on many, many more. However, I think that it is worth interrogating the ways in which this theme in particular might have lent itself to the extended and varied treatment that constitutes this long work. The Art of the Fugue theme was not, as far as we know, or as far as I have ever heard, taken from somewhere else. (As, for example, the theme of A Musical Offering was, or as the themes of all chorale-based pieces are.) Bach wrote a number of other fugues on themes that are largely based on a minor triad, like this one. That is true of the subject of the fugue from the Fantasia and Fugue in G Minor, BWV 542, and, in an even more thoroughgoing way, of the stand-alone Fugue in G Minor, BWV 578. The Canzona in D Minor, BWV 588, is based on a subject that could in fact qualify as a variant of The Art of the Fugue theme (Example 2).

(If that piece were dropped into the middle of The Art of the Fugue it would be quite possible to justify it, at least as far as themes and motifs are concerned, as part of the work. It would seem an interesting variant that the semitone by which the subject departs from the confines of the perfect fifth is the one going up, whereas in the original subject it is the one going down, and that the two of those outline the notes that give the minor mode its harmonic flexibility or instability.)

I have heard or read suggestions that this theme or subject is so simple, basic, plain, that it is astonishing that Bach could construct a massive edifice upon it: that his ability to do so is a particular proof of the power of his genius. I do not disagree with that conclusion, in that it took a genius to create this work. However, I am not inclined to agree with the premise. It seems to me that constructing this theme was indeed part of the genius: that it is specifically and purposely designed to carry the weight of all that was developed out of it, and potentially more. I will come back to this later on.

That brings us to one of the most famous and important things about The Art of the Fugue: that it is incomplete. The movement we regard as the final one, while already the longest in the piece, breaks off in the middle of a measure. It is not a neat ending; it is not the end of a section—just an abrupt crashing from music into silence.

The reason that fugue is incomplete is that Bach died before he could finish it. Perhaps, he had it composed in his head. It seems likely that Bach or any composer would have had to have a fairly strong idea as to where a big contrapuntal structure such as this movement was going before venturing on starting it. It is a complicated fugue with multiple themes. But that does not mean that he had worked out the ending in detail.

In any case, we do not have the last measures of this movement, and therefore we do not have all of The Art of the Fugue. This creates a set of dilemmas for performers. Should one simply break off, playing all and only those notes that we have, allowing the “ending” to be jarring? Or should the performer or performers play one of the many endings that composers, scholars, and performers have composed over the last hundred years or so? Or should one look for a nice closing cadence as close as possible to where the piece currently ends and stop there? The fundamental fact is that none of these portrays Bach’s true intentions.

I have always favored the practice of ending abruptly. This preserves a certain “purity” of playing only Bach. It also forces us to confront in the most direct way the fact that things do not always go the way we want. That breaking off is beyond jarring: it can be deeply distressing and filled with anguish. It is an ending determined, as endings often are, not by any person but by death itself.

There is no way to maintain that this troubling breaking off is what Bach intended. I have had colleagues point out to me that by playing only and all of what we have on the page, we guarantee that we are doing something that Bach could not possibly have wanted. And every completion that has been attempted has been predicated on some analysis of what Bach might have been planning. Therefore any one of them has a chance at least of being similar in concept to what Bach would have envisioned. If nothing else, the length of the piece gets closer with each added measure to wherever it would have ended up if Bach had been able to finish it. And the abrupt breaking off is replaced by a normal ending. In between, the further working-out of the counterpoint might well be something like what Bach would have done. That is presumably the goal for those who have written such continuations, and each person has brought knowledge, care, and analysis to that project. But it is not Bach’s ending, and the piece is no longer just a Bach piece.

The first published edition, supervised by some of Bach’s surviving family and colleagues, chose a version of the third plan. The printed edition ends with the last solid chord, so to speak, before the spot where the manuscript source breaks off. This is an A-major chord in a piece in D-minor and indeed sounds like a dominant. It is a chord, and the rhythmic structure of what has preceded it gives it some solidity. But it does not sound stable, which raises an interesting question about authority. This is the approach apparently sanctioned by those closest to Bach. What authority do we give to that? What do we know or believe about how likely it was that they got that idea from J. S. Bach himself?

We tend to believe that this movement, an ostensible triple fugue that was very likely intended to end up as a quadruple fugue, was clearly meant to be the last section of the overall work. It certainly looks the part. However, we do not know for certain that if he had had several more years, Bach would not have added much more. Perhaps this triple (quadruple?) fugue would have ended up as a centerpiece rather than a culmination. Or perhaps it was really intended to be a centerpiece even without more movements. We do not have absolute certainly about the intended order of the movements, only very well-informed guesses.

Speaking of performance: we also do not know for certain what Bach’s intentions were for the performing forces that are brought to bear on this work. The surviving manuscript sources and the first edition say nothing about what the music is “for.” It is all in open score—four staves for a four-voice piece, three for a three-voice piece, and so on. There are no instrument names or any words on the pages of music talking about instrumentation or performance. There is a significant amount of evidence that this was probably intended to be a work for keyboard instruments, though that is not absolutely certain. And accepting that, it is less clear whether it was for harpsichord or for organ. There is a tantalizingly similar amount of suggestive evidence for each. Another real possibility is that the piece was intended equally for each of those two instruments. There was a long tradition of writing music that fits that profile, mostly from the generations before J. S. Bach. And there is a great deal about this piece that suggests that the composer wanted it to resonate in part as a throwback to those older generations.

The question of what instrument or instruments to use in playing a piece is crucially relevant to performance, to put it mildly. And since this series of columns is really about my own efforts to grapple with The Art of the Fugue as a performer, I will return to this in considerable detail.

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.

Further thoughts on
counterpoint II: a miscellany

I mentioned at the end of last month’s column that I have been rethinking some of my ideas and practices about teaching rhythm and counting. This is the result of recent experiences teaching students contrapuntal voices. I have noticed—more than I previously observed—that moving from an understanding of the rhythm of individual voices to an understanding of the way the rhythms of those voices fits together is not always easy or natural for everyone. It is helpful to address it directly, and I developed some new ideas about how to do so.

As outlined in my April 2012 column, my approach to teaching rhythm and counting involves ignoring time signatures, bar lines, and the “one-and-two-and” structure that we often employ. Rhythm is about ratios, and my experience has suggested that grappling with ratios directly—understanding that a dotted quarter note lasts as long as three eighth notes, that a half note lasts twice as long as a quarter note, and so on—is the best way for a student to become comfortable with rhythm. This is true for a beginner learning to understand rhythmic notation for the first time and also for a more experienced student who is having trouble with a particular rhythm or needs a refresher course. This has the advantage of being simple and completely accurate. I have seen much more trouble arise when students worry about whether a particular note is “on the ‘and’ of two” than I have seen clarity arising out of this way of describing rhythm.

This is an over-simplified summary of an approach that differs from other approaches in emphasis, since the learning of note ratios is always fundamental. This is not the place for a complete restatement of what I wrote six years ago, or to explain why I believe that it is a good approach. You can find it in the above-mentioned issue of The Diapason, which I have posted at http://gavinblack-baroque.com/Diapason column April 2012.pdf.

When a student needs to work out the rhythm of a passage, I suggest counting individual notes in relation to a suitable short note value. For example, if that short unit is the eighth note, then each eighth note is counted as “one,” each quarter note is counted “one-two,” each half note “one-two-three-four,” and so on. This does not involve denying that those beats also relate to positions in a measure, but it just deemphasizes that at first. In learning the rhythm of a single line or passage, the texture of which involves all of the notes, voices, chords, etc., being in the same rhythm as one another (say in the manner of many hymns), this approach is very successful.

Therefore, it is also successful when learning individual voices of what will be a contrapuntal texture, regardless of its eventual level of complexity. So the following two “voices” (the pitches are not important) could each be counted as indicated in Examples 1 and 2. As with any rhythmic counting, the numbers have to come at an even pace.

Each of these examples contains nineteen eighth notes, and the two of them fit together. But the sort of counting that I have suggested would be extraordinarily hard, if not impossible, to follow in Example 3.

The first-order solution is that the rhythm of each voice should be internalized before the voices are put together. This is a goal worth striving for in the practicing process. However it seems sensible to readmit traditional measure-based counting at this point.

I have purposely created an example that is not divided into measures. But it could be, like Example 4, which then allows for the regular (“one-and-two-and”) approach to counting.

I believe that it is a good idea for this sort of counting to be secondary. To the extent that working out the rhythm of each voice separately is something that must be approached consciously and deliberately, I think that my per-note way of counting is useful. In addition to being sensible and effective in itself, it can promote an awareness of the importance of the middle and ends of notes, whereas “one-and-two-and” counting, especially with counterpoint, can focus attention disproportionately on the beginnings of notes. As soon as the measure-based number for a note has been spoken or thought, the next step is to see what notes in other voices correspond to the next counting numbers. This can shift a player’s overall focus toward a more homophonic feeling.

Thinking about applying the normal measure-based templates to counting multi-voiced pieces has made me more open to other ways of keeping track of the rhythm of pieces that are not derived from a strict awareness of the voice structure. For example, there is net or overall rhythm. Sometimes, while the rhythm of each voice in a contrapuntal passage is different from all the others, the surface rhythm is quite simple. That rhythm might be thought of as a new note every eighth note.

Here are a few examples of writing in which this concept might make things easier. Example 5 is from Bach, Art of the Fugue, Contrapunctus 8. Example 6 is from Mendelssohn, Prelude and Fugue, op. 37, no. 1 (fugue). Example 7 is taken from Bach, Well-Tempered Clavier, Book II, Fugue #2.

In the last of these, the net rhythm is more complicated, but still simpler than each individual rhythm. It is interesting that the first three measures of each piece have the same overall surface rhythm, which in turn is the rhythm of the fugue subject. In the opening measure, the fugue subject is alone, in the second it is combined with a countersubject that does not change the surface rhythm, and in the third measure only the surface rhythm alludes to or quotes that subject.

If the printing is neatly aligned, it is possible to derive all of the rhythm from the surface rhythm by how things line up. Sometimes it is useful to picture a cursor line going steadily from left to right and to identify whatever it touches as what is to be played at that moment. But this should all be secondary, understood to be forms of assistance, not a primary way of understanding rhythm.

Some observations

Here are a few more observations about counterpoint, some of which may be a bit abstract:

It is natural to think of counterpoint as being something that is easily differentiable from harmony. After all, there is counterpoint that exists outside the norms and expectations of tonality or functional harmony. But for most of the music that we play on the organ and other keyboard instruments, pieces that are rigorously contrapuntal are also completely embedded in harmony. This is something essential about the meaning of the counterpoint itself: that is, the way that the flow of contrapuntal voices/melodies comes across to us, and therefore the way that the directionality of the different voices interact with one another function, is determined crucially by where the voices are moving harmonically.

For this discussion, I have invented an exercise. Try playing a piece of contrapuntal music with all but one of the voices transposed, and not each transposed by the same amount. The simplest case would be something like Example 8, from the opening of the first Bach Two-Part Invention.

This is going to sound discordant, to put it mildly. But that reaction or judgment is not necessary. The point is that it sounds radically different from the “real” version, although, analytically, a good deal of the counterpoint itself remains unchanged. A little bit of this exercise, possibly even just the amount that I have written out here can be eye-opening for a student. (It is not bad as an odd sort of sight-reading exercise either, and it is much harder with more than two voices.)

A bit of exposure to this oddity can also make the ears more sensitive to the ebb and flow of harmony-based motion or pressure in contrapuntal works. Even though the interaction of voices is always shaped in some way by the separate voices’ harmonic direction, the evident force of that phenomenon is stronger in some places, yet weaker in others. It is also more divergent in some places and more in sync in others. The places where the force of the harmonic direction of different voices is most in sync are cadences and moments that feel cadential.

Many years ago, probably when I was still in high school, an older friend of mine recounted something that a friend of hers had said. This friend once removed was an extremely erudite and thoughtful music listener, thinker about music, and keyboard player. The comment that was relayed to me was: “Helmut Walcha’s problem is that he is too focused on the counterpoint.” I immediately felt that I was learning something—not so much about music or playing or performance, but about attitudes toward musical work. The first thought that occurred to me was that Helmut Walcha was not the one with the “problem!” The phrase “Helmut Walcha’s problem is . . .” really meant, “The reason that I do not like Walcha’s playing is . . . .” That comment and my reaction to it at the time taught me that many people take their own reactions for objective truth, and that it made me uncomfortable. That in turn has shaped a great deal of my own approach to my development as a player and teacher.

What does that comment tell us about counterpoint? I have never thought that it was an apt description of anything I heard in Walcha’s playing. That may be in part because I grew up listening to him, and, at that time, his approach was my own default. But it has made me sensitive to the question of what it would mean to pay too much attention to counterpoint and too little to other things.

My guess is that this commentator was probably referring to Walcha’s relatively steady approach to rhythm, and also, just as importantly, to his focus on consistently phrasing subjects. (For what it is worth, he was also reacting to hearing recordings, not to any conversations with Walcha or to any direct knowledge of the roots of his approach.)

This leads to a host of questions:

Is it correct that relatively steady metronomic playing is associated with bringing out counterpoint clearly, whereas playing that is rhythmically free is associated with harmonically derived music, or with an approach to playing music that is more focused on harmony?

What about the business of “subject phrasing?” If a phrase, theme, or motif happens more than once in a piece, is it important to articulate and phrase it consistently? Does doing that enhance the extent to which the counterpoint seems like counterpoint?

Is it important, or is it good or bad, for the notes of different voices that are written ostensibly at the same time to happen at exactly the same time? Could there be something good or necessary about notes being somewhat staggered at times? The reason that I associate this question with the Walcha-related anecdote is that in his playing, notes do line up rhythmically to a great extent. Furthermore, the above-mentioned commenter believed that Walcha was too focused on counterpoint. But there are many players and theorists who believe that counterpoint is enhanced by staggering: it is difficult for the ears to follow separate lines if the notes of those lines coincide with one another exactly. Which of these is true? Does it depend in part on habits of listening? Is it really about clarity of counterpoint, or is it about some other aspect of style?

How does this relate to thoughts about basic counting in counterpoint expressed above? I suppose that I feel most interested in the notion that any melody including a contrapuntal voice has some logic by which it might be stretched out or otherwise inflected rhythmically. Also, two voices that occur at the same time might have different logic. They might not line up all the time, but not because the phenomenon of their not lining up should be sought out, rather, because the internal logic of each has them manifesting slightly different timing. This may be why I am more interested in counting individual voices that are somewhat removed from each other and from the template of measures. But then all voices have to be together enough in the end so that the piece is coherent.

I present all of this as questions or ideas that are interesting to think about or, more to the point, to engage with in conjunction with students. None of it is hard and fast; none of it represents answers or conclusions.

One last topic: notes that we play have overtones. On the organ some of those are the inherent overtones of the pipes, while some are the higher stops added for a particular purpose. Especially in the former category, there are often overtones that, while they blend in enough to make the sound coherent, can also be heard as faint separate notes. And the rather cool thing is this: different overtones are relatively audible on different notes. So in playing a theme you might hear the twelfth over the first note, the fifteenth over the second note, the twelfth again, then the seventeenth, and so on. In Example 9, in this melody, you might happen to hear the higher (gray) notes as very faint, audible accompaniment to the “official” theme.

This is a kind of shadow overtone counterpoint that is always present, at a greater or lesser degree of audibility, and is present separately in multiple contrapuntal voices when they combine.

Gavin Black is director of the Princeton Early Keyboard Center, Princeton, New Jersey. He can be reached by email at [email protected].

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.