On Teaching: The Art of the Fugue, part 6

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.

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.

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.

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.

The Art of the Fugue, part 4

Over the next two months, I will continue my analysis of Johann Sebastian Bach’s The Art of the Fugue, BWV 1080, with a focus on my own experience of learning the piece. Following that, I will expound on the piece itself: namely analysis, form, history, and more. The later stages of the discussion will refer back to the long program notes I originally wrote in 1985 that formed the content of the July and August columns. This will include looking at some of what I wrote there in greater detail and from various points of view.

The ideas constituting this month’s column are set down in no particular order—not quite as a stream-of-consciousness narrative, but with some of that miscellaneous quality, somewhat reflective of how I learn a piece as monumental as The Art of Fugue. Of course, there is a big part of that process that is highly structured, especially the act of practicing.

The Art of the Fugue is monumentally important to me. I care about it more than any other piece of music, which is not a statement I make lightly. I have experienced the work, both as a listener and as a performer, While performing, it has a level of emotional power that is both deeply satisfying and difficult to live with. It is a known phenomenon that once in a while a person simply cannot listen to some particular piece because the emotional effect is too strong, too disturbing. I have a similar experience with The Art of the Fugue.

I can remember once hearing from a musician that he could not listen to the Bach Saint Matthew Passion because it was overwhelmingly emotional—but that he could and did participate in performing it. Being involved that way did not weaken his emotional force. Rather, it gave it somewhere to go that made it manageable. That is different from my experience with The Art of the Fugue. I find the piece more intense and powerful—and that intensity and power more difficult to assimilate—when playing it than when listening to it.

I do not think it is that I “like” my own performance better than the ones I might listen to. That is, in itself, a complicated concept. I make the interpretive/rhetorical choices that I want to make, whereas other performers make the choices that they want to make. So my own playing is at least striving to be that which I would find most powerful. It does not always succeed. Consequently, ideas that are not the ones that I have thought of myself can end up striking me as powerful.

I suspect this is not about liking interpretive choices or a particular performance. It may be connected with another aspect of my relationship to The Art of the Fugue. I wrote in the column from June 2018 that I experience a kind of impersonalized, societal superego looking over my shoulder while I perform with harpsichord performance than I do with organ performance. This is not that I necessarily think that my organ playing is more successful than, or better than, my harpsichord playing. But for some complex set of psychological reasons I have a more settled sense of ownership in my organ playing. In a similar way I seem to be discovering that I have an extremely solid, even unshakeable feeling of ownership in this piece. That sense feels exactly the same, in nature and in strength, whether I am playing it on harpsichord or organ. I intend to use that sameness to overcome some of the weakness in the feeling of ownership that I sometimes have at the harpsichord. In other words, some of the strengths of the way that I feel about The Art of the Fugue will, after I experience performing it on the harpsichord, be transferable to other harpsichord performance situations.

My early history with The Art of the Fugue

The first time I performed The Art of the Fugue was May 8, 1985, on the Fisk organ at Westminster Choir College, Princeton, New Jersey. This was the first of my two graduate recitals for the Master of Music degree in organ performance. I presented two recitals; the school’s policy stated that one could play either one recital from memory or two with music. It was easy for me to choose the latter. On the day of my first lesson in January 1985, I put The Art of the Fugue score up on the music desk before my teacher Eugene Roan came into the room, and then with some fanfare announced to him that I wanted to play it as a recital. He agreed immediately, even though it was clearly a stretch for me to learn it within the projected time! (I was 27 years old then, a late-bloomer as a player.)

This was an important step in the evolution of my belief that everyone should be allowed and encouraged to work on that which they find the most deeply important, engaging, and exciting. An interesting difference exists, however, between the project that we began that January and the normal approach that I take with my students as to their repertoire choices. Normally, if a student wants to work on something that is a “stretch,” I make it clear that I am very happy to oblige. But I also note that one key to making that process work is that there be as little time pressure as possible to allow the process to unfold naturally.

In the case of my first pass at The Art of the Fugue, we knew very well that we did not have any time flexibility, and the piece is long and difficult. There are passages that are still, at a minimum, tied for being the most challenging music that I have ever tried to learn for performance. So it was a bit of a gamble and a high-wire act. One consequence of this was that I spent that late winter and early spring doing something that I had never done before and have not done since: actual ten-hour practice days. I was taught up until then that it was counterproductive to practice for more than four hours a day. For those three months I averaged something like eight hours, five or six days a week, with some of those ten-hour days thrown in.

This was grueling and tiring, physically and mentally. I have never wanted to do anything like that again. But simultaneously, it was fun, exhilarating, and clearly something that could become addictive, even though it seems not to have done so for me. It also was effective. I learned the piece: not perfectly, but well enough to give a performance that made the people glad they were present. (That concert was not recorded. I am almost certain that many of the tempos were slower than what I would now want, and that was in part out of necessity. I also remember there being plenty of wrong notes.)

I believe that the full-immersion approach to the initial learning of the piece left me in a position to revisit it later with a kind of serenity and comfort that feels like quite a luxury when dealing with something so imposing. That practicing experience was, among other things, kind of mind-bending. I felt sort of spaced out, vertiginous, in another world much of the time. I now wonder whether my sense of bonding with the piece comes in part from my having encountered the nitty-gritty of learning it for the first time. Though a lot of effort was involved, it was also sort of as if I had learned it in a dream; therefore, it felt in a way like something that had been magically bestowed on me rather than something I had done.

Instrumentation in The Art of the Fugue

The Art of the Fugue was not designated by its composer as written for any particular instrument or combination of instruments. For my purposes in planning out a performance, this is liberating. We are all very aware of transcription as a kind of thing in itself. If I take the notes of a Beethoven string quartet and try to execute them on the organ, that is a transcription. Transcription has been an important aspect of organ literature for ages. In some way—which is not rigorously defined—transcription is seen as different from other performance. (As a personal confession: part of my own frustration with the common practice of performing harpsichord music on the piano is not that it is done, but that it is never categorized as “transcription.”) I have a lot of faith in composers’ abilities to know what they are doing with sonority, and I have a preoccupation with shaping music and performance to sonority, so I have never been that interested in playing transcriptions myself.

But what is or is not transcription with The Art of the Fugue? Neither a harpsichord performance nor an organ performance can fall into that category. How about a clavichord performance? Bach never specified clavichord in so many words for any piece of his, whereas he did for organ and harpsichord. How about a performance by an ensemble of any instruments that the composer could have known? There is a fair amount of reason to assume that he had keyboard performance in mind, but it is not proven beyond a reasonable doubt. What about instruments that the composer could not have known?

Even though we care about what is or is not a transcription, it is not really important to know how to answer these questions. I enjoy knowing that the various ways that intrigue me to perform the piece all have similar claims to being “valid,” while each one has its own light to shed on the work. The ways of distributing the piece on instruments that interest me the most are the following:

1) on organ, played “like organ music.” That is a deliberately silly way of putting it, but what I mean is with ample pedal, by and large putting bass lines in the pedal, typical of Bach’s other organ music. One feature of this approach is that it allows the three-voice mirror fugues to be played in trio-sonata texture. In some other movements, the distribution of the four voices over two hands and feet enables the independent motion of the voices to be especially clear.

2) on organ, mostly or entirely manuals. This approach opens up the interesting idea of playing on a chamber organ or trying out lighter textures.

3) on harpsichord. Part of the interest for me right now of this very normal, obvious, and mainstream approach is that I have never done it.

4) on two harpsichords. For several years about ten years ago, my occasional student and current colleague George Hazelrigg and I performed and recorded The Art of the Fugue in a thoroughgoing arrangement for two harpsichords. That is, every movement was played by two instruments, usually with each of the four voices on a different manual. This provided an extraordinary variety of colors, but all within the landscape of colors that the composer knew. It made the note playing simpler for each performer, but introduced the challenge of chamber-music-like coordination.

It is fascinating to me that in the entire Art of the Fugue there is exactly one note that is unplayable on the organ (because of compass) and one spot that is unplayable by one performer on the harpsichord (because of hand span). Since there are plenty of arguments in favor of playing the work on either of those instruments, it almost seems like he is teasing us!

Since I have played this work on the organ frequently in the past, learning it and playing it on the harpsichord is the first priority for the current project. That is true both in that, in a pinch, it is more important as a project for me and in the sense that I plan to do it chronologically first. However the real point is to see how it feels to have both performances in my fingers and feet simultaneously and to try to get comfortable playing it one way one day and the other way the next day or soon thereafter. There are two main components to this: getting comfortable with the differences in sonority and touch between the two instruments and the interpretive/rhetorical differences that these make necessary, and getting used to playing some notes now in the pedal and later in the hands.

In one of my first columns in The Diapason, addressing the question of why playing manuals-only is often considered easier, I wrote “ideally, the more resources one can bring to bear on playing a piece—like ten fingers and two feet rather that ten fingers alone—the easier it should be.” Working on The Art of the Fugue simultaneously with pedals and without is a good test of this. Often the fingerings required to play all four voices of a four-voice movement are extremely complex. The gain in out-and-out easiness created by only having to finger the three upper voices is considerable. It is also usually meaningfully easier to make the voices seem clear with this lighter load. On the other hand, the bass lines themselves, while most are amply playable by the feet, are also often extremely challenging. Both sides of the equation are heightened in intensity, and there is the matter of keeping both approaches fresh and reliable at the same time. Will there be moments at the organ when the outer part of my left hand inadvertently starts to play the pedal line? Will there be moments at the harpsichord when the same outer part of my left hand drops out, relying on a pedal keyboard that is simply not there?

I close this month with a couple of stray thoughts. I notice reading through the piece these last months that I feel significantly less connected with Contrapunctus II than with any of the others. That certainly does not mean that I do not like it. I like it a lot, as I do the whole piece. Maybe just a tiny bit less. And, as a practical matter, I have a much less well-developed sense of what I want to do with it than I do with any other movement. It is the one that begins with the version of the theme seen in Example 1.

And I have also noticed that when a fragment of The Art of the Fugue starts going through my head, more often than not it is the opening of the long and imposing final movement. I do not know why this is the case, but I just want to notice and muse about all such things.

To be continued.

Gavin Black is director of the Princeton Early Keyboard Center, Princeton, New Jersey.

The toccata principle

Studying J. S. Bach’s The Art of the Fugue inevitably leads to thinking about form. Whatever lens you view it through, the formal shape of that piece is important to its impact. Some of the qualities of abstraction that have been ascribed to the work may encourage us to focus too much on form or to attribute to form an even larger role in shaping the impact of the work than it really has. Paradoxically, I have thought recently about a formal principle that is very different from anything that is found in The Art of the Fugue. It stands almost opposed to it. 

I call this the toccata principle. This principle of shape or form is a bit elusive to describe because it is not “a form” as such, but rather a particular way of using contrast and continuity. It is a principle that can shape a piece and be responsible for creating form and structure. It is found in pieces that are constructed largely through other means. I have a feeling that looking for this principle in places where it might not be evident on the surface can help illuminate what is happening rhetorically in many situations.

There are elements of music—pieces, movements, passages—that are constructed according to what seems like a consistent evolution. Something happens at the beginning, it continues, and when it changes it does so according to some sort of logic. The texture does not change drastically or very often, and when it does change, the change is not jarring. This is nothing rare or arcane: it is by far the norm or a common form found throughout organ repertoire and in classical music in general. Each movement of The Art of the Fugue fits this description. So do the Bach trio sonata movements, the vast majority of his fugues and his chorale preludes, most Mozart concerto or sonata movements, and much of the output of Brahms and Bruckner. 

A different sort of construction occurs when a piece (or movement or passage) is created out of short elements of music that are very different from one another, making an overall shape as much out of contrast as out of continuity. This is the principle according to which most of Frescobaldi’s toccatas were clearly and explicitly constructed. This is why I tend to use “toccata” as a shorthand or tag for this sort of construction. This principle, however, also pervades much of Frescobaldi’s output that was not given the title “toccata.” It was picked up by, among others, Frescobaldi’s pupil Froberger, who was probably responsible for transmitting an awareness of this technique to a wide swath of the musical world north of the Alps. Froberger was widely traveled and quite influential. The North German organ praeludium grew out of this form.

Naming pieces

One of the things that I remember hearing in classes, lessons, and hallways during graduate school years was that a “Praeludium” in the Buxtehude, Lübeck, or Bruhns sense was not a “Prelude and Fugue,” at least not in the Well-Tempered Clavier or Mendelssohn or Shostakovich sense. At the time this felt like kind of a new idea. Some pieces by Buxtehude and others that were clearly in many short sections (some contrapuntal and some not) and the manuscripts that were titled “Praeludium” or “Toccata” had, according to then-modern tradition, been re-titled “Prelude and Fugue.” This in turn led to an often-futile search for the section that was “the fugue,” which was distinct from “the prelude.”

One way to frame the distinction between the Frescobaldi/Froberger/Buxtehude toccata or praeludium and the WTC-type prelude and fugue is that the latter is a piece in two movements, each often quite unified, whereas the former is a piece in one movement but with many sections. As I wrote above, the continuously spun out sort of musical unit often coincides with what we call a movement. This is almost circular or a matter of agreed-upon definition. If a piece starts and unfolds in a unified manner with logical development and then ends with a cadence and a double bar, we will consider this a movement, unless it is the entire work. It is easy to say that Bach’s Prelude and Fugue in E Minor, BWV 548, for example, is a piece in two movements. That would be evident to a listener who had never heard the piece, or heard of it, and had never seen the layout of the printed music.

In a piece that is constructed from contrasting sections, the contrasts might be along some of the following lines: contrapuntal versus non-contrapuntal; regular in meter versus rhythmically static, recitative-like, irregular, or disjunct; slow versus fast; using dissonance in a regular, prepared, and resolved manner versus using dissonance for immediate or shocking effect; somewhat vaguely: harmonically lush and compelling versus harmonically bare and tentative; unified within the section as to texture (in the sense of normal prevailing number of voices or notes) versus irregular or varied within the section as to texture (for example, chords interspersed with scales); major versus minor; ending with a cadence versus ending abruptly; and more.

In the first toccata of Frescobaldi’s Second Book of Toccatas and Partitas (1627), there are eleven sections. This is in a piece that takes about four minutes to play. The opening section consists of chords, trills, and scale passages; the second contains a bit of imitative counterpoint in which the point of imitation in sixteenth-notes is accompanied by quarter-note chords as it migrates from voice to voice; the next section is composed of all dissonance and written-out trills; the fourth is again contrapuntal, but with more rhythmic variety in the voices; and so on. The piece ends with a long, rhythmically free cadential section, prior to which is a sort of jig fugue that almost could have been written by Buxtehude or Pachelbel. My purpose here is not to give a very thorough analysis of the piece, but to demonstrate that the sections are short, on average, and clearly contrast with one another.  

Buxtehude’s Praeludium in C Major, BuxWV 137, is one that I tried to learn in my very earliest days playing the organ. It was known to me in those days as Prelude, Fugue, and Ciacona. This made some sense as far as the fugue and ciacona were concerned: the fourth section of the piece is in imitative counterpoint, quite thoroughgoing, and it makes sense to call it a fugue; the seventh and penultimate section is manifestly a ciacona. But where’s the prelude? There are three quite distinct sections preceding the fugue: together they could be the prelude, I suppose. But they are not one coherent whole. The distinction between the opening section and the second section is as crisp as that between the part before the fugue and throughout the fugue. Then what of the sections between the fugue and the ciacona? In order for this work to have an accurate and convincing name that is a kind of blow-by-blow description, the name would have to be Prelude, Fugue, Interlude, Ciacona, and Coda—or something like that. In fact, it is a praeludium in one movement with eight contrasting sections.

All of this about titles is not necessarily important, as I am sure that the more accurate names are now in general use. But this nomenclature does tend to put a sort of screen or filter between the player (or student) and the actual structure and rhetoric of the piece. What is most interesting to me about that structure is the notion that a certain kind of experience creates the need for a different experience, and that it is this need—played out in infinite detail—that creates shape. 

It is the skill or genius of the composer of such a piece to make the details meaningful. How much dissonance or static rhythm and of what kind creates the need for what kind of lush harmony or compelling, dance-like pulse? What does it mean for a passage of irregular, ever-changing texture to be followed by regular, imitative, maybe almost chatty counterpoint? This is independent of the sort of shape that is created by continuity or recurrence, that is, the kind of shape that is found in The Art of the Fugue and in much of the music that we play or hear.

My use of the word “toccata” to label this compositional approach comes, as I said, from my having first encountered it in the toccatas of Frescobaldi. But words serve as names of pieces when and how composers want them to, and it is important not to take those words to mean more than they mean. At a certain point in music history, the word “toccata” came to denote a piece that is outwardly virtuosic and fast. This has been known to cause people to assume that any piece with that name should be presumptively treated as virtuosic and fast. But the term simply did not mean that at all in the seventeenth century. Likewise, by the nineteenth century, the word did not have any flavor whatsoever of the sort of structure that I am talking about here. The Widor Toccata, for example, is in a form that is about as opposite to this as could be: a perpetuum mobile spun out of one compelling gesture that seemingly cannot be stopped! (Or that one doesn’t want to stop.)

Bach wrote several pieces that come down to us with the word “toccata” in the title. Seven of these are harpsichord toccatas, and six of these are arguably constructed in a Bachian version of what I am describing here. The seventh is clearly not: it is basically an Italian concerto, as much so as the Bach work that actually bears that name. Of the organ toccatas, the D Minor, BWV 565, is in this sort of form; the so-called “Dorian” is emphatically not; the big C-major Toccata, Adagio, and Fugue is, though the sections are dramatically longer than those of any corresponding Frescobaldi, Froberger, or Buxtehude piece; the F Major is probably not: it is sectional in its construction, but the sections display a lot of unity.

Not all of the pieces that Frescobaldi himself titled “Toccata” are in precisely this form, though most of them are. “Toccata VIII” from Second Book of Toccatas and Partitas is clearly different, and the toccatas from Fiori Musicali are mostly not constructed this way. Also, many works of Frescobaldi’s that are given names of contrapuntal forms—canzona, ricercar, etc.—are constructed according to this sort of sectional contrasting plan, usually with the contrapuntal sections longer than all the rest.

Why in particular do I believe that it is fruitful to share these ideas with students? It is extremely easy to gravitate toward surface continuity as a source of shape and direction in music and to try to use our understanding of that continuity to guide interpretive choices. This underlies the way I normally pick pieces apart and I believe represents a common approach. We want to know what comes back, and how different themes relate to one another. We use this to make certain decisions, starting with basics like shaping similar themes in similar ways. So I think that students do not often look for contrast, surface discontinuity, or abrupt, apparently illogical change, or they are reluctant to make differences noticeably different. The notion that some pieces will have a more convincing overall shape and greater emotional impact the more we let differences be really different is, maybe, counterintuitive. But it is both true and sometimes a useful corrective.

To come back very briefly to the somewhat speculative mode of some of my Art of the Fugue discussion, we want evident continuity in life. But in real life, though there is often a lot of continuity, we never know for sure what is going to happen when we next turn the corner or even as we keep walking straight! I suspect that the Frescobaldi and Froberger toccatas, though in a very easy-to-listen-to harmonic language, were in fact getting at some of the same sense of dislocation and questioning that is found in some nineteenth- and, even more, twentieth-century music. It is interesting that Bach used the sectional/fragmented/contrast-based approach much earlier in his career than later. Was this just his moving away from early models, or did it reflect something evolving in his approach to life?

And then there’s Beethoven.

There was a specific incident that kicked off the most recent chapter of my own exploration of the toccata principle. I was listening to Beethoven’s Fifth Symphony. This is a piece that it is very hard not to experience as a cliché. I had never disliked it, but I had never gotten as much power out of it as I do out of, for example, Beethoven’s seventh or eighth symphonies. I had probably always found it simultaneously stirring and a bit annoying. This time listening, though, I suddenly had the thought: “Oh! This is a Frescobaldi toccata!” And so it is. It is printed out in four movements. But those are not the real divisions. It is an overarching work with sections that have continuity, more thematic recurrence than Frescobaldi or Froberger, but that also have contrast and a sense of fragmentariness in spite of their length. 

I do not (yet?) have a rigorous measure-by-measure analysis of how this works, but I find it convincing, and it greatly enlivened the piece for me. I also suspect that Beethoven in particular used fragmentary contrast more than I (at least) had noticed. This is something that I want to continue to examine.