On Teaching

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.

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 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.

Further thoughts about rhythm

In the very late 1960s and early 1970s, when I was first interested in the organ and listening to a lot of organ music, I had an LP recording of late-nineteenth-century French organ selections, pieces and excerpts of pieces by several composers, played by several different organists. It was a miscellany, a real sampler. All of the pieces were new to me then, as were the organs and the performers. The piece that impressed me most was the first movement of Charles-Marie Widor’s Sixth Symphony, played by Xavier Darasse. I should probably say that the passage that impressed me was the opening of that movement (Example 1). I remember quite clearly, fifty years later, that I listened to the opening of that track over and over again. I probably destroyed that part of the LP, but it helped to solidify my love for the organ; thus it was worth it!

Several weeks ago, as I decided to write a column or two focusing on various aspects of rhythm, that passage started going through my head again. It has scarcely been out of my head since, except when I have been listening to something else. Every passage of music has some relationship to the concept of rhythm. In spite of my early love for it, the first movement of that Widor symphony is not one that I have performed or analyzed. But thinking about it now and finally analyzing it a little bit, I think that there are all sorts of interesting things occurring with the rhythm of those first few measures. In particular, there are fascinating relationships between the rhetorical and theoretical aspects of rhythm, and this is part of what I address in this column.

The rhythm of the striking opening chords of the movement is demonstrated in Example 2. The rhythm of those powerful chords, and of the melody that is their treble line, is treated as a motive throughout the movement. But the surface rhythm, the rhythm of new notes, whatever voice or part of the texture they come from, is demonstrated in Example 3. That extra quarter note is a passing note in the pedal part, the bass line.

This is all straightforward, just a description of what is in the score. But it is fascinating to me that I hear two things going on at once, two different ways to describe the rhythm of this passage, both valid and meaningful. This seems to be a wrinkle in the relationship between counterpoint and rhythm. Lines of counterpoint, in the way that we usually conceive of them, are almost always characterized in part by having at least some rhythmic difference one to another. But here we have a passage that is seemingly homophonic. But the fact that the rhythm of that last quarter note of the second measure comes across as being on a lower level of importance rhythmically injects an element of counterpoint. This is subjective, but it is an interesting confirmation that the bass/pedal line is used over the next few measures to open the passage into more and more palpable counterpoint, as shown in Example 4.

If we do not know where notes are coming from rhetorically, then our sense of what the rhythm of a passage is can only be the surface rhythm. Turning that the other way around, if we notice hierarchies of rhythmic importance in different notes within a texture, that may be a clue as to some of what is going on rhetorically and contrapuntally in that passage.

For me, this is a new and slightly different way of looking at the relationship between rhythm and counterpoint. This means that I have not yet worked out how to help students apply it to pieces they are working on. There is a lot of music—from Byrd fantasias through Beatles songs, and including a lot of organ repertoire from all time and places—that is clearly not fully, rigorously contrapuntal, but in which counterpoint keeps breaking through. It is probably true that the vast majority of tonal music falls into this category. But nonetheless I have always had a problem feeling comfortable with it conceptually. Is it counterpoint or is it not? I understand that this is just the imposition of a rigid framework. But still, the concept that I am sketching out here seems to be able to help me get more comfortable with counterpoint flowing in and out of a piece or a passage.

My second answer to why this passage started going through my head has to do with the relationship between rhythm and rhythm as rhetoric. The rhythm of the notes at the beginning of this piece is well-defined and clear. But what is that rhythm doing? In a lot of circumstances, the rhythm of the first measure—just two half notes—would suggest a downbeat and an upbeat. But the way that I hear this first measure is something different and harder to describe. I hear each of those chords as a kind of world in itself, neither coming from anywhere rhythmically nor leading anywhere, but just rather insistently being. It is as if the second chord has so much gravity and weight that it refuses to be in a hierarchical relationship to the first chord or to the downbeat of the next measure. This is subjective, my way of hearing it. Assuming for the moment that this is correct or at least meaningful, is it about rhythm? A plausible and normal answer to that would be no. The rhythm is what it is, and everything else is a different aspect: affect, aesthetic, sonority, the push and pull of the harmony, interpretive choices, and so on. But it strikes me that it might be more interesting to expand the concept of rhythm to include more about what the rhythmic pulses and impulses are doing.

I believe that this concept or image could be interesting and helpful to students. It might provide a way of broadening the comfort zone of some students who are making choices about how to precisely execute rhythms on the page. If so, that would probably be through allowing choices about freedom of rhythm, bending and stretching the notated rhythm to feel more like an essential part of the rhythm itself. It might also provide me or any teacher with a way of helping the student to think about interpretive rhythmic choices without simply suggesting details of those choices to the student. I am now eager to work with a student on this piece!

In a way, I have put the cart before the horse, describing some ideas that occurred to me once I decided to write a column about a certain subject. As a result of one conversation with colleagues and a few interactions with students, I revisited a few of my ideas about rhythm, the relationship between notated rhythm and rhythm in practice, and certain practical matters about teaching rhythm. The latter include metronome use, counting, how to approach counting during slow practice, and a few other matters. The core of what I plan to write about is a concept that intrigues me: the possibility of deriving rhythm fundamentally, though only in part, from something other than the notation. I will talk about this at length in my next column.

I finish this column with a few more circumscribed yet fascinating points. The first is an anecdote from well over thirty years ago that has stayed with me all this time. I was then beginning to look for ways to participate in chamber music, and I connected with various colleagues as best I could. There was one player with whom I had a session or two of running through pieces and with whom I started to talk about giving concerts. As I came out of one such session, another colleague caught sight of me and said concerning my rehearsal partner, “You know, she really can’t count.” I did not know what to say, and I ended up with something like “Umm . . . ok,” and I did not let that comment affect my decision to go ahead and work with this fine and interesting musician. That comment was false in experience. This player had no more tendency to misread a rhythm or waver in rhythm or tempo than anyone else. But she was someone who often played purposely and quite freely. I learned a lot from her in this respect. I was left wondering what the real source of the uncalled-for carping criticism was. Did that other colleague have a bad experience with the person with whom I was working? Or misremembered or mistaken her for someone else? Or had it been a case of mistaking intentional, interpretive rhythmic freedom for an inability to count?

This latter idea always intrigues me and can be confounding. How do we know whether something that we hear (as to rhythm, for the purposes of this discussion) that departs from the most literally accurate is a mistake or a purposeful gesture? What different attitudes do we bring to such an event if it is one or the other? Is there a gray area in between? The attitude that we bring to mistakes that our students make is pretty clear—it is part of our job to point them out and help the student to understand what the problem is, how to correct it or to avoid similar things, and so on.

But what if the student says, “No, I meant to do that?” There is a strong pull to ask why and to accept that any deviation from what seems to be on the page is all right if there is a good reason. The discussions that arise from grappling with situations like this can be very fruitful indeed, but I have always thought that it is too restrictive. I hope that the concepts I will discuss next time can be used to help students understand what is going on rhythmically when they feel the pull to do something other than what seems to be the literal meaning of the notation but cannot express why. Furthermore, I hope that this can also help teachers address this situation with students without simply dictating outcomes.

I am reminded of a review that I read once of Joseph Szigeti’s recording of the Bach sonatas and partitas for violin. I apologize, as I have been unable to find this review, an unusual issue for the internet era. I am certain that it was written by B. H. Haggin. As best I remember, Haggin liked the recording and got a lot out of the playing and the pieces. But he also felt that the pieces themselves were not very interesting, that Szigeti, with his rhythmically free and idiosyncratic approach to Bach interpretation, had made great music out of pieces that were intrinsically dull exercises. I believe that this assessment was not as unexpected at that point in history as it would be now, though I do not agree with it. It seems to cast an interesting light on rhythm in performance. The reviewer’s perspective was that the player’s striking rhythmic choices were what we might call “wrong” in the sense that they were not really based on anything intrinsic to the music. They were imposed upon the music and thereby made the music great when it really was not. Is this a good situation or a bad one? How would we react if we thought we heard this happening with our students?

The last item that I mention here is an observation that I made while driving recently. I rolled down the window and shortly thereafter heard the sound of two cars passing me in quick succession going the other way. There were two whooshing sounds probably about 0.7 seconds apart. There had not been any cars ahead of them for a while, nor were there any following behind. So the two sounds were isolated. Although translated into the terms of musical rhythm this was just two notes out of any context, and it immediately evoked for me a very specific moment, namely the opening of Beethoven’s Sonata in E Minor for piano, opus 90 (Example 5).

The two car sounds seemed to deliver the rhythm of this opening gesture. Why and how? Two notes in a row is so commonplace in music that it is almost silly to evoke a specific instance of it as a thing in itself at all! Even if the two cars sounded clearly like an upbeat and a downbeat, that hardly narrows things down at all. And it cannot be harmony or sonority—what I heard had no pitch or harmony, and the sonority was that of a couple of cars. So what made that passage come into my head? I do not have an answer, but it adds to my sense that there is something more to rhythm than what we see notated on the page or can describe in words.

A special note: I will be playing selections from J. S. Bach’s The Art of the Fugue on harpsichord as part of the New York City concert series Midtown Concerts on Thursday, October 28, at 1:15 p.m. at the Church of the Transfiguration, 1 East 29th Street, New York, New York. I take the liberty of mentioning this since I have written extensively in these pages about my Art of the Fugue project. This will be the first public manifestation of that project and my first public concert in two-and-a-half years. If any readers can make it, I would of course be overjoyed to see you there

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].

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

Further thoughts about rhythm, part 2

Continuing from my September column, I offer here a few additional anecdotes and ideas relevant to rhythm and the teaching of rhythm. In my next column I will explore the question of how to teach rhythm or “counting” in a way that enables a student to connect those concepts as directly as possible with rhetoric and the student’s interpretive stance.

I begin by revisiting the anecdote from the last column about my colleague who, in the eyes of a particular third party, “couldn’t count.” Since I wrote that, I have had further relevant thoughts. I remember that as I walked into the rehearsal studio after that exchange, I was very sorry to have been told my colleague’s opinion. I did not want to approach my work with this fellow musician with any preconceptions. And while I certainly did not assume that the older colleague was right, I found it hard not to have a question layered on top of my focus during rehearsal. “Was that rhythm correct? Is this where I learn that she indeed cannot count?” That was distracting.

I wondered why he wanted me to focus my attention on her rhythmic deficiencies. Why did it matter in the overall picture? Why tell me as I headed into the rehearsal that “she can’t count” rather than that “she is an amazingly compelling performer?” This seems like a manifestation of bias in favor of that which can be quantified—that which seems more objective or safer to describe.

Since that day decades ago, I have become very aware that there is a strong pull in all sorts of areas of life to focus on things that can be measured and described in a way that is objective to some extent. It is a truism that in evaluating a competition, for example, or even just in reviewing a concert or a recording, it is relatively easier to note that a performance either does or does not get all the right notes, or that the rhythms are or are not all in strict accordance with the notation, or that the tempo is or is not the same as what the composer requested.

It is much more difficult to describe how expressive or moving a performance is. This is not a bad thing, and competition judges and reviewers certainly do not fail to grapple with the elusive side of things. But this has some bearing on teaching rhythm and counting. On paper, rhythm is one of the most objective matters about music—at least with our familiar rhythmic notation. Quarter notes are twice as long as eighth notes, etc. In a way, some of what is non-objective can even be described objectively. Certain dotted-note patterns, for example, are not meant to be what they apparently look like on the page, and we can often describe the ways that they differ from that presentation.

But how do we teach subtle variations in rhythms that look the same on paper? Is it an acceptable part of our understanding of rhythm for there to be such variations? If we think not, is that for musical reasons, or is it because of this pull toward the objective? If a quarter note is really always exactly twice as long as an eighth note, if all the eighth notes are really exactly the same as one another, what does that mean for a student or for how we teach? And if they are not, what does that mean? Is it possible that rhythmic notation means “these notes should be in any rhythmic relationship that would be expressed more closely this way than any other way?”

Another story from many years ago: I was coaching an amateur chamber music group—a violinist, a flautist, and a pianist who was exploring the harpsichord as part of this project. At that time, in my own work as a player I was exploring Sweelinck and beginning to discover some ideas about freedom of rhythm. At one point I played a segment of a Sweelinck toccata for the members of the group and drew their attention to a particular passage. This was one where I felt that the rhetorical force and expressiveness of the music could be enhanced by playing very freely. I had an approach to that passage that involved drawing out the development of harmonic tension and, when it was resolved, using timing to make it seem difficult to go on. That is a trite and inadequate description, but the point is that it called for freedom, and the musicians in the room found it very effective. I also played through the passage as written, and they found that almost embarrassingly boring and pointless, which was exactly what I intended to convey. So far, so good. But when we had finished this and were ready to get back to rehearsal, one of the musicians said, “Of course, you couldn’t do that with Bach.”

So, the question I had, and still have, is, “Why not?” Anyone may or may not appreciate the rhythmic choices performers exercise. In theory, there could be a plausible analysis of a Bach piece that concludes that free rhythm, or any particular approach to rhythm, might not be effective. And the question of what the composer himself would have thought always looms over our thinking about an issue like this. But none of that is what was meant by that remark that day. We discussed it, and the ensemble member specifically meant that since listeners’ expectations about Bach were pretty well formed already, unlike their expectations of Sweelinck, it would be imprudent to go too far in violating those expectations. To some extent, the way that music had been played and heard in then-recent decades had become part of the actual identity of that music. This seems to be another way in which something objective can gain a kind of privilege or priority that it might not have earned in any substantive way.

Another question that I will delve into more next month is, why rhythm? That is, what is the goal of having music organized into regular or somewhat regular micro units of time? Is it to create a sense of pulse or momentum? Is it something about comparability of experience throughout the duration of a piece or a movement? Is it very specifically about creating the palpable sense of a regular beat in the listener’s ear?

I mention it here to introduce an experiment I once conducted that was predicated on the observation that many people are of the opinion that Helmut Walcha’s recordings are rhythmically conservative. I obtained an interesting result.

I had always reacted to Walcha’s recording of Sweelinck’s Fantasia Chromatica as having both extreme steadiness and inexorable forward momentum. At the time that I did the experiment, I took it for granted that the way to achieve those qualities was to keep the beat very steady. But I must have suspected something that led me to investigate. I put on the LP and measured the beat at the opening. I then picked the needle up and dropped it a bit farther in. I measured again. I did it a third time, maybe a fourth. They were all quite different. This led to the intriguing notion that maybe inexorable forward momentum, and even the very sense of steadiness itself, might sometimes come from something other than regimented sameness of beat.

I have now repeated this exercise using more modern methods: the piece playing on my computer and an online tempo tool. The beat at the beginning hovered around 118, and later on it was over sustained passages as high as about 126 and as low as the mid 90s. That is very much like what I measured thirty years ago. I am intensely interested in the relationship between literal sameness of beat—or departures from that—and a subjective sense of steadiness, momentum, and pulse. Is it possible that sometimes a performance that features a doggedly steady beat comes across as uneven to listeners? If so, how can this be?

There are two games that I have played while riding in a car that both have to do with the use of time in music. First, if you are riding along a fairly busy two-way street or highway, pay attention to the sound of the cars passing on the opposite side. On a busy road cars will space themselves out almost regularly, since all else being equal, people pay at least a little bit of attention to following distance in front and behind. But there’s an emphasis on “almost.” The line of cars is never spaced out exactly evenly. So as the “whoosh” of each successive car goes by, see how far from even those sounds can be and if you can still accept them as conceptually even. How far apart can sounds 2 and 3 be—compared to the time between sounds 1 and 2—and can you still hear that timing as rubato or agogic accent rather than just discontinuity? For me there is a wider range of timings that I can assimilate to evenness than I would have expected.

If you can accept a stream of not quite even cars as conceptually even, is there anything interesting about the shape of the unevenness? Does it have any rhetoric to it, groupings or patterns of weak and strong beats, or impulses? One fascinating feature of this exercise is that each instance of it is ephemeral: you can hear it only once, never again the same way.

Another exercise I enjoy while driving is this: when going under an overpass, I try to experience the time in the shadow of that overpass as lasting forever. Since it will come to an end, usually in seconds or less than a second, I attempt to experience it as simultaneously brief and infinite. This feels even more intense if it is raining. It seems to me this has implications for rhythm in music. The ostensible rhythm, flow, motion of any increment of music is always about the next thing: when will the next beat come? But the state of being of each note, harmony, sonority, or beat, is also a thing that exists for as long as it exists, and that has identity and importance.

(It is probably best to do the above exercises as a passenger rather than as the driver, unless you are very sure that none of it will distract you from driving. I wonder how different any of this will seem if we have nothing but self-driving cars on the road!)

Are there other little slices of everyday life that might illuminate aspects of rhythm and the role of time in music? Rain is an interesting one. There are pieces of music that are inspired by or attempt to depict rain. What is the rhythm of rain like? It is more regular when it is fairly light. What about walking? How regular is that, and how does walking respond to outside conditions? Can one walk while hearing in one’s head a passage of music that moves at a pace different from the footsteps?

It occurred to me a few years ago that I often experience trills as containing some of that simultaneously brief and infinite quality that I get out of my second driving exercise. I sometimes suspect that that is what trills are essentially about, though that is speculative and unknowable. The fast and unmeasured quality of (usually) the middle portion of a trill seems to take it out of time, while, like all music, it is in the end bounded and defined by time.

I will pick this up again next month.