On Teaching

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.

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

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

Further thoughts about rhythm, part 4

After writing my last column and in the course of searching for further ideas about rhythm, I came across this quote, which was new to me and I quite like. It is from a review of Rhythm and Tempo by Curt Sachs published in 1953 in Journal of Research in Music Education, written by Theodore F. Newmann:

The essence of all musical expression is that of creating a feeling of organic movement. And that factor, above all else, which contributes to a work’s organic unity, its total feeling, is rhythm. Rhythm is not a matter of divisions of time and accent but rather a relation of tensions—the preparation of new expectations by the resolution of former ones. It is rooted deeply in the framework of all living organisms. It permeates the very body of music—its tempo, melody, harmony, and form. Rhythm is, in fact, the most vital element in music.

I might quibble about the absolute terms in which some of this is expressed. Rather than “the essence” I might say “an essence” or “one essential part.” Despite my focus on rhythm right now, I would not say that it is “the most vital” element in music—certainly one of the most vital, and one that, defined broadly enough, must be present.

What I really like is the part about expectations. This is a powerful way of framing the theoretical background for my second mode (as per last month) of determining rhythm in music. The ebb and flow of tension, the creation of expectations—and then the fulfilling or the subverting of those expectations—is the source of the rhythm of my second sort. And this operates at every level, from a whole piece to the motion from one short note to the next. Newmann’s quote is a beautiful expression of the notion that rhythm can be derived from and described as something other than counting beats. For me, this description also establishes that the expectation-based sense of unfolding rhythm is primary. It is not just a system of departing from the rhythm created by the beat structure. If anything it is the deeper, more essential source of rhythm.

How is it possible to reconcile the simultaneous existence of these two radically different ways of defining, projecting, and perceiving rhythm in one piece of music? I do not know if I have a thorough or systematic answer to that. Both forces being discussed here are real, and therefore they do coexist pretty much regardless of whether we know why. Not having an answer to how or why that works may reflect something about how flexible it is in actual practice. It may also relate to the phenomenon of people responding differently as listeners to the choices made by performers. After all, expectation is a listener’s experience. And if a piece or passage of music creates and then fulfills or subverts expectations, then the actual flow of that experience is very likely determined in large part by the listener’s experience, training, philosophical stance, temperament, and so on. Different listeners will hear what is being performed in a way that is literally different.

If a piece of music is ostensibly measured and structured in a regular meter, then any overt conflict between the two approaches to rhythm would take this form. The intuitive, listening-based approach might well lead to something other than playing the rhythm as written, and playing the rhythm as written might lead to ignoring the ebb and flow of tension and expectation. One axis along which a solution to this conflict might exist is that the sense of pulse is remarkably strong and resilient.

My experiment with Helmut Walcha’s recording of Sweelinck, as described in my December 2021 column, page 11, is a manifestation of this resilience. As I wrote then, my reason for testing out the literal metronome steadiness of the recording in the first place was that the performance came across to me as remarkably and inexorably steady. So it was interesting and telling that the metronome reading varied so much across the piece. I have conducted similar tests on other recorded performances. For example, about eighteen different recordings of the beginning of the first movement of Charles-Marie Widor’s Sixth Symphony yielded similar results. Some of my odd driving-based experiments about time have this same import.

A Chopin anecdote

There is an anecdote about Chopin that I have come across in writing twice over the years, though I cannot remember where exactly. One version framed the story around his mazurkas, the other around his waltzes. It works equally well for either, as they are in ¾ time. The point is that a friend of Chopin’s said to the composer that when he played one of his own waltzes there were four quarter notes in each measure, not the notated three. Chopin denied this. The friend made him sit down and play and kept strict track of the timing, and Chopin was indeed taking four quarter notes worth of time between bar lines. This story implies three things: that Chopin was playing very freely, holding some supposed quarter notes for as much as twice as long as they “should be” held; that there was nonetheless something that could be identified as “the quarter note;” and that Chopin himself intuitively accepted what he was doing as being a manifestation of three quarter notes per measure.

It seems also possible that if the intuitive, expectation-based approach to rhythm is applied thoughtfully in a way that is really derived from careful, involved listening, then it might enhance the sense of regular pulse while being less regular than a purely beat-based rhythm would be. If the sense of momentum that is associated with the concept of regular accent-based meter is as robust and as difficult to destroy as I suspect, and if an expectation-based shaping of rhythm can make the ebb and flow of intensity the most compelling that it can be, then it could make sense that the latter approach would make the accentuation patterns that define regular meter more rather than less convincing.

The actual results of the two approaches do not always have to be very different from one another. For some performers and listeners experiencing repertoire, the listening-based intuitive approach might well yield results that are quite regular in their actual rhythms.

In musing a bit about how to introduce this idea to students, I start by quoting something that I wrote in my column from April 2015, page 17:

I often suggest to students the following practice tool. Once they have identified a spot where they want to make a rhythmic gesture (usually of the sort that might be described as “rubato”) they practice that gesture, in the privacy of the studio, in as exaggerated a manner as possible: take the risk of executing a gesture that is utterly tasteless, mannered, “schmaltzy.” This is to counter the fact that we usually only visit the gestures that we think we want to make “from below” (so to speak), that is, only compared to and judged in comparison to not making such a gesture, or to a modest version of the gesture. This stems from and then reinforces a philosophy that teaches a kind of reluctance about such gestures. If you hear a rhythmic inflection from both sides, you get a different sense of exactly how it might be effective.

When I wrote the above, I invoked the word “rubato.” Now I would be inclined to avoid that, since it is a term that relates the flow of rhythm to the underlying regular meter. The relationship is real, but I would want to encourage the student to move away from considering that relationship to be primary or of overriding importance. In applying this practice suggestion with many students over many years I have observed that almost everyone finds it easy to identify spots where they intuitively want to create rhythmic gestures that are not identical to what a strict reading of the metric notation would suggest. While these gestures fluctuate in number from piece to piece, it is more common for the student to believe that their interpretation of some of them are wrong.

Experimenting with notable works

As an experiment, try giving a rhythmic inflection different degrees of magnitude—including the highly exaggerated, but not limited to that—and try to experience and analyze what is happening with each different shape. For example, consider the very beginning of J. S. Bach’s Toccata in D Minor, BWV 565. Play the opening mordent and then listen for when you think that the following scale passage “wants” to come in. Try taking longer next time. What has changed? Have you lost the moment when the impact would have been greatest, or does the added suspense increase the impact? Does it sound like you caught a sort of wave of expectation when you initiated the scale passage, or did you miss it? If you missed it, could there be another one coming up, different yet also fulfilling?

Questions like these are easy to highlight with a moment in an intrinsically free passage like this, but they are potentially present all the time. Returning to the pieces that I invoked at the beginning of this series of columns, I would say that the first barline in the opening of the first movement of Widor’s Sixth Symphony is also a place where the dynamic of this sort of rhythm is clear. A student can play it metronomically and then try various timings, listening as closely and open-mindedly as possible. What is gained or lost by various different timing possibilities? What does the timing at that barline imply or suggest or even necessitate about playing the second measure itself? Would the answers be different if this were not the opening of the piece? Is the answer to that question different if we stipulate either that it was a recapitulation or, on the other hand, that it was a new idea introduced in mid-piece? Does the use of this motif later in the movement as written affect choices here at the beginning?

It is interesting to listen for intuition-based timing of quick notes within a texture. In Example 1, in this Mozart Piano Sonata in A Major, K. 331, how can we determine exactly where to play the sixteenth notes?

My own approach to figuring this out would be to leave those notes out at first, making the rhythm of the first half of each of the first two measures the same as the rhythm of the second half. I would play this a few times, just like that, as if it were the piece. Then I would play it a few times hearing the sixteenth notes in my head, but not playing them and then add those notes back. I often do not know and cannot seem to determine as a matter of counting and calculation where I want to place short notes after dotted notes. To use a piece I have played a lot, I have no idea exactly what ratio I give to the pervasive dotted rhythms in Bach’s Prelude in E-flat Major, BWV 552i. I can only hear whether they do or do not seem to do the right sort of job in creating momentum from one long note to the next.

When one asks a student to listen carefully to every moment in a passage and to discern as much as they can about rhythm through that listening, interesting things happen. Some of these are advantages while others are pitfalls. One great advantage is that this tends to keep the student from rushing. Not everyone has a tendency to rush, but most of us do at least some of the time. One reason for rushing is that we pay the most attention to the things that we must do physically—and for organ and harpsichord that means initiating the notes and releasing them. As soon as one note is safely played, there is some pull toward either the moment of release or the moment of initiating the next note. The sort of listening that I am describing here focuses the attention as much on the middle of a note as on the beginning and end.

Listening this way tends to lead to slower playing. That has been true for me, to a fault some of the time, though it is a perfectly natural outcome of this approach. The way to counter this tendency is through awareness and honesty. This listening approach is both a practice technique and something to bear in mind while actually performing. As with any other sort of practice, it is important and good to utilize it at a slow tempo, but as with any slow practice, it should be ramped up to the desired tempo in a systematic way.

It is natural to prepare for the moment when you believe the next note should occur and then play that note. This makes that moment in the music late by definition and leads to slow playing. It is probably acceptable for this to happen early in practicing a passage, as long as you are aware of it and work on evening it out as you get to know the music better. I have also been guilty of this in performance, not recognizing it clearly enough in practicing, and therefore not working to smooth out the process.

This is analogous to something that can happen when using a metronome, when one listens for the metronome beat and then plays the note. Something like this can also happen with releases. If you hear the instant at which you want to release a note and then release it, the release is late. A release that is executed by pushing off—down, then up—will also be late if the downstroke is timed to the desired moment of release. There is a sort of leap of faith when executing something, whether the timing of the beginning of a note, as we are discussing here, or of the end, without waiting to confirm that the looked-for time has arrived.

A few miscellaneous points

What is the meaning of any given note value? We know the answer: a quarter note is equal to two eighth notes or to half a half note; a whole note is four quarter notes, etc. But here’s another definition: a quarter note (or whatever note value) is whatever a listener will hear or accept as a quarter note. This relates directly to the Chopin story above.

Watching a TV game show recently, I heard the host say to a contestant, “Time is ticking away!” Why? Why is time defined as made up of discrete entities, ticks of a clock? Is it just because old clock technologies produced audible ticking? Or is there really something more fundamental about time that requires us to think that way? This vignette from a fraught moment in a game reminds us that thinking of time as ticking tends to create a sense of impatience or even panic.

The beating of the heart is sometimes evoked as a possible source for the notion of beats in music. This makes sense because the heart does beat fairly regularly in the absence of a medical issue. That beating is audible to the one whose heart it is, though not usually in a way that rises to the level of conscious awareness. If you quiet the outside world, you will easily hear your heart beating. But no heart beats as absolutely steadily as the beat we hear from a metronome. If the heart is a model for musical beats, maybe it should confer some flexibility onto those beats. If the heart is the model for a beat-derived sense of musical rhythm, breathing should be the model for a sense of rhythm based on expectation and fulfillment.

What is rhythm? That question has recurred to me as I have thought about and written about rhythm over the last few months. This is a prime example of putting the cart before the horse. After all, how have I been thinking about rhythm without first sorting out what it is? But there is no one answer to this very fundamental question, and we all work with rhythm without having established a clear definition.

I searched the internet with phrases such as “What is rhythm?” and “rhythm in music.” I was not looking for any answers as such, but to get an idea of some of the “headline” ways in which any sort of definition of rhythm is encapsulated. The results were very interesting. There were two basic kinds of results: 1) simple descriptions of some of the mechanics of the way that rhythm is depicted in some sorts of music, such as “Rhythm in music is the regular motion of half-notes, quarter-notes, etc.” or “Music has a regular beat sometimes indicated by a metronome marking;” and 2) complex but certainly intriguing philosophical discussions of concepts of rhythm.

One set of answers to the question of rhythm is contained in the fact that we work with rhythm when we make music. Music moves through time. Rhythm is predicated on the phenomenon of time passing as we listen to music or create it.

Music moves through time in a way essential to its nature. The same can be said for dance, though I have less experience talking to people who have had a deep involvement with it. Drama—live theater, television, movies—also moves through time, but in a way that seems meaningfully different as much of what is going on is dialogue. The semantic content influences the way one experiences the flow. (This is in part also true of vocal music.) Painting, drawing, sculpture, and other visual and graphic arts do not move through time the same way. Time passes as one experiences that sort of artwork, but visual focus is up to the viewer, as is shifting of that focus as a viewer encounters the work of art. There is no set time that the rhythm of viewing a painting, for example, will occupy overall, and no set ratio between times allotted to different parts of the whole. There is also no set order in which those parts will make themselves felt to the viewer, including any aspects of repetition.

I have always thought it fascinating that if you hit the pause button while a CD or any music file is playing, there is silence, whereas if you do the same on a video recording, a still image is displayed. Music has no existence without the passage of time, without motion and change.

Would a piece of music that existed in time but never changed seem to have rhythm in any sense we would recognize? This is an abstraction, since we do not encounter music that never changes. Maybe the closest we could come would be to play a note on an organ and hold it forever. But even that would change. There is always a miscellaneous fluctuation in the sound or in the way that the sound reaches the ears. Maybe a computer-based instrument could create a sound that really would never change even at the level of what the most sensitive instruments could measure or any ears could hear. If someone were to listen to (part of) such a piece would there be anything that they would experience as rhythm? Maybe not, but what occurs to me is that they would experience the inner rhythm of their own shifting reaction to the unchanging sound.

I see from framing the last thought the way I did that I want something to happen in order to accept that the quality of “rhythm” is present. So possibly rhythm is not just music moving through time, but things happening—things that we can hear—as music moves through time. I understand that this is sort of obvious and phrased in a deliberately simple or even naïve way. Maybe it is even really a tautology: if we are listening and something happens, we notice it. Since it happens across time, there is rhythm to it, if we define rhythm broadly or just decide to apply that word to that phenomenon.

But as the first set of answers that I found in my internet search reminds us, there is something specific about how we use rhythm, ​​not necessarily what rhythm is in most of the music that organists, pianists, harpsichordists, or other classical musicians grapple with. That has to do with regular beat, which presumably means that the “something happening” happens at regular time intervals, and some sort of way of grouping that regularity. This is expressed with a naïve pretense that we do not know it perfectly well already. It points to a vast set of questions as to why this should be standard. How did it evolve? What does it do that is different from what we might be able to do with musical sounds not organized that way? Are there necessary relationships between this regularity and other aspects of music in this range of styles: melody, harmony, texture, and so on? To answer these questions is not the point here, since the truth is that no one knows, although there has been a lot of interesting research and speculation.

So where does any of this leave us as to the teaching or grappling with rhythm in our own playing? Grappling with rhythm means deciding when to play notes. The thought that has formed in my mind over the last few years is that there are two fundamental ways to do this, and they are opposite. They are both important, but very different in how straightforward they are to describe.

The first of these is the normal one for most music that we play. It is the one that we engage with all the time, the regular beat and meter phenomenon. I like to describe it this way: there is a regular beat that exists outside of the piece and before the beginning of the piece; the notes of the piece will fit in with that beat once the piece begins. That beat defines one note value, and the other note values are all clearly defined in relation to that one. There could be many other ways of describing this same thing. And to avoid its being a caricature, we should add that although the regular beat exists before the piece begins, it is in a sense a separate entity from the piece itself, and to a large extent governs the motion of the piece.

This is consistent with this concept that the actual notes sometimes deviate from the place where that regular beat says they should have been. That then becomes a matter of taste, of judgment, of awareness of a composer’s intentions and so on. Although this deviation is normal and frequent, it is defined as an aberration, and therefore it is often felt to require specific justification.

The second, opposite pole is a lot harder to describe. At any instant in a piece of music, there is some prevailing sound—a note, more than one note, the dying away of released notes, the ambient room sound, any combination of these things and others—and something about that sound will suggest when it feels right for the next sound to happen. That suggested moment is the appropriate time to play or sing the next note or notes. This perceived sense may sometimes be caused by the phenomenon of notes having come at a certain regular pace up until that moment. But it may also be caused by other factors that have nothing to do with regular pulse. These could include something about the inner behavior of the sound in the time since anything was last expressly played, shaped by the nature of the performing medium or by the room acoustics; anything about harmonic development and the ebb and flow of harmonic tension; something arising out of the desire for a certain kind of forward momentum; a need either to sustain a mood or to change the mood; and so on.

Each of these two poles can be found to a greater or lesser extent in any piece or passage that we play, and they interact in an infinite number of ways. The second idea is often most obviously at work in recitative. This only starts with “official” sung recitative. It also includes instrumental passages that imitate recitative and are marked as such—for example, the section in the first movement of Widor’s Sixth Symphony that immediately follows the opening about which I wrote in my September 2021 column (pages 10–11), or sections of Bach’s Chromatic Fantasy and Fugue, BWV 903, or Toccata in D Minor, BWV 565.

More interestingly, perhaps, it includes passages that strike us as being in recitative style without being marked as such. This applies to many other sections of those same Bach pieces, for example. The opening of BWV 565 is full of fermatas, unmeasured and written-out arpeggios, and tempo changes, all of which add up to making it an absolute necessity to find some source other than a grid of beats and accents to figure out when each successive note is best played.

The opening of Bach’s Fantasia in G Minor, BWV 542, is not aesthetically like the opening of BWV 565. It has no fermatas, tempo changes, or other direct suggestions that the rhythm suggested by the mapping of the notes onto the regular meter is not perfectly viable. When I played this piece decades ago, that was how I derived my sense of when the notes came. I recall being very focused on counting it correctly. Now, when I sit and read through it, I am more focused on listening to each sonority and trying to feel or intuit when what comes next should occur. This is not in the absence of an awareness of how the different note values stack up against one another or where the strong beats are. In this case it supplements that. The feeling of pressure or momentum to move to the next note or cluster of notes comes in part from an awareness of the imperatives of the beat structure. For example, everything about the opening chord and the act of moving away from the opening chord comes from sonority, ideally including whatever I can hear of room acoustics.

So how does this concept differ from a simple acknowledgement that it is possible to play ordinary measured music either rather strictly or more freely? This is a common though not uncontroversial subject to debate, be it in a friendly or heated way. One point I like about this approach is that it seems to be true. That is, whether it is something a composer intends or a performer tries to bring out, it is palpably the case that each moment in a piece of music has some sort of inherent momentum. It can vary in strength and be perceived differently by one person and another. After all, this momentum is something that arises in part from what a given performer or listener wants to do with a piece, their prior aesthetic predilections and tastes, and a host of other factors. This is never something that can be defined by one person for another: it must be heard and felt.

One way to demonstrate that this intrinsic momentum is real is to stop a piece at a random place. A jarring quality that experience creates comes from unfulfilled expectation or broken momentum. That momentum cannot be just that of a regular beat pattern—they stop all the time, and it does not bother us.

Another matter that I like about this concept is that it ties in with the notion of playing a piece as if you were improvising it. Even if your sense of the directionality and momentum of the sonorities does not lead you to do anything very different from a fairly strict rhythm, as soon as you start listening for that momentum you are behaving like someone who is creating the piece.

Also, just as a matter of my own discipline, trying to listen like this prods me not to let my attention and hearing faculties wander too much, to pay attention and to care about each note. This is one of the key points in working with students around this idea.

Next time I will write in some detail about that: how to introduce this idea to students, what some if its advantages are, and what some of its pitfalls are, how to help students reconcile this approach with whatever amount of respect to the notated rhythm is due, if that ever rises to the level of conflict. I will end this series about rhythm with notes on a few stray ideas and observations about rhythm that are either germane to the above ideas or interesting on their own account.

Stories and conversation

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The Art of the Fugue, part 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.