On Teaching: Repetition !

Repetition II

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

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

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

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

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

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

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

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

Further questions regarding repetition

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

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

“Really?”

“Really!”

or even more extended:

“Really?”

“Really.”

“For certain?”

“For certain.”

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

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

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

“Would you like some toast?”

“Would you like some toast.”

and so on.

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

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

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

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

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

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

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

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

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

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

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.

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.

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 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.

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

The way of the world

The meta theme of this column over the last several months has been unpredictability. As I have recounted, it was as early as October that I became aware that a shoulder injury was preventing me from working on upcoming performances of Johann Sebastian Bach’s The Art of the Fugue. This was a bit awkward, as the subject of the column was supposed to be the process and progress of my work on that piece. Then after surgery in December, I found myself unable to write, which precluded my January and February columns. When I was ready to resume writing, I found that I could not find a fruitful way to write about The Art of the Fugue or about music and teaching in general—partly because I still was not actually playing, and partly because of my state of mind as I recuperated. I started recounting some of my experience of that recuperation, particularly of physical therapy, which had some interesting implications for the music learning process and teaching.

Then the current public health crisis hit. As I write this, a scheduled presidential primary is not taking place, sections of the country are in quarantine, most businesses in the area where I live are closed, and various curfews are in place. My practice of watching a bit of a baseball game or golf tournament to take a break from writing is in abeyance—most of what we all do is in abeyance. When you read this, six weeks or so further on, things will likely be different, but we do not know in what ways they will be different. All of our mid-March selves hope that by early May things will have turned the corner. But we do not know.

I am not sick, nor is anyone I know personally. That is one of the things that may change. My shoulder feels almost fine—close enough not to impede most activities—and I have gotten past the malaise that accompanied my early recovery period. Therefore, I should be able to focus well on writing and on practicing. Indeed I should be able to take advantage of the relative absence of things to do to catch up. But rather than that, I find it harder to concentrate and focus right around now than at any other time that I can remember. So do many people.

I have written about my attempts to be assiduous during my physical therapy exercises, and that those attempts have been fairly successful, if not quite as successful as I had hoped or even assumed. I can report that on one recent day I simply forgot to do them; I forgot that I was a physical therapy patient. The next day, my initial reaction was to wonder whether I should bother to start them up again. I did, though it was a kind of half-hearted job.

This is a global concern that affects everyone’s focus. I have read and agree that teachers in general should not evaluate or judge their students right now. Perhaps we need to do away with grades and exams for now and tolerate mediocre or late work. For this week and next, I am not seeing students for any sort of regularly scheduled lessons, not even remote ones. These are said to be the two weeks when we either will or will not turn things around. Nothing about long-distance teaching would violate the kinds of measures that we are being asked to accept and implement. My reason for taking a short break is about focus. As I recently put to a colleague, I need to take a deep breath. I believe that a number of my students also need this, though I am aware that for some of them lessons right now would be a good distraction. (I have balanced that possibility with my own needs at the moment by making it clear that I am happy to chat with anyone informally or answer questions by email.)

My time off has reminded me of something. While this is a global concern, every student always has their own concerns. I think that I try to be aware of that as a general matter and to react to whatever a student brings to a lesson based on their life circumstances. Music is a part of life, interconnected with everything else. Our awareness of this is heightened at a time like this, but so is our awareness of the complexities. Some people would like for the time being to put lessons aside and focus on the gravity of the situation; others would like to delve even more deeply into music as a distraction or as an affirmation of life, or as some of both. Some people use their involvement with music to help them with difficult things by heightening emotions and awareness, while others use that involvement as a way of gaining access to joy or peace or certain kinds of understanding.

A few random thoughts from the last month or so:

1) I mentioned in an earlier column that during my convalescence I was experiencing music more by hearing it in my head than by actual listening. I later realized that most of the time whatever piece was going through my head was doing so at a very slow tempo. For example, there was a time when the piece in question was Mozart’s “Rondo Alla Turca,” the last movement of the Sonata in A Major, K. 331. This is a piece that I have never played. I tapped out the beat in my head at about quarter note equals 95 beats per minute. The slowest recordings that I found of it in a brief survey were at about 120. Another time, the piece was one that I have played a lot: Bach’s Fughetta super Dies sind die heil’gen zehn Gebot, BWV 679. As it went through my head, I discovered that the eighth notes were going at about 110 beats per minute. Recordings of it that I checked were all between two and three times that fast.

So I began to speculate, are these the tempos that I really want? I certainly like the admittedly abstract experience of “hearing” them that way internally. Each of those pieces, and others, seemed to have a wonderful feeling of suspense and freedom as well as a convincing overall arc. But this is imaginary. Would I like actually hearing them this way? These tempos were extremely slow. If I really would like them this slow, does that mean that I could expect other people to? Or is it something quirky about me, or about how one hears one’s own playing as opposed to anyone else’s? As I get back to playing and teaching, I want to re-think tempo, mainly as a matter of influence. Where should we get our tempos? Our own innermost thoughts? If not that, why not? Do students feel free to try to get in touch with their own innermost feelings about tempo? What about other interpretive matters? Where might those feelings come from? How can I help students connect with them?

2) There are periods in history that have seen the creation of music that reflects difficult times. Composers in the seventeenth century lived through the Thirty Years War. I have always assumed that this is one source for the sadness and intensity of much of the organ music of Scheidt, for example. The mid-twentieth century was of course another such time, and Messiaen’s Quartet for the End of Time is one response to it. As I write this it is much too soon to know what scale of misery, dislocation, and sadness the current public health emergency will end up creating. But I find that this current state of affairs gives me a more real and human awareness of how such things might have affected people—even those great artistic figures whom we struggle to know not just as names or monuments but as people—all those years ago.

3) I noticed something interesting in my approach to physical therapy exercises. It is usually not the exercises that are new, difficult, or painful that I am tempted to skip or shortchange. Rather, the ones that have become easy, that seem to have “worked.” Take, for example, rolling a big ball along a table. I essentially could not do this at all a month ago. But now it seems so effortless that after I have done it once or twice, it takes more willpower than I can always manage to do it the prescribed thirty times. This reminds me of one of the characteristic dangers of the practicing and learning process: that a piece or a passage that has become basically learned—or seems to have done so—will be neglected thereafter. I do this, and students do this. When there is limited time or concentration, it is tempting to focus on whatever seems to need the most work. That is not always a source of danger, but it has to be monitored for becoming one. Often the passages that seemed easy in the first place or that seemed to get learned easily end up being the shakiest in performance.

I say that I am prone to doing this, and that is true. But it is fascinating to see myself falling prey to the same temptation in a situation when I am without any particular expertise or overarching awareness of the dynamic of what is going on. To put it another way, I am doing the work at someone else’s behest, something that I never do when playing music. This may change my way of thinking in my own practicing or conversations about it.

4) I have been trying to turn back these last few weeks to thinking about the music that I want to play. That means The Art of the Fugue, of course, at least in large part for now. However, I find myself thinking more about counterpoint in very general terms, that is, about the concept of counterpoint as a part of life. This is abstract and, perhaps, just the musings of someone who was abstracted from normal life and activity for a couple of months for one reason and now expects to be for another couple of months for different reasons. But I have felt strongly the force of what I think of as the basic definition of counterpoint, namely two or more things that are different from one another happening at the same time. This is a way of looking at it that at least somewhat downplays such specifics as voices, motifs, and subjects, not to mention answers, inversions, countersubjects, cancrizans, diminutions, and so on. It requires us only to have an awareness of what it means for things to happen at the same time and of what it means for things to be different from one another. There can be interesting things to say about each of these around the edges, since they are both recognizable, familiar concepts that arise not out of music but out of life.

I had that thought vividly the first time I entered the physical therapy clinic. Here were people (the patients), none of whom had ever met or heard of each other, and who were not exactly meeting now. They were there doing similar but different things in a kind of dance or counterpoint. Of course, this is a clichéd or trite point.

As far as music is concerned, this reminds me of several ideas about counterpoint that occurred several years ago, mainly as a result of my experiences with theater, in particular immersive or participatory theater. (I have briefly alluded to this in prior columns, and will soon—the Fates permitting—write about it at length and relate it to memory, to the passage of time, and to The Art of the Fugue.) The notion is that whereas it is normal, valid, and important to think of counterpoint as a conversation between two voices or among more than two voices, it makes a different kind of sense and has a different kind of power to see counterpoint as a representation of or analogue to all experience, whether of people passing through the physical therapy center together or of the planets circling one another—or millions of people working from home and staying in touch as best they can.

To be continued.