On Teaching

Gavin Black is the director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached at .

Counterpoint II
In last month’s column, I discussed teaching the playing of contrapuntal music on keyboard instruments, focusing on ways of conceptualizing counterpoint that might be interesting and useful to students without being intimidatingly technical or complicated. This month I want to continue that effort. I will also discuss ways of unraveling contrapuntal textures, to help students understand those textures and feel comfortable playing them.
A contrapuntal piece is, fundamentally, a piece that is in voices, and, as I wrote last month, the concept of voices in keyboard music is both elusive and powerful. The concept of voices in, for example, a vocal quartet or a wind trio is not the least elusive. Each singer or instrument is capable of producing one note at a time and thus playing or singing a melody. When a voice is temporarily silent (i.e., has rests), then the musician carrying that voice is still present, not singing or playing, but representing those rests. The concept of voices at a keyboard instrument is elusive because, conceptually, each voice clearly does not emanate from its own source—a consciousness, a person, an instrument—and, practically, because voices can cross and become confused with each other, or blend together in a way that sounds like chords.
Of course, there are certain cases in which a keyboard instrument can clarify or solve at least the practical side of this problem: two-voice counterpoint in which either the voices don’t cross or, better, are played on different sounds, that is, different keyboards; or three-voice counterpoint in which each line is clearly on a different sound, that is, two manuals and pedal. It is possible that one reason for the greater prevalence of clearly contrapuntal music during the harpsichord era, as opposed to the piano era, was the availability of two-manual domestic keyboard instruments. However, this was probably only a minor reason, since those larger instruments were the exception in most times and places, and the vast majority of contrapuntal keyboard music was indeed written to be played on one sound.
The abstract nature of contrapuntal voices in keyboard music is probably one of the sources of its particular emotional and philosophical power. When a musical voice is heard that is clearly a person—a singer or an instrumentalist—then there is a sense of personal communication that helps to define the character of the listening experience. This personal communication may be, in a way, illusory. (I recall a famous discussion by a prominent opera singer some years ago of how during an intense scene in a opera she was most likely—while singing—thinking about what kind of pizza to order later on!) However, it still shapes our reaction to the music. In keyboard counterpoint, while the overall piece may seem to come from one place—the performer and at one remove the composer—each voice on its own comes from somewhere that is abstract and anonymous. Thus a listener can fill in a sense of where the voices are coming from, and what meaning or emotional content this sense of where they come from conveys. This will be, for different listeners, emotional or philosophical or religious in nature, or something that can’t be pigeonholed. In any case it is not something that needs to be—or, most likely, even can be—defined or described in words.
The relevance of the above discussion to the work of a student wishing to begin studying keyboard counterpoint—and to his or her teacher—is probably twofold. First, it is a reminder that indeed keyboard counterpoint has its conceptual and historical origin in vocal and instrumental counterpoint. This can help develop a basic sense of what a “voice” is. Second, and perhaps even more important, it is a reminder that keyboard counterpoint, whatever its origins, is its own thing with its own power and meaning. It is not (musically, even if it is historically) derivative, and it should not be considered inferior. Attempts to determine anything—technical or interpretive—about how to play keyboard counterpoint by direct analogy with singing or with playing instruments should be taken with a grain or two of salt. Of course, such analogies are useful and should be considered, along with all other possible sources of ideas and inspiration, such as dance, bird songs, any and all genres of music, the rhythmic feeling of walking through the woods, or bicycling, or swinging a golf club, or one’s heartbeat. But it should not be assumed that playing contrapuntal music on keyboard instruments is a never-quite-as-good substitute for something else.
(Of course I mention this because we are often told, or at least somehow absorb the idea, that the human voice is the best instrument, or the “only perfect” instrument. Again, it is wonderful to draw both inspiration and, sometimes, concrete interpretive ideas from singing. But it is crucial not to practice, play, and perform always looking over one’s shoulder in case there is a singer back there who could be doing the same thing better!)
So, as I mentioned briefly last month, I believe that the best way to introduce a student to the idea of voices in contrapuntal keyboard music—with the above caveats—is to make the analogy to individual sung or played musical lines. A contrapuntal voice is a musical line, or melody, that could in theory be produced by a singer or by someone playing a melody instrument. A voice in a keyboard piece can exceed the range of a vocal part or of any given instrument: it should be made clear to the student that neither very wide range nor extravagant leaps are rare or problematic in keyboard counterpoint. (Again, I mention this because it does arise as a concern. If a student comes to understand the concept of a contrapuntal voice by analogy with a sung voice or line, then a keyboard line that exceed the bounds of what a singer can do might seem to be illegitimate. This can lead students to worry inaccurately and unnecessarily that they are making mistakes in their analysis of the voice structure of certain pieces. This is another of those things that seem obvious to those who have worked with it for a long time but that is not necessarily clear to anyone who has not studied it yet.)
The first practical step in introducing students to playing music written in voices is to ask the student to play individual voices—melodies—starting with ones that are easy to find, that is, that do not have to be teased out of a complex texture. These can in principle be anything: voices taken from simple contrapuntal pieces, coherent melodies from pieces that are not otherwise contrapuntal, songs (classical or popular), lines from instrumental pieces that are not officially for keyboard instruments, hymn tunes, etc. The purpose of doing this is to reinforce what a contrapuntal voice is, and to give students (in particular their ears more than their fingers) a chance to become more deeply accustomed to following melodic lines. Learning, playing, and listening to pedal lines is also a good idea at this stage. These can be extracted from pieces, and it is of course perfectly OK to learn a pedal line without going on to learn the whole piece. It will just be a leg up if the student ever happens to want to come back to that piece.
The appropriate next step is for the student to play one melody while listening to another. An ideal way to do this is for the student to have learned one voice of a two-voice piece, say a Bach Two-part Invention, or a bicinium by Scheidt or Sweelinck, and to play that line while the teacher plays the other line. On organ, this can be done with various registrations creating various kinds of balance, all the way from the student’s line predominating enough that the teacher’s line is no distraction at all, through a nice even balance, to the point where the student’s line is almost drowned out, and following it is a challenge.
(This exercise is of course aimed primarily at students who are beginners at playing contrapuntal music. However, it is not a bad refresher exercise for anyone, at any level of experience. This is probably true of most of what is being discussed here.)
There are two parallel next steps, which can be done in any order, or essentially at the same time.
The first of these is to ask the student to work on some two-voice counterpoint: a Bach Two-part Invention, or anything else that has that structure to it. Technically, all else being equal, this is the easiest kind of counterpoint to play, simply because there are fewer notes than in a three- or four-voice piece. Conceptually, it is easiest—and the best starting place—because with each hand playing one voice, the physical, dance-like connection between the musical line as a concept and the act of playing that line is the most direct. (This connection is also very direct and compelling when playing a contrapuntal voice on the pedals.) It is extremely important that the student practice each separate hand/voice until it is, by itself, second nature. The act of putting the two voices together should be well prepared enough to feel natural and easy. Ample practicing of separate hands is usually (probably always) a good idea, with any music. In this case, it is important in particular because the student’s main task when putting the two hands together—that is, playing the whole two-voice texture—is to listen well. It is important that the physical side of playing not demand so much concentration as to distract from the listening.
The next step is to work on extracting contrapuntal voices from textures of three or more voices: that is, at first, not playing them, but just following them. The basics of knowing which voice is which are not always obvious to someone who has not yet done much of this kind of work. It is fine to start this process with something as basic as a traditional four-part hymn setting. In that type of writing, it should be quite clear from a combination of placement of notes on the two staves, stem direction, and musical sense which notes belong to which voice. These are the same things that ideally should (and usually do) make the voices clear in the score of a more complicated contrapuntal piece. Next could come slightly more elaborate and challenging hymn-like pieces, such as the Brahms Es ist ein Ros’ or the Vierne Épitaphe, and after that three- and four-voice fugues. The point is to find pieces in which there is not a one-to-one correspondence between voices and staves. The exercise can be done by having the student go through and point to all the notes of a given voice, or highlight voices in different colors, or actually write out the separate voices on separate staves. The point is simply to practice discerning which notes in a complicated texture belong to which voice.
(I should mention that there are certainly students who are beginners in actually playing contrapuntal keyboard music, or who feel that they need systematic work in that area, but who, perhaps because of theoretical study or something in their background, really don’t need to go through the process described in the last paragraph. That is, they know perfectly well how to discern what the voices are in any texture. This is wonderful, and no one should be made to do anything that they don’t need to do. The point is to make absolutely sure that everyone knows, without its seeming to be any sort of bother or obstacle, how to follow the voices in any contrapuntally constructed score. If a student says that he or she can already do that, then the teacher’s job is just to make sure that this is true, in a friendly and discreet way, and go on!)
The final step, and in a sense the most important, is for the student to work on a three- or four-voice contrapuntal piece by first learning each voice separately, then practicing all possible pairs of voices, then putting the whole texture together. In the course of doing this, the student can also begin a motivic analysis of the piece. For this purpose, I advocate avoiding technical terms, even basic ones such as “subject,” “countersubject,” and “answer.” Instead of using those terms, I ask students simply to look for and notice anything and everything that happens more than once. This often leads to a more thorough and nuanced analysis than would arise by applying technical terms to various motifs. It is also usually quite interesting to do. Next month I will take all of this up in detail.

Gavin Black is director of the Princeton Early Keyboard Center in Princeton, New Jersey. He is at work this fall on a recording of Bach’s Art of the Fugue in a version for two harpsichords. He can be reached at <[email protected]>.

Counterpoint III
This month I want to outline, as systematically as I can, a method for taking any contrapuntal keyboard piece apart into separate voices, practicing those voices separately, and putting the piece back together. This builds on some of the ideas discussed in the last two columns. I will also begin to discuss motivic analysis, which I will expand upon next month in wrapping up this series on counterpoint.
To begin with, I will mention some of the reasons for approaching this kind of music in this way, since it involves, up front at least, more work than it would take just to finger and practice the piece. Any student who is being asked to put in this extra work deserves to know why it is being suggested, and thus to have a chance to become convinced of it and motivated, inwardly and enthusiastically, to do it. The first reason is in a sense philosophical. If a piece is convincingly contrapuntal—written in voices that are completely or very largely consistent, that is, each is a coherent melody from the beginning of the piece to the end—then the composer certainly wrote it that way on purpose. Therefore it makes sense to assume that the performer ought to understand it that way as well, at least as a point of departure for making decisions as to how best to play the piece. This is somewhat analogous to an actor’s knowing the grammar and syntax of the language in which a play is written before performing in that play. It is possible to learn a part phonetically, in a language that you do not understand, but this is unlikely to lead to convincing rendering of the phrases and sentences, or possibly even of the words.
A second reason arises out of the first one. An actor playing a part in a language that he or she doesn’t understand might be able to give a convincing performance of that part through coaching. That is, someone who does understand the language could demonstrate ways of speaking the words and phrases that are appropriate, and the actor could mimic that native speaker. This could perhaps provide one—but certainly only one—convincing performance. However, it would deny the actor any scope to vary and develop that performance or to opt for a different interpretation. Likewise, a student working on a contrapuntal piece can certainly be coached by someone—possibly the teacher—towards a performance of that piece, through that coach’s suggesting phrasings and articulations and other interpretive details. A conscientious student could realize those suggestions and thereby give a performance that might be well worth listening to. However, the student would not have much basis on which to vary or change that interpretation, and would not really have learned anything much about interpretation or performance. The notion that a teacher ought not to tell a student how to interpret a piece but rather let the student work out and discover interpretive ideas him- or herself is of course something that applies equally well (or equally poorly: it is in fact a controversial idea, though one that I believe in strongly) to any music, contrapuntal or not. If, however, we accept for the moment that a student should have maximum autonomy in shaping interpretation and performance, then certainly for counterpoint the more intimately familiar the student is with the voices the more he or she will be able to focus on shaping those voices and bringing them to life.
A third reason is that the ears and the mind can follow what they recognize. If you enter a room in which half a dozen people are talking out loud in six different languages that you do not know, you will hear a blur of sound, a cacophony. If, however, you do know one of the languages, you will be able to follow what the person speaking that language is saying. Those sounds will form themselves in your mind into words and phrases, and separate themselves out from the rest of the decibels. Likewise, if the ears and mind of a player know and can recognize each of the melodies that are going on at once in a contrapuntal passage, that player will have a good chance of being able to follow each of those voices as a discrete melody. The best way to predispose one’s ears to recognize each melody amongst all of the others is to have listened to it independently, enough times to have almost memorized it, not necessarily to be able to play it without music, but to be able to anticipate in the mind where it is going next. If a student, or any player, has only heard each voice while also hearing other voices then it will be unnecessarily difficult to hear the voices independently, and difficult to come up with—or indeed to implement—any interpretive ideas.
The fourth reason is of a different sort. I said above that working out a piece one voice at a time involves more work up front. The fortunate fact, however, is that this approach actually saves time and makes things easier in the long run. If a player’s ears and mind know—in the manner discussed in the previous paragraph—what the voices are doing and where they are going, then at the stage of fingering, pedaling, and learning the whole texture of the piece, the fingers and feet will have much less tendency to stumble or hesitate than they would if this first stage of learning has been omitted or shortchanged. This is emphatically true even though the fingerings will almost always be different for separate voices than for those same voices as part of the complete texture.
Working out a given piece this way saves time in learning that piece. It is also true that working out several pieces in this way saves a substantial amount of time in learning the next piece and the one after that, and so on. This is especially true within a particular style or compositional type. So, for example, if a student takes the time to learn three Bach fugues by studying the voices as rigorously as possible, then the next Bach fugue that he or she works on will go very quickly, and might even seem “easy,” or almost so! (certainly “easier”). Working on these Bach fugues will not help as much with a piece by Cavazzoni, Louis Couperin, Reger or Moondog. It will help some, but each new style or type of music has its own quirks and tendencies that can best be learned by working on that type of music. Also, any piece worked out in the manner described below will be very solidly learned, and not easily forgotten.
So here are the steps to follow in taking the voices of a contrapuntal piece apart and then putting them back together again:
1) First, it is important that the act of reading the voices not be an impediment to fluent practicing. The student should already have spent some time going over the art of reading individual voices in a keyboard score, as discussed last month. However, if the teasing out of the voices still seems difficult, then prior to practicing the voices, this reading should be made easier. This can be done by highlighting voices in the score, by acquiring several copies of the score and highlighting each voice in a different copy, or by writing out the piece in open score. (The latter can nowadays sometimes be done most easily by computer.) Some pieces are indeed available in open score, either through a bookstore or online. In any case, the literal reading of the voices should be made as little a problem as it can be. It is also a good idea, for the first few instances of a student’s working out a piece this way, to choose music that is easier rather than harder to read, say a three-part invention or a chorale prelude in which only the middle two voices are written together on a staff, rather than a five voice fugue on two lines.
2) It is a good idea, as with most kinds of practicing, to work with small and manageable sections of music. These can be as short as a few measures at a time. It is fine to let the working sections coincide with musical sections of a piece—a fugue exposition, or a phrase of a chorale—but this is also not necessary. It is also not necessary to start at the beginning of a piece.
3) Once a section of music has been chosen to work on, the student should go through and play each voice of that section as many times as necessary to make each voice seem familiar—really familiar. That is, the student should stick to separate individual voices until he or she could sing those voices in the shower without having to stop and think about it. Each voice should seem as familiar as “Happy Birthday” or “Jingle Bells.” The physical practicing of the separate voices, at this stage, need not correspond particularly to the way they will be practiced later as part of the whole texture. For example, an inner voice that will end up passing back and forth between the hands should be practiced—at this point—by one hand or the other. (In fact, both hands should take turns playing it, in preparation for 4) below.) It is also acceptable to play a pedal line in the left hand, if that would facilitate this process, while also spending time practicing it in the pedals. None of this, as I mentioned above, will end up creating problems. When the time comes to put the whole texture back together, the advantages gained by the ears’ extraordinary familiarity with the voices will outweigh any memory that the fingers might have of having played the notes with a wrong fingering. It is also OK to keep the voices slower than they will end up being later on.
4) Next, the student should put all of the possible pairs of voices together. This is the most important step in this process, and the prior steps really exist to make this step work as easily and thus as fruitfully as possible. In a three-voice piece there are three pairs of voices [SA, SB, AB]. In a four-voice piece there are six [SA, ST, SB, AT, AB, TB], and in a five-voice piece there are ten [SA, ST1, ST2, SB, AT1, and many more!]. (This count is a good reason to start with a three-voice piece in learning and implementing this technique.) In principle, all of the pairs of voices are equally important, and each pair has the potential to reveal interesting things about the ways in which the voices interact. It is important to practice all of the pairs an ample amount, but in particular not to short-change the pairs that are, just because of acoustics, harder to follow in the full texture. These are, usually, pairs involving inner voices or non-adjacent voices. Although the mere playing of these pairs of voices—with the ears becoming more and more attuned to them at a subliminal level—is the main point of this exercise, this is also a good stage at which to begin to notice specific things about the ways in which voices interact. In playing a particular pair of voices, do you hear echoes or repetition of motivic material, or anything that sounds like question and answer? Are there interesting rhythmic relationships between voices? Are there passages in which the phenomenon of quicker notes in one voice against slower notes in another voice is significant? This is a good time to notice anything and everything that happens more than once (something that I will discuss at much greater length next month). Is there a leap of a fourth in one voice, followed by a leap of a fourth in the other voice a little bit later? Are they both up, or down, or are they opposite? Is there a rhythm in one voice that is taken up later in the other voice? In augmentation or diminution? Does the soprano voice reach its highest note at the same time that the bass voice reaches its lowest? Or its highest? Everything like this is worth noticing, even though certainly not all of it has a definable or important theoretical role (and even though it is utterly impossible to notice everything: that cannot be the goal).
5) Once the pairs have all been played a lot and feel comfortable, the student should step back, work out fingerings and pedalings for the whole texture of the piece or passage, and begin to practice it in his or her normal way. This can, and usually should, include separate hands and feet (as opposed to separate voices), and slow practicing. I believe that it is not necessary to practice all of the groups of three voices in a four-voice piece, or all of the groups or three and four voices in a five-voice piece. If the player’s ears hear the individual voices and the pairs of voices clearly, then the whole texture will fall into place nicely.
Next month I will discuss approaches to motivic analysis and other kinds of analysis in learning contrapuntal music, and will wrap up a few odds and ends.

Gavin Black is director of the Princeton Early Keyboard Center. He can be reached by e-mail at <A HREF="mailto:[email protected]">[email protected]</A&gt;.

Counterpoint IV
A student who has worked on a piece of contrapuntal keyboard music in the ways outlined in my last few columns will be able to play the piece with great security, accuracy, and confidence. The student’s performance of that piece will project a strong sense of the contrapuntal lines as individual, autonomous melodies with shape and direction. This result is as close to being certain as anything in the realm of human endeavor ever is: this systematic working out of separate voices is an extremely powerful tool.
However, nothing in that method deals directly either with interpretive questions as such or with aspects of performance that might arise out of motivic or harmonic analysis. The method can work with many different interpretive stances as regards tempo, articulation, phrasing, registration, rubato (or lack thereof), agogic accentuation, etc., and many philosophies regarding memorization, concert programming, authenticity (or, again, lack thereof), fingering, pedaling, posture, etc. In this column I will discuss questions involving form and structure, and suggest an approach to motivic analysis—I prefer to call it motivic awareness—that I believe is useful and flexible, and that arises naturally out of the learning and practicing approach outlined in the last few columns.
Almost every piece of music deals in some way with issues of sameness and change. In some types of pieces, the way in which those opposite poles are presented is very clear. For example, in a chaconne or passacaglia, the repeated harmonic pattern provides sameness or continuity, while the various melodies, rhythms, and textures that unfold over that harmonic pattern provide change. In a rondo, the ritornello represents continuity and everything else represents change or development. In sonata-allegro form, on one level continuity is represented by a recapitulation, and change by the development section. However, the balance (or tension) between sameness and difference may also be manifested in other, more subtle ways, such as having two principal themes that are very different from one another. In general, in tonal music change is represented by departures from the tonic and continuity by the return to it.
In pieces that are largely or entirely contrapuntal—built up of melodies happening in different voices—questions of overall structure, including the handling of continuity and change, are dealt with in large part through recurring melodic themes or motives, and through the patterns of recurrence of those motives. A motive is a recognizable bit of melody, and when it recurs, it is recognizably the same, or close enough to being the same that a listener’s ears and mind will accept it as being the same. In some types of pieces, some recurrences of themes will be at least somewhat predictable. In a fugue, the beginning of the piece will be shaped by each voice entering in turn with the same theme—the fugue subject—and the end section of the piece will involve the return of that theme in some or all of the voices. In between there will almost always be passages—sometimes long, sometimes short—during which the fugue subject is more or less absent. A chorale-based contrapuntal piece will often have one or more recurring motives derived directly from the chorale melody. In a piece that is canonic, the different voices will present the same melodic material at different times.
(Notice that at least some of the reasoning in the above paragraph is circular. I wrote that “in a fugue” such-and-such will happen. I could just as well have written that if such-and-such happens, we will call it a fugue.)
In principle, a piece could be fully or partly contrapuntal without having very much—or indeed any—recurrence of themes. A piece could be written in three or four or more voices, and the voices could share no thematic material at all, and each voice itself could fail to repeat any recognizable themes. However, this essentially never happens. There are pieces—for example, several of the Orgelbüchlein chorales—in which motives are shared by only two out of the four voices (Puer natus, Heut’ triumphieret Gottes Sohn) or in which the voices share little or no thematic material from one to another, but do each repeat and develop motives as they go along (Ich ruf’ zu dir). But a piece that is worked out rigorously in voices and in which melodic motives play no role is a rarity, to say the least. There seems to be, and to have been over the centuries, a strong consensus that a voice-based texture and a motive-based rhetorical structure go together.
This makes it natural to assume that the first goal in interpreting such pieces is to bring out the theme(s), (subject(s), motive(s). I have often had students who were pianists new to organ and harpsichord ask me how it could be plausible to play a fugue, for example, on those instruments, since they do not permit the player to use dynamics to make the fugue subject stand out from the rest of the texture. Of course it’s possible to do this occasionally, when the logistics of the notes and the fingering happen to line up just right, but it can not be done in a thoroughgoing way. However, sometimes students assume that there must indeed be a way to do this, and that it must be in fact the hidden art—the secret!—of playing counterpoint on harpsichord and organ. At first glance this seems to make sense: if themes and motives are important, even crucial, to contrapuntal keyboard music, then surely it is important or crucial that listeners be able to hear those themes.
However, this idea bumps up against an interesting historical reality. It was precisely during the time when the only keyboard instruments available for performance were those instruments on which the player cannot bring themes out explicitly that the writing of contrapuntal music for the keyboard most flourished. The decline in the predominance of rigorously contrapuntal music in the (newly written) repertoire after the Baroque period corresponded exactly to the rise of the piano and the replacement of the harpsichord with the piano in everyday use. So apparently composers have seen the piano’s ability to use dynamics to highlight particular parts of the texture to be inconsistent with, or at least not conducive to, the writing of counterpoint. Instruments on which the changing timbre up and down the keyboard helps to make individual voices clear and autonomous, but on which individual motives cannot be brought out have been seen by composers as most conducive to writing counterpoint for the keyboard.
This, in turn, seems to me to point to perhaps the most important concept for a student, or any performer, to bear in mind when thinking about shaping performances of contrapuntal pieces on a keyboard instrument. On the one hand, the music is at its very essence made up of motives or themes, not just notes. These motives are the philosophical and rhetorical building blocks of contrapuntal music. They are the words and phrases, while the individual notes are the phonemes. But, on the other hand, there is no reason to consider any one theme or motive or subject within a given piece to be more important than any of the others.
In the course of working on the separate voices of a contrapuntal keyboard piece, any student—even one who is not yet very experienced with this kind of music—will become, perhaps unwittingly, a real expert on the motivic content of that piece. Simply as a result of having listened a lot to each voice and, by definition, to all of that voice’s melodies, themes, motives, or subjects, that student will have become perhaps the world’s leading expert on what is going on melodically in that line. This expertise may well be largely subconscious. I believe that the best way to point a student towards making that awareness of the motivic content of contrapuntal voices explicit, and thus heighten its ability to help enliven the music, is to ask the student simply to try to notice anything and everything that happens more than once.
This is a deliberately simple, colloquial, almost naïve way of looking at themes in contrapuntal voices. One purpose of starting out by looking at voices this way is to avoid a prejudice in favor of motivic ideas that have what might be called a professionally sanctioned importance, such as fugue subjects, countersubjects, or motives derived from a chorale. If these things are present, then a neutral search for anything that happens more than once will certainly find them. If, in a particular piece, such themes really are the most important thing about the motivic structure of the piece, then that will become apparent, because those themes will occur more, and/or in more important contexts, than other recurring events that the student may find. But again, even themes that recur more frequently are not more important in performance than themes that recur less often. That is, there is no reason to treat them differently in performance than other motives. It is a good working assumption that anything that a composer took the trouble to do more than once should be treated as rhetorically important.
The question arises of how we know—how a student can tell—what actually constitutes something that happens more than once. In principle, what we are looking for is simple: intervals, melodic shapes, and rhythms that are the same one place in a voice as they are somewhere else (in that voice or in another voice). Some points to remember in looking for such things—or in helping a student to do so—are as follows:
1) It can be useful to make copies of a piece and use different copies to highlight different themes or other recurring events.
2) It makes sense to notice and highlight first of all anything that jumps out as being obvious. This will often include—but not be limited to—“official” motives such as fugue subjects or chorale phrases. Longer motives are the easiest to notice right off the bat.
3) It then makes sense to scan any as-yet unhighlighted sections of each voice looking first for rhythmic patterns that recur, since those are often easiest to spot, and then for intervals or melodic patterns that recur.
4) There is no harm in identifying something as a recurring theme when, according to someone else’s analysis, it might not be. It is more interesting to notice more similarities than to notice fewer. If something seems far-fetched (“there is a major sixth here in m. 4, and another one there in m. 7” or “the note A occurs in each of these three measures”) then it might be far-fetched—in which case it will probably melt away upon further consideration—or it might turn out to be real. If on reflection it seems real, then it might lead to some insight about the piece or to a more rhetorically convincing playing of the piece or of that part of it. It would be a shame to miss out on this.
5) At the same time, it is not necessary to expect to find everything the first time through. The act of looking through voices hoping to find recurring motives will almost certainly lead to playing all of the notes more meaningfully—more like words and phrases and not just phonemes—regardless of whether you do or don’t find all of the plausible recurring motives.

I have recently done (actually re-done) a quick analysis of two very basic Bach contrapuntal works, the first Two-Part Invention and the first fugue of the Well-Tempered Clavier. In the former I have found that one half-measure in both voices together (m. 6, second half), one measure in the upper voice (m. 13, third beat through m. 14 second beat), and a further half measure in the upper voice (m. 21, second half) consist of material that is not part of any motive that recurs. That’s all: ten beats out of a total of 176 in the piece. Of those ten beats, six occur in cadences. In a cadence the relative importance of harmony goes up and the relative importance of counterpoint goes down. (Cadences express sameness or togetherness rather than diversity or change.)
In the fugue, there are 432 beats of voice-writing (27 measures, four beats per measure, four voices). Of these, no more than about 40 beats are constructed out of thematic material that does not recur, and there is no moment in the piece when there is not at least one voice presenting recurring material. The fugue subject occurs officially 23 times. However, part of the recurring material consists of fragments of the fugue subject. The analytic approach being described here makes it unnecessary to consider those notes anomalous or fragmentary, but still permits an understanding of how they relate to the rest of what is going on.
In both of these pieces I have now found more notes that seem to me to belong to recurring melodic ideas—i.e., more things that happen more than once—than I did the last time I looked them over some years ago. Our ability to notice should grow with experience.
Sometimes looking for anything that happens more than once can be revealing in unexpected ways. Years ago when I first studied the Praeludium in E Major, BuxWV 141, by Dietrich Buxtehude, I happened to notice that the opening four notes—the rising tetrachord b-c#-d#-e—recurred at least a time or two. I decided to look for this motive wherever I could find it in the piece. The recurrence of that simple, almost throwaway bit of melody turned out to provide a structural roadmap of the whole work. It occurs in one form or another at all of the important transition points in the piece, and actually serves as a guideline to the affect of the different sections. It would never, however, be identified as any kind of subject that is developed contrapuntally in the work.
(Since there is not space here to delve into the details of these three examples, I have posted them on the Princeton Early Keyboard Center website, <A HREF="http:www.pekc.org">www.pekc.org</A&gt;, with highlighting in several colors, and thorough commentary. I have also posted some expanded discussion of the relationship between this kind of contrapuntal learning and various aspects of interpretation, including a perspective or two other than, and different from, my own.)
In essence, this approach is very simple, as simple as it sounds: notice everything that happens more than once; notice as much as you can, but don’t worry about noticing everything; let your awareness of musical words and phrases enliven your playing of the music.
Next month I will turn to the interesting and sometimes vexing—but comparatively circumscribed!—subject of the playing of repeated notes.

Gavin Black is Director of the Princeton Early Keyboard Center in Princeton, New Jersey. This spring he will be playing recitals around the Northeast. Details and contact information can be found at gavinblack-baroque.com.

Buxtehude BuxWV 141, Part 6: the final section
This month’s column wraps up our detailed look at Buxtehude’s Praeludium in E Major, BuxWV 141, by examining the final section, a 20-bar fugue lasting from m. 91 to the end. Next month we will look at the final movement of the Boëllmann Suite Gothique—the Toccata—and then in the column for May, I will provide an overview of the process of studying these two pieces that has occupied this column for about a year.

Analysis
The fugue subject (Example 1) is introduced in m. 91 of BuxWV 141, in what turns out to be the alto voice of a completely regular four-voice fugal texture. There are several interesting things for the student to notice about this subject and about the way the fugue based on this subject develops in Buxtehude’s hands. Before going through a few of them, however, I want to review what I think is the principal purpose of engaging in this kind of analysis for the student actually learning a piece. Analysis can serve many purposes. For one thing, it is—or should be—intellectually interesting and satisfying in and of itself. It also satisfies, specifically, the puzzle-solving or detective instincts that many of us have. It can help us understand—or move closer to understanding—why the composer wrote the piece the way that he or she did. This might, again, be interesting in itself. It might also lead to discoveries about interpretation, perhaps in conjunction with knowledge about performance practices that prevailed around that composer. Analysis of a piece can also help us learn about connections and influences among composers, and in particular to understand what it was that a subsequent composer learned—perhaps, if we are lucky, in specific detail—from the composer whose work we are analyzing.
However, for a student learning a piece or a passage, analysis of that piece or passage also serves simply to increase the student’s awareness, both conscious and unconscious, of what is in the piece and, in particular, of what is coming up next at any given moment. This awareness—which comes into play, in somewhat different ways, both with memorized and with non-memorized performance—is the most important prerequisite for playing a piece securely and comfortably, and thus for being able to project an interpretation in a convincing manner. This is why I tend to emphasize simple motivic analysis, which I describe as “noticing anything and everything that happens more than once.” There is nothing about a passage the noticing of which won’t contribute to security of performance.

Fugue subject
The first thing that stands out about the fugue subject of this final section is that it is intimately related to the opening four notes of the Praeludium, the short motif that I pointed out in my first column about this work (Example 2). In fact, it is probably fair to say that this subject is derived from that opening motif. This is explicit in the end of the fugue subject (Example 3), and implicit in the opening (Example 4), where it is inverted and decorated, but still meaningfully related to the opening motif.
Of course, it is possible to give a name to the four notes that we hear at the opening of the piece: they are a rising tetrachord, and the later instances of this motif that pervade the piece are tetrachords, perhaps rising, perhaps falling, perhaps augmented or diminished or decorated in some way. I am always a bit concerned that this kind of terminology can tend to trivialize the thing being observed. After all, every piece has tetrachords in it, usually many. It is so simple that it scarcely rises to the level of a theme, motif, or subject. However, the point isn’t that it is a tetrachord or any other particular theme, simple or complicated, common or (close to) unique. And the point isn’t to tie this theme to any other piece. The point is specifically that it happens to be the opening gesture of this piece, and that it is then found recurrently throughout the piece. The fugue subject under discussion here is the culmination of the development of that theme.
This fugue, twenty measures long and in four voices, has eight full and unambiguous subject entries. There are also, at mm. 100 and 101–2, three entries that are full-length but in which the second half of the theme is somewhat altered. (Are these “fugue subject entries”? Does it matter?) Beyond that, the first half of the theme occurs by itself, without the second half, approximately ten times; again there are a few spots that are hard to categorize precisely, such as the alto voice in the first half of m. 104 and again in m. 107. The second half of the theme also occurs several times by itself, for example in m. 98.

Tetrachord motif
Stepping back from the fugue subject or its halves to the tetrachord motif derived from the opening of the Praeludium, we see that this motif is found in almost every spot in this section where the fugue subject itself is not present. These spots are the second half of m. 98 into m. 99 in the tenor voice, m. 103 into
m. 104 in the alto voice, and elsewhere. If a student goes through these twenty measures highlighting the tetrachord motif every time it occurs in any genuinely plausible form—simple, inverted, ornamented—the moments in the piece that do not have at least one voice highlighted will be—at most—as follows: part of m. 103, the final whole-note chord, and (maybe) the two 32nd-note flourishes in mm. 106 and 109.
This section is, as noted above, a fully worked-out fugue in which the four voices all maintain integrity throughout and the rules of counterpoint are followed. However, looked at through the lens of the tetrachord motif, it also appears to be a piece of the sort that is built around the inexorable repetition of a single motif that is always present: that is, the kind of piece that might be described as a chaconne or passacaglia. Even though fugue is a quintessentially contrapuntal form and chaconne/passacaglia is fundamentally a harmonic form, the two can actually coexist, and many of Buxtehude’s fugues do indeed shade over into being chaconnes. This gives them, or tends to give them, a driving or hypnotic feeling.
(A wonderfully unambiguous example of this is the short fugal section that begins at m. 55 of the Praeludium in C Major, BuxWV 136. The subject is exactly one measure long, the section is seven measures long, and the subject is heard once in each measure, in one voice or another. This short passage can be analyzed as a fugue without compromise, but it is also—without compromise—a chaconne. The chaconne theme migrates from one voice to another, but that is only somewhat rare in chaconnes, not against the “rules”.)
The two flourishes that are constructed of 32nd-note rising scales, found in mm. 106 and 109, could be seen as the apotheosis of the tetrachord motif, constructed as they are out of two of them in a row, sped up. Is this a convincing connection? I am not sure; a scale is pretty basic and common, and clearly the main point of these flourishes is to heighten visceral excitement leading to the final cadence. The main point against considering these scales to be a direct outgrowth of the opening four notes of the Praeludium is that the scales begin on the beat, whereas the tetrachord motif most emphatically begins just after the beat. Nonetheless, in playing this piece myself, I have always found it meaningful to hear those two half-measures as being an outgrowth of the four-note half scale that has been so important in the construction of the work. I would again say that it doesn’t matter what conclusion a student comes to about this, or indeed whether he or she comes to any conclusion at all. The act of noticing and thinking about the question will help fix the piece in the student’s mind and make the performance more secure and convincing.

Practicing this section
So, how should a student approach the actual practicing of this section? I believe that there are several practice possibilities that work especially well for these measures. To start with, since this passage is both fairly short and extremely well worked out as a fugue, it is a good section to choose for a rigorous application of the technique of practicing separate voices and pairs of voices. I would organize this practicing as follows:
1) Divide the section into either two or three shorter bits. These will each be somewhere between six and ten measures. They do not have to correspond to natural musical divisions, though of course they can.
2) Choose one of these shorter passages and play each voice through several times, slowly and accurately. It is fine to keep the bass voice in the hands for the time being, even though it is certainly a pedal line. Each of the two inner voices should be played, at this stage, an equal number of times in each hand.
3) Combine the voices into pairs. With four voices there are always six pairs: SA, ST, SB, AT, AB, and TB. They are all equally important and should all be practiced a roughly equal amount. Note that for these combinations the alto voice and the tenor voice each have to be sometimes in the right hand and sometimes in the left. It is extremely important to keep the tempo slow enough that this process feels easy.
4) Repeat this with each of the other short sections.
As I have written elsewhere, I do not consider it particularly necessary or useful to try to put together the groups of three out of four voices. (There are four such groups of three.) Of course, the three upper voices may well be practiced as a group under the heading of “practicing the hands.” That is a practical/technical step rather than a musical/listening step, as the above exercise is.
Another specialized technique that can be incorporated into the learning of this passage is that of actually leaving out notes that are rhythmically lighter and that, on a piano or violin, for example, the player might well play quietly. This is an extremely useful technique on instruments that do not offer dynamic inflection of individual notes, that is, for keyboard players, on the harpsichord and organ—so much so that I will at some point devote a column to it. In this piece it has a special relevance to the motivic analysis that we did above. If the student plays the theme leaving out the off-the-beat sixteenth-notes, then the structure of the theme becomes abundantly clear. Then, when those unaccented notes are added back, they stand a good chance of coming across to a listener as light, without the player’s having had to do anything very calculated to make them light. The theme without the off-the-beat sixteenth-notes looks like this (Example 5, with the newly-created eighth-notes played detached).
Of course I have used some judgment about which notes to omit. You could actually make a case for leaving out—again, obviously just for purposes of this exercise—the first note of the theme. The student can play the theme this way one voice at a time and also with pairs of voices.

Fingering and pedaling
The next set of steps is the usual: working out fingering and pedaling, practicing hands and feet separately, putting hands together, putting each hand with the feet, and, finally, putting the whole texture together. The bass voice is clearly a pedal line here. (Remember that with Buxtehude, the sources do not always make this clear.) There are a few spots—I have found them in mm. 96 and 97—where the two hands alone cannot reach all of the notes, and the bass line is well suited to the pedal. The pedaling has a couple of interesting issues to work out. The first of these is the transaction in the middle of the theme in which the feet have to move down by two successive thirds (Example 6).
It seems inconceivable that the F-sharp would not be played by the right toe (though someone could prove me wrong about this). How should the D-sharp and the B then be played? There are a number of possibilities that the student can explore, and they have somewhat different implications for articulation. (I myself would play the D-sharp also with the right toe, trying to make the articulation that this pedaling automatically creates as subtle and light as possible. It is also possible to play the D-sharp with the left toe, and then the B either also with the left foot—creating a significant articulation—or, reaching under, with the right toe. This latter might be awkward or might not, depending on both the build and the habits of the player.)
There is also the question of how to pedal the last four notes of the theme, the rising tetrachord. In many passages in the repertoire, legato can be achieved equally well with toe/heel or alternate toes. Here alternate toe is made difficult, at least, by the pattern of sharps—at least if the left foot takes the low B. Since there were physical constraints against heel pedaling in the late seventeenth century—high benches, small pedal keys—a passage like this forms part of the evidence that in general in those days organists did not expect always to play legato. That is a big subject, beyond the scope of this series of columns, but it is something for a student and teacher to think about. Successive toe pedaling is easy here, and leads to a non-legato approach to, at least, the eighth notes. When the pedal plays the opening half of the fugue subject without the latter half, as it does repeatedly in the last third or so of the section, the pedaling is straightforward, as it also is with the quarter-note passages, since those notes are fairly slow. These pedalings are straightforward, but still have to be thought out carefully and practiced well.

Hand choices
Since all three upper voices belong in the hands, the same issue arises that we have discussed in the last few columns: the dividing of the middle of three voices between two hands. There are many places in this section where multiple solutions are possible, for example, mm. 93–94, 97, 102–3, and more. As always, the student should not forget to take a comfortable hand position into account in sketching out the hand choices for those spots. Another important consideration is that of allowing faster or more intricate notes to be played with as little interference as possible from other notes in the same hand. So, for example, in m. 101, I would have no temptation whatsoever to take any alto voice notes in the left hand, whereas in m. 105 and the identical m. 108, I would take both alto voice notes in the left hand. In mm. 106 and 109, I would take all of the tenor and alto notes in the left hand to facilitate the trills.
A special hand-choice issue in this piece is the fingering of the 32nd-note scales in mm. 106 and 109. They can be played in the right hand, split between the two hands, or even, somewhat counter intuitively, played by the left hand, with the right hand taking the high e′′ in m. 106 and the middle e′ in m. 109. This latter would only make sense for a player who finds it easier to play upward scales rapidly and fluently in the left hand than in the right hand. (This makes sense physiologically. Each hand can play more naturally going towards the thumb than going away from it. This is the “drumming on a table” effect.) These flourishes can work any number of ways, but it is, again, something that the student should make a point of thinking about and planning out well.
Everyone that I have known who has worked on this piece has found the passage in the second half of m. 102 (Example 7) to be the most difficult to finger and play securely. This is because of several things: it is impossible for both of the two voices playing sixteenth-notes to be unconstrained by other notes; the tenor voice and the alto voice keep bumping into each other; and the placement of the sharps makes some fingerings that would otherwise be possible impossibly awkward. This is a passage for the student to pick apart very thoroughly, with no preconceptions about which hand or which fingers should do what. It is important, probably, to change fingers on all of the hidden, that is voice-to-voice, repeated notes. It is almost certain that it is a good idea to divide the alto voice fugue subject fragment between the hands. Therefore, it is important to listen carefully to that motif as it passes from one hand to another to make sure that it flows the same way in two hands that you would want it to flow in one.
This ends our detailed look at the Praeludium in E Major. Next month, back to Boëllmann.

Gavin Black is Director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached by e-mail at .

Buxtehude BuxWV 141 – Part 2:
Fingering, pedaling, and
practicing, part 1
In this month’s column, we will look at the opening section of the Buxtehude E major Praeludium in great detail as to fingering and pedaling, and outline ways of practicing that section. When we return to this piece, after beginning our look at the Boëllmann Suite Gothique, we will analyze the section that begins in m. 13 with regard to practicing and learning that section. These two sections offer several different textures and types of writing; each suggests a different approach to the very practical act of learning the notes. These textures include the one-voice opening, the multi-voiced but not strictly contrapuntal measures that immediately follow, and the rigorously contrapuntal—fugal—section that begins in the soprano voice in m. 13. Each of these textures recurs in this piece, and of course throughout the repertoire as well.
This and the next few Buxtehude columns will focus on the steps necessary to learn the right notes securely and efficiently. I will try my best to do this in a way that leaves open as many different interpretive possibilities as possible. In particular, I do not mean to take sides in any debate about how much to incorporate “authentic” fingerings and pedalings, or about what those are or might be in any particular case. That does not mean that I will not mention them or include them among the possibilities. As I hinted but did not quite state last month, I will not discuss any work on memorization. (I have, like many performers and teachers, somewhat mixed and complicated feelings about memorization, but I do not consider it to be a necessary or integral part of learning a piece well and performing it in a way that is both solid and artistically worthwhile. I will discuss memorization as an issue unto itself in a later column.)

Fingering
Since the opening of our Praeludium (see Example 1) is a monophonic statement of three rather long measures—49 notes—the first question that arises is which hand or hands should play it. (This foreshadows the most important practical question about any passage of keyboard music; namely, which notes should go in which hand. This question must precede detailed questions about fingering, and it is often overlooked or shortchanged by students. More about this later.) Since the passage is basically high—in the right hand region of the keyboard—and is probably not going to be played in a way that is prohibitively fast for one hand, it makes sense to start out by assuming that it is a right-hand passage.
However, it also makes sense to look for places where taking some of the notes in the left hand would make things easier. Each student can look the passage over and make this judgment for him- or herself. It might, for example, make sense to take the four sixteenth notes of the third beat of m. 3 in the left hand. These notes are lower than the rest and using the left hand to play them would put that hand in a good position to participate in playing the chord on the first beat of m. 4.
It is also possible to share the notes more or less equally between the hands, though I myself have not been in the habit of doing so in this passage. An advantage of sharing the notes between the two hands is that it is just easier to execute. This becomes more important the faster a player wants the passage to go. A disadvantage to dividing the passage up between the hands is that it gives more to think about in the learning process and to remember in playing, and probably takes longer to learn.
On a more positive note, an advantage to keeping the passage in one hand is that it is probably easier or more natural to project the overall rhetorical shape of the line when the shape and spacing of the notes is felt in the most direct physical way by the player. None of these considerations is absolute, and a teacher and student can think about them and work them out.
Just for the record, the fingering that I myself would use to play this passage is shown in Example 2. This is largely a common-sense and hand-position-based fingering. For example, the choice of 1-3 to begin the passage is entirely based on the way that my own fingers happen to fall over those notes, given my posture and my arm angle. (The arm angle stems from my preference for letting my elbows float out from my sides, which in turn is—for me—part of a relaxed posture.) The first four notes could just as well be played 1-2-3-4 or 2-3-4-5. The choice of 3 rather than 4 for the D-natural 32nd note late in m. 1 is designed to make it easier to reach the coming G# with 4 (rather than 5). The point of playing that G# with 4, in turn, is twofold: first, to place the (long) third finger on the F# and the (shorter) second finger on the E; second, to make it easier then to reach the high B on the final half-beat of the measure with finger 5. (It would also be fine to play those notes—G#-F#-E—with 3-2-1.) For me, keeping the thumb off of raised keys is a guiding principle.
A reason for not playing the third beat of m. 1 with 2-1-2-5, etc. (but rather with 4-3-2-5, etc.) is that the gesture of turning the second finger over the thumb to play the G# moves the hand away from the upcoming (high) E, and therefore makes the playing of that note awkward—at least, that is how it works with my hand. In m. 3, the non-adjacent fingerings of each of the beat groupings are all designed to move the hand in the correct direction for whatever is coming up next.
This fingering is not intended to be a recommendation or even a suggestion: it is just how I would probably do it. There are many other ways. (Some of these might be more historically minded—with more disjunct or pair-wise fingerings—or less so—with substitution or more use of the thumb, even occasionally on a black note.) The important thing is that teacher and student work out a fingering that is appropriate for that student. Sometimes that process involves a lot of specific input from the teacher, sometimes little or none. A teacher should always look for ways to let the student assume increasingly more responsibility for working out fingerings. I tend to give very few specific fingering suggestions, but keep an eye out for spots where a student may not have succeeded in finding something that works well. In those cases, I will invite the student to analyze the spot again, perhaps with more input from me.
So in this case, once a fingering has been worked out, the most effective approach to practicing the passage is clear. That is, since it is only one line and one hand—at least, certainly one hand at a time—there is no concern about how to combine parts, and in what order. The plan is just to practice it. First, choose a very slow tempo: slow enough that playing the right notes with the planned fingering is actually easy. This might, for one player, be sixteenth note equals 60, for another 80, for another 45. For an advanced player or a good reader it might be faster, and it might be all right to think about a pulse for the eighth note even from the beginning. Anything is all right, as long as the student does not start with too fast a tempo. Then, having played the passage several times at this starting tempo, the student should play it several times a little bit faster, then a little bit faster still. At some point, the beat in the student’s head will naturally shift from the sixteenth note to the eighth note, then to the quarter note. The crucial thing is not to get ahead of a tempo that honestly feels easy. This, if practiced rigorously, will lead to unshakeable security.
Meanwhile, the rest of the opening section is multi-voiced, a mix of not very strict counterpoint and homophonic writing. In this passage, the main practical question is which hand should play some of the inner-voice notes. As I mentioned above, this is extraordinarily important. I have seen students waste a lot of time or even make an easy passage almost unplayable by assigning notes to hands in an awkward way. This is usually caused by assuming too readily that the notes printed in the upper staff should be played by the right hand and those printed in the lower staff should be played by the left hand. In fact, there should never be such an assumption unless the two hands are meant to be on different keyboards, providing different sounds for different parts of the texture. In general, the two manual staves between them present a note picture, and we have ten fingers with which to play that note picture in the most reliable way possible.
In each of the measures in Example 3, there are notes in what is more or less the alto voice that are printed in the upper staff; some of these might be best played in the left hand. The notes that I have highlighted are those that I would choose to play in the left hand. Again, this is not by any means the only way to do it. The first criterion that I use in working this out is that “extra” notes should be placed in the hand that otherwise has less to do. That is at work very strikingly in mm. 7-8, and the beginning of m. 9, but also elsewhere. Sometimes hand choices are made based on the need to prepare what comes next. That applies here in m. 11, where I am not taking several notes in the left hand that could, or in a sense should, be in the left hand, so as to make it possible for the left hand to play the (tenor) E in the chord in m. 12. (There would be other ways to deal with this, involving substitution.)
Sometimes the notes of a passage in a middle voice can be divided between the hands just to make that passage easier—less inclined to get tangled. This is the case here in m. 5 and to some extent in m. 10. An overriding consideration is hand position: how can notes be divided between the hands in a way that best allows each hand to remain in a natural, comfortable position?
After the hand assignments have been worked out, the next step is to work out fingering. (In the process, some hand choices may be changed.) As always, fingering will depend in part on factors that differ from one player to another, including the size and shape of the hands, existing habits or “comfort zones,” and artistic goals concerning articulation, tempo, and other matters. Example 4 shows a possible sample fingering for one of the more convoluted of these measures. As always, there is a lot here that could be done differently. For example, it could make sense to play the E that is the first note in the top voice of the first full measure with 5, or the D#/B right-hand chord later in that measure with 2/1. It would also be possible to take the A#-B in the first full measure with the left hand, probably with 2-1. The above is just one way of doing it.

Practicing
Once the fingering has been worked out, the next step is practicing. The principles of practicing are always the same, and they are both so important and so difficult psychologically (for most of us, certainly including me) that they can’t be repeated too often: break the music down into manageable units—short passages, separate hands and feet; practice slowly enough; speed up gradually and only when the unit being practiced is really ready for it. In the case of the passage under discussion, one sensible way to divide things up might be as follows:
1) the right hand from the last few notes of m. 3 through the downbeat of m. 9
2) the left hand from the downbeat of m. 4 through the second beat of m. 9
3) the right hand from the first high B in m. 8 through m. 12
4) the left hand from the half note D# in m. 8 through m. 12, and
5) the pedal part, which I will discuss in its own right just below.
(Notice that the sections are designed to dovetail, not to bump into one another. This guarantees that practicing in sections will not cause fissures or awkward transitions to develop. This is quite important. It also applies to practicing across page turns.)
Each of these units should be played many times at, initially, a very slow tempo: as always, slow enough that it feels easy. For most students it would probably make sense, given the somewhat complex texture of this passage, to start with a beat—in the student’s head or from a metronome—that will represent the 32nd note, so that each of the sixteenth notes will receive two of those beats. This 32nd-note beat might initially be at 100, or 80, or 120: whatever feels comfortable. Then each unit should be sped up gradually.
(Some musicians express concern that starting the practicing procedure with beats that represent very short notes—many levels down from the “beat” suggested by the time signature—will result in playing that lacks a sense of underlying pulse, that is too divided into small fragments. However, it is insecurity as to the notes, fingerings, and pedalings that is by far the greatest cause of rhythmically unconvincing playing. At the early to middle stages of learning a passage, the best thing that we can do to predispose that passage towards convincing rhythm is whatever will get the notes learned the most securely. The use of very small note values early in practicing is so removed from later performance, in time and in feel, that I have never known it to come back and haunt or influence the quality of a that performance.)
Some variation is possible in the mode of reconnecting the separate hands. In general, the slower you are willing to keep things, the more promptly you can let yourself put components of the whole texture together. There is some speed at which any given student could indeed skip the step of separating hands. For most of us, in moderately or very difficult passages, this tempo is very slow indeed, and in general it is not a good idea to aim to do this. (Not a good idea partly because it taxes our boredom threshold and partly because separate-hand practicing also allows us to hear things clearly.) In general, if each hand feels really solid at a certain tempo—ready in theory to be performed by itself at that tempo—then it is possible to put those hands together at a somewhat slower tempo. How much slower varies from one situation to another. The overriding principle is a familiar one: when you put the hands together, the tempo should be such that the results are accurate and the experience feels easy—no scrambling, no emergencies, no near misses.

Pedaling
The pedal part in mm. 4–12 of this piece is simple though non-trivial. I would play the fifteen pedal notes with the following feet, all toes:
l-r-r-r-l-r-l-r-l-r-l-l-r-r-l
Other possibilities involve, for example, playing the first note of m. 5 with left toe (crossing over) or playing the second note of that measure with right heel; or playing some of the two-note groupings that span bar lines (between mm. 6–7, 7–8, 8–9) with one foot, either all toes or toe and heel. Once a student has decided on a pedaling, he or she should play through the pedal part slowly, not looking at the feet, until it is second nature. Since the note values are all long, getting the pedal part up to tempo will not take as long or go through as many stages as it would with some other passages. However, it is extremely important not to shortchange the practicing of even this fairly simple pedal line. This is all the more true because in general lower notes and slower notes play the greatest part in shaping the underlying pulse and rhythm in organ music. This pedal line is both.
When the pedal part seems very solid, then it is time to begin practicing it with the left hand. It is often true—for most players—that “left hand and pedal” is the combination of parts that requires the most work. Therefore it should be started as soon as each of those parts is ready. It is also often true that once left hand and pedal is very secure, and the right hand part is well learned, and the two hands together are secure, then the whole texture will fit together without too much trouble. However, it certainly never hurts to practice right hand and pedal as well. In the case of this section, there are a couple of places where the strongest rhetorical and rhythmic interaction is between the something that is being played by the right hand and the bass line in the pedal. This is the case, for example, with the transition from m. 3 to m. 4, and also the middle of m. 10. Practicing the right hand and pedal together will draw the attention of the ears to these spots.
Next month we will start looking at the Boëllmann, concentrating on understanding the overall shape of the piece and looking for connections and contrasts.

Further thoughts on counterpoint

Recently, a student asked me during a lesson to remind him about voices: what they were and how to approach them while working on a piece. This surprised me, since we had already dealt with this fundamental aspect of music. This student was a beginner at the time, and I assumed that a basic understanding of what a “voice” is in a keyboard piece was something that I had covered in lessons early on—and thoroughly.

Perhaps I had not done so adequately, but it turned out that there was something else going on here. The student had been using a computer music notation program and had bumped into some oddities about the way that program treated the concept of voices. He was trying to type out a piece that was inconsistently contrapuntal. The program conceived of notes only as belonging to one voice or another and (I gather) kept complaining about his attempts to add notes in the ways that he thought were correct.

I believe that he did figure out how to make the process work, possibly by finding something to click on that enabled chords. But through this experience and aided by the discussion that we then had, he developed a firmer grasp of the notion that a given note might specifically follow another specific note in a voice, not just be the next note in an overall texture. This helped him figure out certain things about rhythm that had previously eluded him. It was also interesting and useful that this experience triggered my quick and unplanned review of the whole matter of voices and counterpoint in keyboard music. Since that time I have been musing about the subject, and this column discusses some thoughts loosely bound together by their connection to the idea of playing in voices and the idea of playing counterpoint. 

I wrote a series of four columns about counterpoint ten years ago. (See the September through December 2008 issues of The Diapason.) Having reread these essays, I see nothing that I would now dissent. But I have ten years’ worth of further experience and reflection, some of which you may find compelling.

First, it is a common conception that counterpoint is a form of conversation: in any contrapuntal context there is a series of dialogues going on. One of the goals for many of us is to play contrapuntal lines with a naturalness that makes this conversational aspect seem real and unforced. I tend to view conversation as something that is intrinsically about pairs—conversation is best exemplified by two people talking to one another. In larger groups, the overall conversation is constructed out of simultaneously overlapping and alternating two-part conversations, enhanced by listening. I tend to conceptualize the conversation of counterpoint that way—that what is going on in a texture of more than two voices is several simultaneous two-way conversations. This informs my process of working on and teaching contrapuntal music. As I wrote in those columns from ten years ago, I strongly favor practicing pairs of voices. But in contrapuntal music of four voices, I do not see any point in practicing all of the possible groups of three voices, let alone the five possible groups of four voices in a five-voice texture, and so on. I believe that going straight from pairs to the full texture is efficient, revealing, and informative. The concept of contrapuntal conversation is well established and amply demonstrated to be fruitful.

Over the last several years I have also come to see a different, parallel way of looking at counterpoint, one that does not conflict with the conversation model, but coexists with it. A contrapuntal texture is an analogue for the world or even the universe—anything and everything that exists simultaneously. That is, for the much bigger real-life contrapuntal texture consisting of billions of people, countless trillions of other creatures, an indescribable number of inanimate but active objects (clouds, waves, or celestial bodies) and so on. A piece of music with three or four voices is a vastly simplified but powerful representation of that bigger, infinite tapestry. Each piece of counterpoint is a representation of a different part of that tapestry or a different way of symbolically representing the whole of it.

This manner of looking at counterpoint came to me as a consequence of my experience attending certain kinds of immersive theater and dance—performances of narrative in which audience members are not all engaged in watching the same narrative unfold in front of them. Rather, they walk around experiencing different aspects of a narrative that is unfolding simultaneously in parts in different spaces. It is a structure that is also in a sense a direct analogue to the structure of all of existence. Most of the theater work in this form that I have experienced has been largely or entirely non-verbal, and therefore the analogy between it and the non-verbal narrative of (instrumental) music is direct and powerful.

It is debatable whether or not this concept holds deeper meaning pertaining to the details of performance, for any particular performer, or for a student. I believe that it has sharpened my focus on the importance of lines that do not happen to be playing primary material (that is, recurring subjects or motifs). In life, after all, everyone is the protagonist of their own story! I suspect that this way of looking at it has tended to help me play contrapuntal lines more vividly and with more rhythmic freedom. Playing individual contrapuntal lines with freedom involves something that can be thought of as a paradox or just a practical problem, since they all have to come out at the same place at the same time. I suspect that conceiving those lines as not just things that the characters are saying but as the characters themselves has allowed me to intuit and explore ways of dealing with that paradox. However, I am in the early stages of exploring this as far as my own playing is concerned. The point is that this is an idea that a particular student or other player might happen to find interesting, thought provoking, or inspiring.

I recently encountered the following quote in a memoir published in 2015 by the actor and director, Alvin Epstein. I offer it as another thought or image that can apply nicely to musical counterpoint as well as to both its ostensible subject of human conversation and to the writing of drama:

In real life, conversations between people don’t stick to one subject or one train of thought and follow straight through-to-the-end, period, and then introduce another idea all neat and orderly. In real life we speak in interruptions, new ideas being introduced before old ones have been finished, old ones coming back again. There are many threads to the way we actually speak to one another, it’s a tapestry.

I take this as a sort of challenge when it comes to playing counterpoint, since the thrust of a lot of our analysis of contrapuntal music is to try to find order and logic. But neither conversation nor the panoply of human and universal experience presents itself as orderly all of the time.

There are two pieces that have odd relationships to the concept of counterpoint that I have always found intriguing. I am speaking in particular of the first prelude from J. S. Bach’s Well-Tempered Clavier and the Toccata from Symphony No. 5 by Charles-Marie Widor. What does it mean to say that these two pieces involve counterpoint? Is that accurate or meaningful? 

The Bach prelude, which is a succession of arpeggios, can be analyzed as three-voice counterpoint. The first note of each half-measure is one voice, the second note another, and the remaining six notes the third. You could generate all of the notes of the piece by writing those “voices” out each on a separate staff, as we might more meaningfully do with a three-voice fugue. It is probably correct to say that this notation actually means, “play the notes of these chords in this order and overlap almost everything.” This ostensibly contrapuntal notation is interesting perhaps mainly as a commentary on the composer’s habits or ways of organizing his conception of music. But what contrapuntal impulse or feeling is there in this piece, if any? I hear the bass line—the first note of each half measure—as a melody, a line, or voice. I then tend to hear the highest note of each half measure—which is played twice per gesture, once on a beat and once off the beat—as a kind of half-heard counter melody. The force or presence of that counter melody shifts in and out from one part of the piece to another in ways that I think reflect the ebb and flow of harmonic tension more than anything else. It feels to me like a kind of half-hidden, impressionistic counterpoint served on a bed of harmony.

As a final tip of the hat to my summer London trip and its relevance to music making and teaching, I recall an experience of me playing this prelude at a public open-air piano at Tottenham Court Road Underground station in London. This is one of those pianos set up for passers-by to use. As far as I know, this is the only time that I have played piano in public, and probably also the only time that I have played from memory in public. 

In the Widor, I hear counterpoint in rhythm, or in rhythm as texture. The two components that are present for most of the piece—the outlined sixteenth-note chords and the actual chords—are made up of essentially the same notes as one another. They cannot be in counterpoint with each other in the usual melodic motivic sense. Yet, I think they cohere into a texture—maybe the quick notes sort of emanate from the chords. But what I find interesting is that when the pedal comes in, I hear it as its own melody or motif. It is also tracking the same notes much of the time. But the different sonority and the longer rhythmic arc make it seem like a response rather than a redundancy.

All of the above is, in a sense, a set of attempts to broaden the concept of counterpoint or of the range of reactions that one might have to it. I close by discussing basic rhythm in relation to voice notation that my student mentioned above was grappling with. If you are unaware of, or confused by, the voice leading in a contrapuntal piece, it can be unclear which notes are placed where rhythmically. For example, if we see something written like Example 1 and understand the voice situation, it is clear that the F′ is on the third beat of the measure and the B is on the fourth beat. That B follows the middle C in the lower voice. It is also clear that the F′ is held through the B, plus or minus any subtleties arising out of articulation. 

However, if the voice-leading situation is unclear to someone looking at this bit of music, it could appear that the notes stack up like Example 2 with the B on a (non-existent) fifth beat—that is, following the entire half-note’s worth of the F′—and the middle C sort of left hanging.

This can be characterized as a fairly basic mistake, one that even a beginner who had learned to read music would not make. In the case of my student, his temporary confusion about the voices—which did indeed cause him to misinterpret certain rhythms in this sort of manner—was caused by that notation program. However, that is not the only time that I have seen straightforward rhythms appear unnecessarily complicated, or just plain wrong, because the voice-leading is unclear or being misunderstood. Untangling voices can be an efficient way of clarifying and simplifying rhythm.

Next month, I will describe some ways that thinking about rhythm has made me rethink some of what I have said in the past about counting and basic techniques for rendering rhythms correctly. I will also write about music that is partially or inconsistently contrapuntal, and some evolving ways in which I discuss that concept with students.