On Teaching

Hand Distribution III

Continuing our trek through the Alla Breve section of Bach’s D Major Prelude and Fugue, BWV 532—looking closely at issues involving hand distribution—we come to a brief section that is influenced by something other than the music itself:

Example 1 shows that if there were nothing else to think about, clearly there is reason not to distribute the two voices between the two hands. That is the first principle of hand distribution, after all. However, in most editions of this piece, there is a page turn right about here. Therefore, the player can gain a bit of ease with that page turn by taking all of these notes in one hand (most likely the right hand). It is entirely possible that the various editors have chosen to position these measures at a page turn in order to help out in this way. Of course, for a player who memorizes the piece this won’t matter in the long run, but it might still help during the learning process. 

This is a special case—sort of a diversion. In fact, analyzing it like this is a useful way to help a student to relax: talking about something practical and not artistically intense, but relevant. However, it is not an unreal concern, and there are other reasons for taking clusters of notes in one hand in order to deal with something else while playing. The main one is probably the act of changing stops. Even something as simple as grabbing all of the notes of the final chord of each verse of a hymn in one hand to change stops with the other is a branch of decision-making about hand distribution.

The rest of this Alla Breve section mainly presents the same issues that we have already seen, with perhaps a few twists. I will go through it all, but concisely, since it is more or less “review”. 

The next short passage (Example 2, measures 48–49) has an outer voice that is more active than the other voices. Therefore it will make sense to keep that voice by itself in one hand, for the most part. Some players may want to break up the middle voice by taking the d′ at the end of measure 48 in the right hand. There may be other modifications that could make sense, but tracking the entire middle voice in the right hand would significantly increase the difficulty of the passage.

Example 3 (measures 50–51) shows the next measure, which has an intricate middle voice. All of the notes of that voice can be reached by the right hand; however, it might make sense to take some or all of those notes that can also be reached by the left hand, to break up the physical act of combining that line with another. The candidate notes are probably the opening c#′, and the b and the a in measure 50.

The next, which is fairly lengthy, has the fast-moving figures in the upper voice. However, the two slower voices are not close enough to one another to be taken in the left hand, clearing the right hand just to track the intricate line (see Example 4, measures 52–59).

For most players, the easiest and most natural way to finger the passage will involve taking in the left hand all of the middle-voice notes that the left hand can actually reach, and taking the notes that the left hand cannot reach in the right hand. On the second quarter note of each of the odd-numbered measures, where the two higher voices come together, there is a special issue to think about. Which hand can best project to the listener the illusion that this is two notes, one of which moves away as part of the upper eighth-note line and one of which is part of the middle-voice quarter-note line? It is actually a trap in a spot like this to try to play the note with two fingers at once, one from each hand. (No one would suggest this on purpose, but students will indeed fall into doing it, probably through indecision.) The choice of hand (and finger) should be made clearly, even though it can be made either way.

For most of the next nine measures, there are no real questions to think about, either because the (manual) writing is in only two voices or because the balance of more intricate and simpler writing makes it clear. 

At measure 65 (Example 5) there is an interesting subtlety to examine. The middle voice takes over the note being held—presumably in the left hand—by the lower voice. Which hand should play the note? The left hand is right there, but with the “wrong” finger—since whatever finger is holding the note, the hidden repeated note will sound better if it is played with a different finger. This is not hard to manage. The articulation and timing of the move from the c#′ to the a in the middle voice might seem to be under more natural control if both those notes are played in the same hand. However, it is entirely possible to practice towards making that gesture effective across the two hands, as I will discuss below. It might seem better to take that eighth- note a with the left hand to give the right hand more time to get up to the c#′′ on the second quarter note of the measure. However, to me that “leap”—the tenth from the a to the c#′′ over the time-span of an eighth note—is the main reason to take the a in the right hand. The physical gesture of moving the right hand up the distance of that tenth will—like a bowing gesture in string writing—give the player the best chance of shaping the articulation and timing of the musical gesture in an effective and natural way.

At measure 69 (in Example 6) there is a brief passage in which any and all of the notes of the middle voice could be taken by either hand.

This is a good spot at which to remember once again that it doesn’t matter on which staff the notes are printed. The decision about which middle-voice notes to take in which hand should be based on comfort and logistics. This is not a bad time to mention that this will vary with the particular hand shapes of different players. For example, it is quite likely that a player with relatively short thumbs will gain more comfort from taking the d′ in measure 70 with the left hand than a player with relatively long thumbs will. 

Measures 71 through 78 display a texture in which the upper voice is mostly holding long notes, while the other two voices are fairly active. A sample of that passage is shown in Example 7.

It makes sense to take the eighth-note middle voice in the right hand, just accepting that one finger (the fifth finger) of that hand is unavailable since it has to hold long sustained notes. 

At measure 79 there is another opportunity to use hand distribution to make the playing of repeated notes sound natural, and to avoid letting those repeated notes disrupt the flow of the voices. My suggestions are indicated by letters, and are shown in Example 8.

The next complicated or involved spot begins at measure 89 (Example 9). This is a longer example of the sort of writing found at measure 36 and discussed in last month’s column. In this case, however, the eighth notes in the middle voice can all be reached by either hand. The player has a free choice as to which hand should play any of these notes and therefore what pattern to follow through the passage. The teacher’s role is mostly to point this out to the student, and to help the student notice the implications of different choices for hand position and articulation (and of course the implications of articulation preferences for hand distribution choices: the more interested a student is in playing the upper half-note line legato, for example, the more middle-voice notes the student will want to take in the left hand). I myself would probably take the third eighth note of each beat in the left hand—those that are a third higher than the lower voice left-hand notes, closest to them—and the others in the right hand. There are other ways to do it.

The next few measures (Example 10 measures 94–96) end the section of the piece that we are analyzing. Again, either hand can reach the middle-voice notes. Choices can be made based on the usual factors: closeness of notes to one another, hand position, and so on. However, this passage also has a special feature. A player might find that the shaping of the timing and articulation of the syncopations/suspensions in the upper voice feels more natural either 1) with those notes isolated on their own in the right hand, or 2) played with the middle-voice notes in the right hand, using a kind of rocking motion to reinforce the feeling of the pacing and articulation of those notes. This is an individual thing: I can easily imagine doing it either way.

When a student (or any player) has made all of the decisions about which hand should take which notes of a (middle) contrapuntal voice, and worked out the actual fingering, then the next step is to practice the passage in such a way that that voice sounds the way that the player wants it to sound. If the hand distribution and fingering are right (comfortable) then this should not be categorically different from practicing any other sort of passage. 

However, there is one concern. It is undeniably a little bit more difficult—or perhaps it would be more accurate to say “less intuitive”—to shape the timing and articulation of the transitions from one note to the next in a contrapuntal voice when those notes are in different hands than when they are in the same hand. It is very important not to let this fact lead a player into making awkward hand distribution choices. (Sometimes it can and should influence those choices when other factors are fairly evenly split). But it should be kept in mind and addressed in practicing. 

The main way to address it is to practice that voice by itself, but split between the hands with the correct, worked-out fingering. This is partly physical practice, but even more it is listening practice. It is easiest to attune the ears to the flow of the line when the line is not covered by other notes, and this will make it easier to hear and follow the line in the context of the full texture. It is always straightforward to extract the line once the fingering process has been accomplished. It can be a good exercise for a student to write out—or type out—the line by itself, add the chosen fingerings, and practice it from that. However this is probably not necessary. 

For the bulk of this practicing it is important not to change the chosen fingering—and it is crucial not to do so accidentally or at random. (It is always OK to rethink fingering consciously, if there is a reason to do so.) It is also important to listen carefully during this practice to the transition moments, where the voice crosses from one hand to the other. It is possible, especially with a line that is physically not hard to play, to play short sections of the line in one hand at this stage to listen for the continuity, and then put it back into the correct (two-hand) fingering, trying to match the one-handed effect. It is probably a good idea not to do very much of this: just once or twice through a given short section of the line being practiced. If a student finds this to be disruptive (that is, if it is hard to go back to the fingering that is really being practiced after visiting the one-hand fingering) then he or she should not do it. 

When a student has practiced a line this way and is ready to put the whole texture back together, he or she should try at first to listen only to the line that passes between the hands and to pay no attention to the voices around it. (Unfortunately, it is impossible by definition to solo out this line, since in all of the passages of the kind that we have been studying both hands and all the voices are—and have to be—on one keyboard.) This is an exercise in focusing, and of course it can’t be achieved literally. You will always hear the other notes, but you should try to focus on the line that passes between the hands, to be conscious of that line and the sonority of all of its notes.

It can be a good exercise to take any line of music—say the top line of a hymn, or one voice of a two-part Invention, or a cantabile melody from the slow movement of a Mendelssohn sonata—assign it an arbitrary fingering that shifts back and forth between the hands, and practice that fingering. (The fingering can be worked out arbitrarily, but should be written in and not changed at random.) This is not to end up playing that line that way regularly, but as training in listening to and executing the transitions from one hand to the other.

Often the issue is not that of passing a line between the hands. In non-contrapuntal music, the question of how to divide the notes between the hands (assuming, as always in this context, that the whole texture is meant to be played on one keyboard) should usually be determined as simply as possible by trying out the physical comfort, simplicity, and convenience of any of the various possibilities. In fact, very often, just remembering that it is perfectly all right to distribute the notes between the hands however they fall most easily is the most important as well as the first step. The rest follows from that. 

It is interesting that the impulse to play upper staff notes in the right hand and lower staff notes in the left hand can be pervasive. I recently took part in a conversation about the wide left-hand chord on the fourth beat of measure 8 of the Widor Toccata (Example 11). For many players, it is impossible (or nearly so) to play all four notes of this chord in the left hand, and for even more players it is at least awkward. The player who initiated the discussion absolutely could not reach those four notes. Nonetheless, the conversation revolved around such issues as which note or notes it was best to leave out, or whether there was a solution based on arpeggiation, or whether Widor’s left hand was really big enough for him to be able to play this chord easily and nonchalantly. 

It took a while for someone to notice the obvious solution, namely that the highest note of the so-called “left hand” chord is within easy reach of the notes of the upper voice, and can perfectly well be played in the right hand. Doing it this way opens up some performance issues similar to some of those discussed above. The timing and articulation of that note must be just right, as a match to the other notes of the chord. That is intuitive if all of the notes of the chord are in the same hand—and less intuitive, more challenging, if the notes are split between the hands. This is analogous to the issues involved in passing a voice back and forth between the hands. It is also important to keep the articulation of the top line going the way you want it while adding an extra note for the right-hand thumb. A player who absolutely cannot reach the entire chord can take on the task of practicing to get these things right. A player for whom the chord is possible but awkward can decide where the balance lies as to what is easiest and what will give the best results. 

Hand Distribution II

I have suggested that beginning in the middle of measure 19 and going on for a while, it is best to take the upper voice—a somewhat wide-ranging eighth-note pattern—by itself in the right hand, and to group the other two voices—both of them slower, and occupying places in the keyboard compass very close to each other—in the left hand. This is logical and satisfies the various points that I listed last month. It also predisposes the important “hidden” repeated note at the beginning of measure 22 to work out to best advantage, with the left hand playing and discreetly releasing the on-the-beat quarter-note d′, and the right hand coming in to play the following eighth note. 

If, by any chance, it is important to the student/player to make all of the half notes and quarter notes of the lower two voices fully legato, then keeping those two voices together in the left hand throughout will require a substantial amount of substitution, which by definition makes the fingering more complex. This could to some extent undermine the gain in simplicity that comes from letting the right hand track the active upper voice unencumbered. It would be simplest to keep the lowest and middle voices in the left hand. (Also, a player whose performing style suggests keeping this passage strictly legato is probably a player who is quite adept at substitution—someone for whom it does not add much difficulty, if any.)

Example 2: Finding the middle voice

The next section is quite different. Example 2 shows that the three manual voices are for the most part doing similar things to one another.

The measure-long passage beginning at the second quarter note of measure 25 is an exception to this and has the same texture as the passage discussed above. It would be physically possible in this measure to take the middle-voice notes with either hand, but it seems clear that taking those notes in the left hand will make the playing of that measure much easier.

Throughout this passage—with no exception—both hands can reach the notes of the middle voice. The middle voice is somewhat more active than the other two—just for the record, thirty-two notes in the excerpt as it appears in the example, compared to twenty-seven for the upper voice and twenty-five for the lower. This is not enough to make a difference on its own. Active or not, it is the middle voice that can be, and perhaps should be, shared between the hands. It can’t be isolated. 

One way to approach a passage like this is to try it both ways: play the top two voices all in the right hand—probably two or three times, just to get used to the feeling; and then play the lower two voices together in the left hand, also a few times. The point of this is not to choose between those two absolutes, but to look for moments of tension. Where, in playing two voices in one hand, do you feel that it becomes awkward or difficult? If you are lucky, those spots will be complementary: places that are awkward in the right hand will seem natural in the left hand and vice versa. If this is the case, then you are very close to having found a pattern of hand distribution that will work and that will maximize comfort in playing. You can sketch out that pattern, create the specifics of the fingering, and begin to practice. You might want to change something as you go along—I will come back to that important concern below. 

In carrying out this procedure, I make a few discoveries for myself. I find it slightly awkward to reach the f#′ and the e′ in measure 24 with the right hand. I find it somewhat awkward to track the middle-voice notes beginning with the last quarter note of measure 27 and going on for about two measures with the left hand. However, I find it easier to get the c#′ at the end of measure 29 with the left hand than with the right. There are various other details. Again, this is all empirical, and it is just about me: no one else will necessarily experience the passage that way. (For one thing, my feeling for hands and fingers here inevitably bears the traces of my having played the piece for more than forty years, and of my initial encounters with the piece when I was very much a beginner, and tried to read through it and learn it without the guidance of a teacher!) However, anyone can discover a fair amount about what will work best by trying it out this way.

Here are a few more analytical or specific things to say about the passage:

1) If you take the a′ on the second quarter note of measure 23 in the right hand, expecting also to take the b′ immediately following it in the right hand, then that gesture—going from a′ to b′—involves contracting the hand. This is, all else being equal, relaxing and natural.

2) Measure 24 is perhaps an especially good place to alternate hands in the middle voice. If you play the d′ with 4 in the left hand, then the left hand can easily play the f#′ with 2, then the c#′ with 5 and the e′ with 3.

3) If you alternate in this way, then you can play from the beginning of measure 23 through the downbeat of measure 25 without changing the right hand’s position.

4) The g#′ in measure 26 will be easier for most players to take in the left hand. This is because it is far enough from the f#′′ in the right hand that the right hand must execute an uncomfortable stretch or assume an uncomfortable hand position in order to reach it.

Answers to questions about what hand distribution is the most comfortable— particularly in a case like this, where any number of things are possible—may depend in part on interpretive choices. Certainly in this passage, as I mentioned above concerning the earlier part of this section of the piece, if the player wants to make the lines truly legato, that choice will have implications for hand distribution that are different from what might apply if the notes are by and large detached. Full-fledged legato will tend to require more substitution and might in general lead to a need for more even sharing of the voices. It will be easier to finger the outer voices legato if neither hand has to track the middle voice for very long at once. (More substitution and a more even sharing of the middle voice might be alternatives to each other.) If the player wishes to keep the lines detached, a wider variety of hand distribution choices will work fluently and well. In effect, more fingers are available, since fingers that are already holding notes are nonetheless available to play the immediately following notes. Since interpretive choices can—and should—change as someone gets to know a piece better, and also just over the course of a player’s career, fingering choices and hand distribution choices have to be revisited from time to time. Even in the first stages of learning a piece, hand distribution choices might have to be revisited as the specifics of the fingering develop. This is sort of a paradox: you literally can’t create fingerings until you know which hand is going to play which notes, but you might want to make changes in your template as to which hand will play which notes based on the way the fingering works out in practice. (This is only a concern with passages like the one we are looking at now where the hand distribution choices are rather open.) There is no way around this: it is part of the process.

Example 3: Dividing the work

The next brief section of the piece is similar in principle to the opening several measures: there is an active outer voice, so if possible it is likely to be most suitable to group the other two voices in the other (in this case right) hand, as shown in Example 3.

This is true even though the two upper voices are quite spread out from one another for much of the time.  The b′ in the middle voice at the beginning of measure 34, for example, is much closer to the lower voice (left hand) notes than it is to the upper voice notes. However, it is very likely that most players would find it hard—or at least unnecessarily harder—to grab that note in the left hand, since doing so would tend to disrupt the flow of the playing of the eighth-note line. Also, of course, there are more of those “hidden” repeated notes, the playing of which can be especially effective if they are split between the hands.

Example 4: Room for questions

The next short section, shown in Example 4, is interesting. The middle voice is the active one, and here it is doing the most active thing that is represented in this Alla Breve section: outlining the chords in eighth notes, like those seen in the upper voice around measure 20 and elsewhere and in the lower voice around measure 32 and elsewhere. As in the passage found in Example 2, the middle voice is the most active, but here it is a lot more active than the outer voices. This raises several questions: which notes of that middle voice are closer to each of the outer voices? For which hand is it easier to play any given note? Is there a musical advantage to letting one hand track (so to speak) an intricate moving line, or this line in particular? Or is there a musical gain from the ease that might be created by splitting that line up? If so, how is it best to practice a fast or intricate line that moves from one hand to another? Is this an issue of its own, or is it essentially just a subset of practicing the notes as such?

Example 5: Xs and Ys

In this particular case, as shown in Example 5, clearly only the notes marked below with “x” can be reached easily by the left hand, though those marked with “y” can probably also be reached by the left hand, though less easily, for most players.

I would probably find it easiest to take the “x” notes in the left hand (possibly not the first one, f# ′) and all of the other middle-voice notes in the right hand. At each of the “x” spots, I would play the two left-hand notes with 3/1. This is predicated in part on my wanting to play the lowest line somewhat detached, and, for me at least, it clarifies and simplifies the right hand fingering quite a lot. I would also expect to play the upper voice detached, but less so. I want the freedom to close those gaps down quite a bit in response to the harmonic tension of the line. A player who wanted to make that line quite detached could more readily play all of the middle-voice eighth notes in the right hand, if that seemed desirable.

Example 6: A simple choice

The next section, shown in Example 6, is a classic case of the most active material being in an outer voice—the upper voice—and the other two voices having slower, simpler material, the notes of which are close to one another on the keyboard. There is little or no reason not to join the lower voices in the left hand throughout this example (after the first note printed here, which the left hand can’t reach).

Example 7: Upper vs. lower voice

The next several measures, as seen in Example 7, present a number of interesting questions, which can be answered a number of different ways. 

As in Example 5, the middle voice is the active and intricate one. The right hand can certainly reach all of the middle voice notes, and the left hand can reach most but not all of the measure. The difference, for purposes of thinking about hand distribution, is that the upper voice is all repeated notes. If the player wants (as I myself would) to change fingers on those notes in order to gain more control over the timing and articulation of the repetitions, then that might suggest taking some substantial number of the middle-voice notes in the left hand—though it might not make it necessary, depending on the player’s hand size and relative finger lengths. If the player does not care about changing fingers on the repeated notes or would positively prefer not to do so, then with (most likely) 5 playing all of those c′′ sharps, the remainder of the right hand is available to play the eighth-note line. This might in turn mean that on balance it makes the passage easier to free the left hand of the need to catch any of those notes and to allow it to track the quarter-note lowest voice, with its couple of fairly substantial jumps. That might in turn depend on articulation choices for the lower voice.

Next month I will continue this discussion and turn to discussing hand distribution choices in other textures. I will also discuss practice techniques for hand distribution choices that are technically sound, but musically counterintuitive. 

Gavin Black is Director of the Princeton Early Keyboard Center in Princeton, New Jersey. He can be reached by e-mail at [email protected]. He writes a blog at www.amorningfordreams.com.

Substitution in thirds

The left-hand version of this exercise for practicing substitution in thirds starts as is shown in Example 1. Again, you should carry out the multiple substitutions in the most comfortable order. Try out various other fingering possibilities, and also try this, and other similar exercises, with added accidentals, as if it were in C minor, for example, or transposed to other keys. Substitution on black notes is physically different from substitution on white notes, since the black notes are thinner and spaced further apart. The principle is always the same: perform the substitutions in the right order, and plan out carefully the direction and angle from which each new finger arrives and in which each old finger departs. If the departing finger is released down and to the side, you have to be careful that it doesn’t inadvertently play an adjacent natural. 

You can also convert the Rameau passage shown in Example 2 (and discussed in the January 2014 column, as Example 9) into substitution exercises by tying the repeated notes and changing the repeated-note fingerings
into substitutions.

Substitution in fifths

Examples 3 and 4 are exercises for substitutions in fifths. Try these all over the keyboard: as written but with added accidentals, in other keys, an octave up or down. As you practice these exercises and a selection of transpositions, try carrying out the substitutions according to various different timings: 

1) As quickly and as smoothly as possible: instant substitution, but keeping the order correct. For example, in the above left-hand fifths it is better to execute the 4–5 substitution before the 1–2. This keeps the hand compact and avoids uncomfortable stretching. In doing the substitution instantly, as one gesture, this order can be preserved by carrying out something that feels like a rolling motion of the hand. (Technically the 4–5 is closer to “instant” than the 1–2, but the gesture is fast and smooth and should feel like one event.)

2) Very promptly and rapidly, but as a succession of separate quick gestures: in the case of these two-note-at-a-time substitutions, the timing of this approach is similar to that of a mordent.

3) Truly timed finger changes. This can be in a number of rhythms. For example, in the rhythm of the fifths above: triplet quarter notes (i.e., with the new chord, the first substitution, and the second substitution spaced out evenly); a quarter note and two half notes; a dotted quarter note and two sixteenth notes. This last rhythm shades over into the final timing concept:

4) Both substitutions as a quick one-piece gesture at the end of the held note, having almost the feeling of a before-the-beat ornament to the
next note.

I have listed these in a particular logical order: from closest to the beginning of the note to closest to the end of the note. It is important to avoid practicing anything at a faster pace than what you can carry out comfortably. Therefore, you should start with a slower (timed) execution of each substitution, and work towards the faster timings and the “instant” un-timed forms as you become fully comfortable with the fingerings and the shapes of the gestures.

Substitution in scalar passages

Examples 5 and 6 form an exercise that has the appealing feature of being simultaneously silly and efficient. It involves playing simple scale passages, and performing extravagant chains of substitutions on each individual note. This is beyond what you are likely ever to do in fingering a piece of music. There are, however, places where more than one substitution occurs on one note, as we will see below.

This can also be practiced in different timings. The “instant” version will of course take a discernable amount of time, since there are so many fingers involved one after another. Don’t try to practice this exercise at a tempo faster than it can be accomplished accurately and comfortably. It can still feel like one gesture: sort of sliding or slithering around on the note. As always, you should pay close attention to hand position and to keeping everything relaxed and comfortable. You may notice yourself occasionally inadvertently releasing a finger before the next finger has arrived to take its place: in effect converting the substitution to a repeated note. Do not try to correct this by holding the notes down harder. It is just a matter of timing. If this becomes a problem, slow down the exercise.

Substitution in counterpoint

Example 7 shows a Reger passage (from the chorale prelude Morgen-glanz der Ewigkeit—discussed in the November 2013 column as Example 10), demonstrating the practicing of separate voices, with a suggested fingering involving thoroughgoing substitution. (This is the left-hand part. I have written the fingerings for the two voices above and below the staff respectively, for clarity.)

The following is a detailed discussion of the logic behind these fingerings, but with an emphasis on the substitutions, and with comments on how best to carry out those substitutions. You should read it and correlate it in detail to what you see in the music before practicing the passage. If as you read this discussion you think of different fingerings that you want to try out, please do so. Make sure that you understand your own rationale behind those fingerings and that you are convinced that they will be comfortable and effective.

The choice of the first finger for the first note makes sense both because that enables you to reach down to the second note easily, and because it puts the hand in the best position to play the a# that is coming up. (This is a comfortable fingering in part because of where the passage lies on the keyboard. Try the same pattern two octaves higher. It will feel quite different and might need a different fingering solution, perhaps playing the opening note with 2, and substituting 1 at the last instant before playing the a#.) The choice of 5 for the d that is the second note of the piece is also obvious. The first substitution (4–5 on the note e) should be performed quickly, both to relax the hand and to enable the second finger to reach the c#. The substitution on the f# should be treated the same way for the same reasons. The substitution on the g# can be performed either instantly or on a measured basis (it is the first opportunity here to practice the latter).

Moving to the second measure, the substitution on the c# on the first beat has to be performed quickly so that the hand can move on to the next notes (d′, e′). In theory, the 4–5 substitution on the a need not be done until close to the time to play the b on the third beat. However, at the moment of the first beat itself, it will be more comfortable to carry out both substitutions quickly, with the 4–5 actually happening first. (This is to keep the hand compact and avoid uncomfortable stretching.) This should be carried out as an instant “rolling” double substitution. The b on the third beat of this measure is an interesting case. It is natural to play it with 4, and it also should have 4 holding it when it is ready to end (seven eighth-notes later, in the next measure). However, it is a good idea to hold it instead with 5 through most of the length of the note. This is to put the hand in the best position to reach the notes in the upper of the two voices, especially the f#′ that is the first note of the following measure. There is no particular reason not to do the substitution from 4 to 5 right away. (You could also postpone it until just before the end of the measure, in which case it would probably be more comfortable to play the d# with 2. The advantage to playing the d# with 3 is that it enables 2 to be poised to reach towards the upcoming f# as promptly as possible. This is a positive reason to do the substitution instantly.)

At the other end of this long-held b, the substitution back to 4 should be done only after the upper-voice substitution from 2 to 1 on e′. This is so as not to stretch the hand out uncomfortably. The purpose of that upper-voice substitution itself is partly to un-stretch the hand and partly to free the second finger to reach up to f#′. The substitution from 5 to 4 on the a should be done only after the thumb has played the f-natural. This is, of course, to keep the hand from being stretched out unnecessarily. On the fourth beat of this measure we come to the first substitution of non-adjacent fingers. The switch from 5 to 3 on the g# is motivated by the underlying rationale for substitution: it makes sense for one finger to play the note, but for another finger to be holding when it is time to move on to the next note. The reason for using 3 in the latter role is that the next two notes are in a downward direction. (It would also be possible to do a 5–4 substitution, and then another 4–5 substitution on the g-natural.) In any case, the 2–1 substitution on the e′ should be done first and very quickly.

The first substitution of the fourth measure, on b in the lower voice, is the first one we have seen that must be really instant: fully a part of the gesture that plays the note in the first place. This is, of course, because of the sixteenth-note motion in the upper voice. The hand must be in position to reach for and then play f#′ comfortably, essentially right away. The two remaining substitutions in this measure can be done at a somewhat more leisurely pace. On the third beat in the lower voice, my suggested 4–3 4 could be replaced by 4 5–4. Or indeed you could do a 3–2 substitution on e′ that is the lower-voice note on the second beat, and then play the rest of the lower voice in this measure with the fingers as they come. The 2–1 substitution on the f-natural in the upper voice on the fourth beat exists for the purpose of un-stretching the hand.

There are four substitutions that must be carried out in the half measure coming up, the last part of this excerpt. The switch from 2 to 1 on e′ in the upper voice and the switch from 3 to 2 on d′ in the lower voice (a note that was initiated in the previous measure) must be carried out in the order in which I just listed them, for the most basic possible reason. The “new” finger in the second substitution was just in use holding another note. It had to be freed from that note—by substitution—before it could take over its new note. These two substitutions are ideal to be played quite measured: the upper-voice substitution on the second half of the first beat, the lower-voice substitution on the second beat. On the second half of the second beat we encounter two substitutions, both of which must be carried out within the time span of an eighth note. For most hands it will be more comfortable to do the 2–1 substitution on d′ first, and then the 4–3 substitution on b. This means that the latter must be very fast indeed. The two should end up feeling like one gesture. 

The fundamental purpose of this fingering could be described as a way to play all of the notes legato without awkwardness or discomfort. This is achieved by a significant increase in the amount of fingering busy-ness: as fingered here, this passage involves sixty-one fingering events to play forty-three different notes. For comparison, Example 8 shows one possible fingering without substitution, based on a willingness to allow many of the notes to be played non-legato. (Remember, however, that Reger in his own hand marked this piece sempre ben legato.)

Try this fingering out, leaving aside for the moment its musical or historical appropriateness. Keep everything light, and make the non-legato gestures smooth and non-abrupt. Is one fingering easier than the other? What differences in feel do you notice?

(Note: Based in part on feedback from readers of The Diapason, I will possibly add further exercises and examples to the final version of this section on substitution. These will deal at greater length with substitution on black notes and with non-adjacent fingers. I will move on next month to exercises and approaches to learning to play with hands and feet together.) 

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.

This month’s column continues the discussion of learning to play more than one note or voice in each hand, specifically expanding it to music in which the multiple-note texture is that of counterpoint. Playing multiple independent voices in one hand is a practice that many players, most particularly beginning students or aspiring players, find intimidating. As always, part of my own aim in teaching this aspect of playing, or in presenting it in written form, is to demystify it and make it seem less scary, though of course without in any way “dumbing it down” or leading students to believe that it can be achieved trivially or without plenty of study. This is an area in which I would most appreciate feedback from Diapason readers. I begin with a discussion of the concept and move on to exercises and practice suggestions.

The distinction between multiple-note textures that are chords and multiple-note textures that are voices is one that is meaningful and important, but not always cut-and-dried. In the setting of the Old Hundredth discussed last month (see October issue, pp. 18–19), there are four voices: each voice might well be sung as a separate melody by members of a choir or of a congregation. For purposes of practicing at the organ, and in particular becoming accustomed to playing more than one note in each hand, it is possible to think of the piece as being written mostly in chords without misrepresenting it, because the voices are mostly in the same rhythm as one another. Voices (in keyboard pieces) that sound together and that are in the same rhythm as one another are, in effect, simultaneously voices and chords. Voices that differ from one another in rhythm are clearly voices as such. If the number of notes in the texture varies a lot, then it is probably a sort of hybrid. At this stage you should feel free just to keep these notions in the back of your mind. You do not have to define the texture of any passage that you are working on: just notice its characteristics. You will perhaps explore these definitions and distinction further, from a theoretical point of view, later on. The distinctions are also somewhat circular, in a way that is artistically meaningful: that is, you as a player can influence, by how you play, the listener’s sense of what is counterpoint and what is chordal texture, when, because of the nature of the writing, both are possibilities.

In fact, the last line of the Old Hundredth can be used to illustrate the process of practicing separate voices—that is, in a texture in which there clearly are independent voices—that fall in one hand. (The last line is best for this because in that line the rhythm does vary a little bit from one voice to another.) This process is, as mentioned above, mostly one of training the ears: that is, training the ears to follow the separate voices as melodies while playing them together (Example 1). (Note that in this example the voices are differentiated from one another by the direction of the note stems. Most publishers use this technique when it is appropriate to the music.)

Start with the notes—the two voices—in the upper (treble) staff. Work out a fingering for just the upper voice, in the right hand. Since the notes of this voice, taken by itself, span a fifth, the fingering could be as simple as the five fingers over the five notes. This would give (in order) 5-3-1-2-4-3-2-1. Now work out a left-hand fingering for the lower of these two voices. (Yes: you will, when putting the voices together, play them both in the right hand. This left-hand fingering is temporary.) This line covers a span of only three notes, and there are many possible fingerings. One would be 1-2-3-2-1-2-1-2-3. Practice each of these lines separately a little bit: until each one seems solid. (Each of these lines is, in itself, fairly simple, but should still be practiced enough to become really well learned.) 

Now put the two voices together—one in each hand, as you have practiced—on two manuals. This makes the notion of the independence of these voices as concrete a physical reality as it can be, and therefore makes it easy and intuitive for your ears to follow it. At first, choose sounds that are similar in volume but different in character. Then, after you have done this a few times, try sounds that are very different in volume: one of them almost, but not quite, drowning out the other. Then play the two voices together on one manual—still in two hands.

Next, go back to playing the entire two-voice texture together in the right hand, using the fingering that you worked out when you worked on this hymn earlier (October, p. 19). After the experience of separating the two voices between the hands, you should be able to hear the voices independently as you play them together—or at least to be able to begin to do so.

Now follow this same procedure with the two lower voices—those that will end up being played together in the left hand. A right-hand fingering for the upper of these two voices (the tenor voice) might be as follows: 4-3-4-3-2-4-3-4. A left-hand fingering for the lower (bass) voice might be 2-1-3-1-5-3-2-1-5. Of course, other fingerings are possible; work out fingerings that seem comfortable to you. After you have learned each line, and tried out various keyboard and sound combinations for playing the two voices together in separate hands, put them back together in the left hand, again using the fingering that you worked out earlier.

At this stage of putting two voices back together in one hand after practicing them (temporarily) in separate hands, you can try to focus your listening on one of the voices at a time, while playing both. In doing this, you may notice that it is easier to listen consciously to one of the voices than to the other, or that focusing on one of the voices tends to make the playing easier while focusing on the other makes it harder. You can then “zoom out” so to speak, and listen to both voices while playing them both. You should also go back and forth: after you have put the two voices back together in one hand, separate them again and play through them in two hands a few times. 

It is, psychologically or as a matter of perception, easier to hear two voices simultaneously and to follow them as separate melodies if you can feel yourself playing them with different physical entities. This sort of practice is a way of enlisting your ears in helping you to follow separate voices when, because they are together in the same hand, the are naturally pulled towards feeling like part of the same entity. 

It can also be useful to ask your teacher or another player to help you with a drill similar to this one. This involves your playing one voice while the other player plays the other voice of the two that will later be combined in one hand. This should of course be done in all of the different possible combinations. You should play one voice by itself two or three times in a row, then you should play it again while your assistant adds the other voice on a different keyboard. (Note: choose keyboards in such a way that the two of you don’t bump into each other.) Next, switch voices. Then, right away, while that experience is fresh in your ears, you should play the two voices together in one hand with the proper fingering.

Here are some further exercises and excerpts from pieces to help you get accustomed to this sort of practicing, with comments about how to approach each one (Examples 2 and 3). In these two exercises, each separate voice stays within a compass of five notes, so the fingering for the hands separated into voices is straightforward. When you re-combine the voices into one hand, feel free to keep the articulation detached if that helps the fingering to remain simple. Here is one suggested fingering for each hand, though as always others are possible (Examples 4 and 5). 

In the following examples, the two voices are more different from one another rhythmically (Examples 6 and 7). Again, neither of the separate voices spans a particularly wide compass, so the fingering and practicing of the separate voices is straightforward. In practicing the separate voices on different sounds, it is particularly interesting in this case to try registrations in which the two voices are quite different in volume, and in doing so, try to listen carefully to the one that is quieter. See what effect this has on your ability to hear the two voices independently when you put them back together in one hand on one sound.

The following is an excerpt from the Fugue in C Minor from Book I of The Well-Tempered Clavier by J. S. Bach (Example 8). The two voices, which are the upper two voices of a three-voice texture, pass a motive back and forth. In performance, the left hand is fully engaged with much lower notes and cannot participate in playing either of these two very active melodies. A possible fingering for the passage might begin like this (Example 9). The fingering of the individual lines, one in each hand, is straightforward, especially since the rests allow for easy repositioning of the hand. 

Since this is a lively and dance-like passage, it is interesting to try the separate voices on colorful sounds: perhaps reeds, flute combinations including mutations, and so on. Again try some combinations that make the two voices similar in volume, and others that almost drown out each voice in turn. Focus on listening to the voice that is harder to hear. When you put both voices back together in the right hand, notice that in some of the spots where the two voices are both present and moving, they are moving at the same rhythm as one another. Can you hear those spots are individual voices rather than as chords? How does that compare to the last half-measure of the excerpt? 

(There are many passages in Bach’s works both for harpsichord and for organ that provide excellent material for this sort of practice. You can browse through The Well-Tempered Clavier, both preludes and fugues, or, especially, the fugues from the various Preludes and Fugues for organ looking for appropriate passages. It is a good idea to do this sort of practicing in fairly short increments: about the length of the Bach example above.)

Here is an example for the left hand, from the Chorale-Prelude Morgenglanz der Ewigkeit from Opus 79b by Max Reger (Example 10). Each of the two voices ranges fairly far. However, each is still fairly simple to finger for one hand. (The upper voice goes high enough that it lies extremely comfortably under the fingers of the right hand). When the two voices are put together in the left hand, the fingering is challenging, especially since the composer has marked the entire piece sempre ben legato. This does not necessarily mean that all notes must always be legato. However, any convincing rendering of the legato style calls for the use of substitution, an important technique which is discussed later in this method. For purposes of using this and other similar short excerpts as part of the project of learning to hear multiple voices clearly while playing them together in one hand, it is acceptable to play the lines less fully legato than you would want to play them if you were learning the piece. (For example, using 5 on certain successive notes in the lower voice can clarify and simplify the fingering quite a lot, in a way that will be useful for a player who is not already familiar with this repertoire. The articulation that that gives might differ from what you would end up preferring if you were to learn the piece. You should experiment with different possibilities for fingering the two voices together, while working on getting to know the voices separated between the hands.) The fingering can be modified later, if necessary. In fact, just out of interest, I will use this same passage as part of the material for discussing substitution later on. ν

This discussion will continue next month, and will then segue into certain special techniques in manual playing, including substitution and playing repeated notes. After that, in the following several columns, I will deal with combining hands and feet. That will conclude the “nitty-gritty” practical aspect of the Method. It will be followed later on by discussion of registration, repertoire, and the history of the instrument.

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.