On Teaching

Gavin Black is Director of the Princeton Early Keyboard Center in Princeton, New Jersey. In the spring of 2011, he will be playing recitals around the Northeast. Details and contact information can be found at gavinblack-baroque.com.

Buxtehude BuxWV 141 – Part 5
So far we have looked at the first three—or possibly four—of what might be seven or eight sections of the Buxtehude Praeludium in E Major, BuxWV 141. (As I discussed in the column of June 2010, there are a number of different ways of counting sections, depending on choices about how to count brief changes of texture at cadences and several other such issues. Are mm. 47–50 their own section? This does not really matter when it comes to understanding or learning the piece.) Several sections remain, and, as with the three already discussed, they display considerable contrast in texture—where that means primarily the extent to which the texture is or isn’t contrapuntal—rhythm, tempo, meter, and mood. Three sections—mm. 60–72, 75–86, and 91 to the end—are truly contrapuntal. The latter two are real fugues or fughettas, constructed quite rigorously from their subjects; the first could probably also be analyzed as a fugue, but really comes across as a sort of contrapuntal mosaic derived from very short motifs.
The other measures—mm. 73–74 and 87–90—are non-contrapuntal. This does not mean that they fail to follow the normal rules of voice-leading when there is more than one note sounding. It means that they are not essentially constructed through the impulses and imperatives of imitative counterpoint, and that the listener’s ears will not respond to them primarily by following an interaction between independent melodies. The first of these sections, mm. 73 and 74, resembles the trillo longo section discussed at length in the November 2010 column. The passage in mm. 87–90 is a texture new to the piece, something like a four-voice chorale, though not with the aesthetic of any chorale meant to be sung.
In this month’s column I will talk about all but the last of the remaining sections. That section, mm. 90 to the end, will be the subject of next month’s column, which will also include some overall thoughts about this Praeludium and the act of learning it.

Measures 60–72
The passage beginning in m. 60 is a contrapuntal section in three voices. It is noteworthy for several things. It is the first section of the piece to have a tempo marking—Presto. Since this section immediately follows one that is essentially unmeasured, it is quite possible that the function of this tempo marking is more to make clear to the player that we are back to measured and regular music than to suggest a specific speed. Of course, it does at least place the music in the realm of “fast” rather than “slow”. This section is in three voices, with the exception of a few beats where a fourth voice briefly appears. (Two of those beats are at mm. 65–66; the other two are part of the cadential measure, m. 72.) The lowest of those voices has a compass that would not have been playable on the pedalboard of Buxtehude’s time. Therefore it is almost certainly not a pedal line, even though it would fall under the feet fairly well. Oddly, the lowest voice does not go very low. Its lowest note is tenor D-sharp, more than an octave above the lowest note of the manual organ compass. Therefore the entire section has a “high” feeling to it.
The section opens as shown in Example 1. This could be read as the opening of a fugue exposition, with a measure-long subject in stretto with itself from the very beginning. However, as the section unfolds, each of the two halves of this theme (Examples 2 and 3) occurs more often by itself than paired with the other half. (The whole theme occurs six times, one or another half occurs separately sixteen times.) Furthermore, two other short themes are introduced, each of which occurs nine times (Examples 4 and 5).
These four short motifs, including the quarter-note that ends each one, account for by far most of the notes of this section. It is this pattern of four short motifs each recurring many times, not really coalescing into “subject” and “countersubject”, which leads me to describe the section as a contrapuntal mosaic. Since for the performer the important point about this kind of analysis is to allow the mind and the ears to know without fail what is coming up next in the piece, the act of going through the score and highlighting each of the motifs is probably worthwhile.

Hand choices
Since the lowest of the three voices is quite high in compass, it is not surprising that the middle voice can fit—almost every note of it—at least reasonably well in either hand. Therefore, this a good passage for a student to use in practicing the art of making hand choices—something that was discussed at some length in last month’s column, though in the context of a very different piece. Here it is possible for the student to play the lower two voices all the way through in just the left hand—omitting just a few notes of the middle voice, in m. 67 for example. Then it is also possible to play the upper two voices in the right hand, again being required to omit only a few notes. Neither of these is at all likely to be the best way to play the passage, of course. The next step is to go through and figure out what choice of hand actually works best for the middle voice as it goes along. This will be different from one student to another, based on existing fingering habits, details of hand size and shape, and musical goals. Any student should be able to work this out essentially for him- or herself, and it is a good exercise to do so.
Once the hand choices have been worked out, since this is a contrapuntal section, the player should practice the middle voice alone with the correct fingering, in order to make the transitions from one hand to another seem as smooth and natural as possible. This can supplement the usual practicing of individual voices and pairs of voices.
(In the few beats where Buxtehude has violated the voice structure by adding anomalous extra notes, it is fine to fudge the voice practicing a bit—omit the extra notes, or expand the voice that you are playing to included, briefly, two notes. As long as the student is aware of doing one of these things, it is fine.)
An important compositional/aesthetic point to notice in this section is that it ends with an incomplete cadence. Everything that develops in mm. 71–72 points strongly to a C-sharp triad on the first beat of m. 73. (It could be major or minor.) However, instead there is nothing there. The timing and pacing of this non-cadence is important, in particular, in setting up the next section.

Measures 73–74
This next “section” is short enough to earn quotation marks—only two measures (Example 6). This section is preceded and followed by contrapuntal sections that are longer than it is, and that are different from it in mood. That is, they are—though also quite different from each other—both marked by strong rhythmic motion and a regular pulse. This section is marked con discrezione, which would strongly suggest free, perhaps even unmeasured, rhythm, even if the overall nature of the writing did not already suggest that. The combination of the shortness of this section with the importance of the contrast that it offers to the sections around it suggests something to me that might seem a little bit simplistic but that I think is valid, namely that within the bounds of what can work, it is a good idea to let this section take as long as it can. That is, the slower and freer it can be, the less perfunctory it will seem as a way station between the contrapuntal mosaic discussed above and the fughetta discussed below. This is just one thought, however; it certainly would not be a good idea to play it more slowly or more freely than seemed appropriate for the passage on its own terms. But all else being equal, perhaps the more time it occupies the more effective it will be.
The elements of this short passage are drawn from other sections of the work. The student should examine the notes of the solo opening measure for motivic connections to the previous section, and the notes of m. 74 for connections to earlier part of the work, in particular the trillo longo section. It becomes apparent that none of this is filler or cadential material. (I should admit that I myself did not notice the relationship between the melodic shapes in m. 73 and the material in mm. 60–72 until I had been studying the piece for quite a few years. There are probably details of the construction of this extremely well thought-out work that I have not noticed yet. Students should be encouraged to undertake as much detective work as they like, picking apart themes and scanning the whole piece for connections.)
Since the pedal note that enters in m. 74 does not change anything about the harmony or anything significant about the counterpoint, it is perhaps there for emphasis. It makes more emphatic the negation or contradiction of two things: first, the B-sharp that has prevailed since m. 71; second, the high tessitura of the section that has just ended.

Measures 75–86
The section that begins after the downbeat of m. 75 is a short fugue in three voices. The subject (Example 7) occurs six times in eight measures, followed by a fairly extended build-up to the final cadence—which this time is completed. This is again a manuals-only section—the lowest voice is too high for the pedal compass. Once again the notes of the middle voice can almost all be reached by either hand. For about five measures’ worth of the section, there are actually only two voices being played, so hand choices as such are limited to the remaining measures. (When there are only two voices being played, there is of course rarely a reason not just to split them between the two hands.) The most interesting spots to think about hand choices and fingering are mm. 78 and 82 and perhaps mm. 84–85. Students should try several possibilities and in particular notice differences in the range of possible articulations with different hand/fingering choices.
A particular feature of this fugue subject is the presence of a repeated-note event at a crucial moment in the unfolding of the theme. The articulation and timing of this repetition each time it occurs is probably more important than any other one thing in shaping the overall effect of the passage. Therefore it is a wonderful opportunity for a student to think about planning repeated notes and to listen carefully to them. As I wrote in the column of January 2009, I believe strongly that whenever possible, it is a very good idea to use different fingers for repeated notes. I would, for example, finger the opening statement of this fugue subject as shown in Example 8 (this is in the left hand, of course).
As always, there are many other specific ways to do it. Changing fingers on repeated notes, in addition to giving the player more control over a wider range of articulation and timing possibilities, is also a free shot at repositioning the hand. In a passage like this, which has an active subject and, just for good measure, four sharps, repositioning the hand can be useful. Here is an example of a repeated-note fingering (in the right hand) that also positions the hand to deal easily with the other notes (Example 9).

Measures 87–90
The last of the four sections that we are looking at here is another fairly short non-contrapuntal passage (Example 10). Since the previous section ended with a convincing and well-heralded cadence in B-major, the opening harmony of this section is another instance of abrupt contradiction. The first note in the pedal sounds like it is inviting a continuation of the same harmonic scheme; when the chord is filled out in the hands it negates that harmony quite clearly. This passage is in the form, more or less, of a four-part chorale harmonization. The Adagio marking suggests a slow tempo for the section. Again it seems to me that, all else being equal, the slower these measures are, the more effective they will be as a counterweight to the rhythmic and contrapuntal material that surrounds them. The same range of possibilities for dividing the alto voice between the hands is found here as in other sections discussed above. In this case, since the lines are slow and not very complex, the choices are perhaps low stakes. However, in a slow bare-bones texture such as this, the addition of ornaments is always a possibility, and that might shape decisions about hand choices as well as fingering. For example, I like to play a trill on the final quarter note of m. 88. In order to accommodate that trill the most easily, I use a fingering like that in Example 11. There is nothing surprising or particularly original about this fingering. The gist of it is taking the first D-sharp in the left hand in order to permit the right hand to approach the trill in an unconstrained way. Students should try out various ornaments: trills, mordents, appoggiaturas, slides. (I sometimes play a slide all the way down from the high D-sharp to the G-sharp in the measure just above, or between the two pedal notes in m. 89.) It is in principle fine to ornament all of the notes, or none of the notes or anything in between. The important thing is for the student to try things out, and react and think.
This month’s discussion ends in the middle of a cadence, since the unresolved final note of m. 90 is resolved by the first note of the fugue subject of the final section. We will resolve this cadence and discuss the rest of the piece next month.

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. 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. He can be reached by e-mail at [email protected].

Buxtehude BuxWV 141 – Part 3: Practicing the first fugal section
This month we return to the Buxtehude Praeludium in E Major, BuxWV 141, looking at the second section of the piece, which begins at m. 13 and goes through about m. 50. This—except for its last three measures or so, which are a transitional passage, cadential in nature, and which we will in the main discuss next month—is a contrapuntal, essentially fugal, section, a fact which has implications for studying, practicing, and learning the music. Much of what I will suggest here will involve revisiting the ideas that I discussed in the series of columns about counterpoint that began in September 2008, applying those ideas to this specific passage.
The fugal section that begins in m. 13 is in four voices. The musical text could by and large be written out on four staves, accounting for all of the notes, with each staff presenting a coherently “melodic” melody. (It departs from this briefly in mm. 32–33 with the addition of a few “extra” notes, and again in the transitional passage.) The voices behave like the voices of a contrapuntal piece: each of the four voices has a different compass, each of the voices is present most of the time but not all of the time, and, melodically, the voices do the same things at different times and different things at the same time. The section is “fugal” in that the voices enter one at a time, each with a version of the same theme, and that theme recurs a lot during the section.

Theme
This theme is as follows, in its first iteration:

It enters first in the top voice, and then in the other voices in descending order. It is present in 24 of the measures of the section, and a motive identical to the second half of this fugue subject is present in another 3½ or 4 measures. The longest stretch without any of this theme present—prior to the transitional/cadential section at the end—is about one measure.
(There is an interesting side note about this theme, one that in a sense is irrelevant to the piece on its own terms because of the chronology, but which should be intriguing to organists nonetheless. The first half of the theme is the same as the fugue subject of Bach’s Fugue in E-flat Major, BWV 552, and the second half of the Buxtehude theme is essentially the same as a recurrent pedal motive in the Prelude, BWV 552. This Buxtehude work seems like a more likely source of Bach’s inspiration for the so-called “St. Anne” Prelude and Fugue than is William Croft’s hymn tune, which Bach most likely never heard.)

Bass voice in pedal?
The first practical question about working on this section is whether or not the bass voice belongs in the pedal. This is often a question with Buxtehude, since the sources for his music do not often indicate pedal explicitly, and in any case are rather far removed in origin from the composer. In this section, there are several reasons to believe that the bass voice was indeed intended as a pedal part. First, it works on the pedal keyboard, and, in order to make it work, the composer has shaped it a little bit differently from any of the three other voices. That is, there is no scale-wise writing in the bass voice that is any faster than the eighth-note, whereas there is such writing in each of the other voices. Second, there are many places in this passage where it is awkward to play all four of the voices in the hands and where the fingering is much more natural without the lowest voice. (This is true, for example, in m. 33 or mm. 42–43.)
There is, as far as I can see, only one spot prior to the transitional/cadential section where it is actually impossible to play all four voices in the hands, namely the second eighth note of m. 44. Someone else might be able to find a clever way to make it work, and it is certainly possible to do so by fudging the duration of some of the longer notes. (Someone with larger hands than mine would have no trouble with it, but the stretch of a tenth is beyond what is normally found in music of this time.) Furthermore, the transitional section ending in m. 50 certainly requires pedal—really physically requires it—and there is no particularly good place to shift the bass line to the pedal if that line has been played in the hands from m. 20 on. So on balance this seems to me to be a section to be played with pedal.
(The closing fugue of the Praeludium in E Minor, BuxWV 142, presents an interestingly different picture. There the fingering is made dramatically easier, more natural, and more idiomatic to the organ playing of the time by not including the bass voice in what the hands are expected to play. However, at the same time the bass line itself is, if not unplayable in the pedal, still extraordinarily difficult and well outside what would have been the norm at the time.)

Learning protocol
The protocol for learning this fugal section starts with the approach that I outlined in the columns on counterpoint mentioned above; that is, playing through each voice separately and then playing pairs of voices. Here are some specific points about applying that approach to this passage:
1) The section that we are looking at is about 34 measures long—long enough that it should be broken up into smaller sections for this kind of practicing. It doesn’t really matter how it is broken up. It is fine to practice separate voices and pairs of voices in chunks of just a few measures, or in significantly larger chunks. One average way to do it would be to have breaks at around m. 23 and at around m. 36. Each voice will naturally break at a slightly different place. So, for example, it would make sense to play the soprano voice from m. 13 to m. 20, the alto from m. 15 to the middle of m. 23, the tenor from m. 17 through the first beat of m. 25, and the bass from m. 20 through m. 24. Then these sections of these voices can be combined in pairs.
2) When playing individual voices, it is fine to finger those voices in ways that will not be used when later putting the voices together. This is especially necessary and important with inner voices—typically the alto voice in a piece or passage that has three voices in the hands. Such an inner voice will almost certainly end up migrating from one hand to the other. However, at this stage it is important to play each voice in a way that is comfortable and natural, and that makes it as easy as possible to hear that voice as a coherent melody. It is also necessary to be flexible about playing inner voices in either hand. So, of course, when putting soprano and alto together it will be necessary to play the alto in the left hand, but when putting alto together with tenor it will be necessary to play the alto in the right hand.
3) At this stage, it is also not necessary to play the pedal part in the pedals. Practicing the pedal line as a pedal line (see below) can come later or can start in parallel with this process of getting to know the voices. However, for carrying out this approach to learning the voices, just as it doesn’t matter what fingering is used, it also doesn’t matter whether the feet play the bass voice or the left hand does. The important thing is that the student be able to listen carefully and hear the voices well while playing them.
4) In putting voices together in pairs it is a good idea some of the time to play the two voices on two manuals, in order to hear them with extra clarity. This is especially useful when voices cross or, as for example with the soprano and alto voices at mm. 38–39, come very close. The two sounds should be similar in volume and different in character.

Pedaling
While studying individual voices and pairs of voices, it is emphatically not a good idea also to finger and practice the manual part of the texture. That will come a little bit later. It is perfectly fine to practice the pedal part, however. It is interesting that in this piece the pedaling choices are more straightforward, and in fact the pedal part is probably easier overall, in the more active fugue subject and subject fragments, than in the measures in which the pedal is playing long-held notes.
The fugue subject can easily be played with alternate toes, starting with the right foot; the subject fragment that occurs in m. 33 and elsewhere can also be played with alternate toes, starting with the left foot. These pedalings are natural enough that I would expect essentially every student or player to use them. (There are other possibilities: for example, using the same foot to play some of the successive quarter notes, or occasionally using heel to play some of the sixteenth notes that are on white keys when the immediately prior note was on an adjacent black key. On the whole, I doubt that many players would find these variants easier or better, but perhaps some would. They could certainly be OK.) This consistent alternate toe pedaling implies nothing in particular about articulation, phrasing, timing, or other interpretive/performance matters.
However, when the pedal part moves more slowly, particularly from m. 43 on, pedaling choices both affect and depend on choices about articulation. To the extent that the player prefers or can accept spaces between these long notes, he or she can apply the principal of playing each note with whatever foot happens to lie most comfortably above that note. As an example that would lead me to the following succession of toes for the eleven pedal notes beginning with the first note of m. 44 and going to the end of m. 50:
l-r-r-l-l-r-l-l-r-r-l
For someone else it might be a little bit different. Creating more legato in this passage would involve different pedaling choices—for example, crossing the left foot under to play the E in m. 44, and then playing the C# in m. 45 with the right foot.
Of course, practicing the pedal line once pedaling choices have been made involves the usual things: keep it slow and accurate; look at the feet as little as possible—ideally not at all; repeat small-enough passages that the memory of the feeling of the passage does not fade before you get back to it. When the pedal part has become secure, join it first to the tenor voice, then to the left hand part as such—once that has also been practiced as outlined below—then to the hands together. (Of course, it is fine also to practice pedal with right hand alone. However, as always, left hand and pedal is most important. Usually if left hand and pedal has been practiced enough, then adding the right hand is something that feels natural and almost easy.)
And do not forget what might be the cardinal rule of practicing: if you hear yourself make a wrong note while practicing, do not stop or hesitate or go back and correct it. By the time that your ears have heard the wrong note, your mind should already have moved on to playing the next note. Next time through the passage you can make sure to adjust what needs to be adjusted to correct what was wrong.

Fingering choices
Once you have played through all of the voices and all of the pairs of voices, it is time to work out a fingering for the three voices that will be in the hands. And, as I discussed in the column from last July, the first task is to decide which notes belong in which hand. This must come before making specific fingering choices, and it must be done in such a way as to make those fingering choices as easy and natural as possible. As I wrote before: I have seen students waste a lot of time or even make a passage that could be fairly easy almost unplayable by assigning notes to hands in a way that was awkward. However, there is not always only one good answer, and the answer is not the same, necessarily, for any two players.
In any situation in which three voices are present and the notes of the alto voice can be reached by either hand—that is, generally, in which neither the soprano notes nor the tenor notes are more than an octave away from the alto notes—the player can, in a pinch, try it both ways. Generally it is nice to put “extra” notes with whichever other voice is less active. So, in m. 19, for example, I would play the first three notes of the alto voice in the right hand since the tenor voice has sixteenth notes, but then play the half note E in the left hand, since the soprano voice then has sixteenth notes. In m. 24 I would play the one alto voice (whole) note in the right hand, even though the soprano voice notes are a bit farther away, since the tenor voice is more active; in m. 25, however, I would shift the alto voice to the left hand since the soprano voice become much more active. Again, these choices are not right and other choices wrong. It is simply very important that each player—each student perhaps with the help of a teacher—work this out carefully and patiently, in a way that feels right.
After the “handing” and fingering have been worked out, it is possible to try an interesting challenge, namely to play the alto voice alone with the correct fingering. This involves letting that voice move from one hand to the other according to the plan that has been worked out. The goal is to play it in such a way that it sounds as natural and cantabile as it would sound played in one hand. It is simultaneously harder to do this outside the cushion of the other voices and good practice for playing that voice well when it is partly obscured by the other voices.

Practice procedures
Practicing the three-voice manual texture of course follows the usual pattern for any practicing. Each hand should be practiced separately, slowly, until it seems easy. The tempo should be allowed to rise only according to a pace that is comfortable: once a passage is learned well at one tempo, it can be played a little bit faster; playing it much faster will often lead to its falling apart. Once each hand is solid at a given tempo, the two hands can be put together at a slower tempo. This can then also be allowed to speed up gradually. The rule about not stopping or hesitating when you hear yourself make a wrong note is always utterly important.
After a player or student has carried out all of the above—individual voices, pairs of voices, pedal part, individual hands, left hand with pedal, and all the rest—there is an interesting exercise to try. Play the section—well learned, all parts together—and consciously listen only to one voice at a time. This is easiest with the soprano voice, next easiest with whichever voice is the lowest at a given time, quite hard with a real inner voice. The ability to do this and also keep the whole thing going accurately and with a feeling of ease will help to reveal the fruits of studying the voices thoroughly and also test the solidity of the overall practicing of the notes.
Next month I will discuss both the transition measures 47–50 and the free section that follows, beginning in m. 51. ■

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

Buxtehude BuxWV 141—Part 4:
Free writing and trillo longo—mm. 51–59
This month’s column is about just a little bit of music—the third overall section of the Praeludium, nine measures long, mm. 51–59. I will provide some analysis of the passage, and offer some thoughts and suggestions about fingering and pedaling.

The Praeludium that we are studying is, as I discussed in the column from June 2010, a one-movement work in several sections. There is both contrast and continuity amongst the sections. Sources of contrast are clear. Some sections are contrapuntal, some are not; some are regular in pulse and rhythm, some are free or essentially unmeasured; some use striking dissonance, some avoid it. Sources of continuity can be more elusive, but can include the use of similar motivic material, or recurring rhythms or harmonies. This is the classic form of the toccata or praeludium as practiced by Frescobaldi and Froberger, among others, and adopted and adapted by Buxtehude as the form of his organ praeludia. It was also used by Bach for organ and harpsichord pieces that we know or believe to come from early in his career: most of the harpsichord toccatas, the famous D-minor organ toccata, BWV 565, and some of the preludes and fugues such as BWV 551.
The section that we are looking at here is essentially non-contrapuntal, in that the writing is not in a set number of voices, although, as we will see, there are recurrent motives. There are fairly quick changes of texture, from one voice in m. 51 and elsewhere to four and five later. Chords are built up out of passagework. There are abrupt changes in the prevailing note values, as in m. 52, which starts with 32nd notes and then somewhat surprisingly sits on the third quarter-note beat with no motion. The lowest notes make up a true pedal part (always a question with Buxtehude, since the sources don’t make it clear, and also since the relationship between the sources and Buxtehude’s original intentions is not always known), since there are stretches that cannot be executed by two hands alone.

Four-note motive
In the following example, some of the notes have been highlighted with either rectangular or oval outlines (see Example 1). The rectangular outlines indicate either an exact form—nine instances, including inversions—or a plausible variant—six instances—of the four-note motive that begins the entire praeludium (see Example 2). This motive is found in crucial spots throughout the praeludium, sometimes as a marker of transitions or important moments, sometimes as part of “officially” motivic material, such as the second half of the fugue subject of the final section of the piece. The section that we are looking at here is clearly chock full of this short motive—it is present almost exactly half the time. This is one of the sources of continuity between this section and the rest of the praeludium.
It could well be argued that this motive is too simple, too ordinary, to count as a real, identifiable motive, or to serve as a source of continuity or unity within a piece. After all, every piece has plenty of short scale passages, and this one in particular is introduced in the most casual possible way. However, it seems to me that if the composer had not intended it to be heard, perhaps subliminally, as a significant motive, then we would not be able to find it quite so consistently through the whole piece. In any case, we do find it, and each teacher and each student—having initially noticed it—can muse about how significant it really is, and decide for him- or herself.

Connections
The second element of this short section that ties it to the rest of the piece is the cluster of notes in the first half of m. 57, highlighted with an oval box. This is a foreshadowing of the fugue subject of the last section of the praeludium (see Example 3), especially as that subject appears when it is in parallel with itself. This happens in several places, such as m. 104, for example (see Example 4).
This section is also clearly related to the rest of the piece by its similarities to the transitional passage that constitutes the end of the second overall section of the piece and that therefore comes just before this section. This transition occupies mm. 47–50. It arises out of the fugue that precedes it without break or interruption. The fugal texture just gives way to non-contrapuntal writing with passagework and built-up quasi-arpeggio chords. This texture resembles that of mm. 51–59, although it has the feeling of both a cadence and coda to the long fugue that has preceded it. The flourish that ends the transitional passage and the pedal solo that begins the third section are more or less versions of each other (see Examples 5 and 6).
(A similar way of linking the end of one section to the beginning of the next was employed by Bach in, for example, the Toccata in C Major, at the transition between the opening manual solo and the ensuing pedal solo, where the first four pedal notes seem to answer the last four manual notes [see Example 7], and in the F-major Toccata and Fugue, where the very last notes of the toccata are echoed in the mordent that begins the fugue subject.)

Trillo longo
One interesting feature of this passage is the use of the term trillo longo, placed over two spots in the pedal part, as seen in Example 1. Of course it seems obvious, on one level, what this term means: long trill. And in both instances it is written above notes that are in the shape of a trill, one that begins on the lower of its two notes. One surprising discovery about this term—trillo longo—is that there is no evidence that it was ever in common use as a technical musical term or as a piece of accepted musical jargon. A bit of research reveals that it is not listed as a musical term in any music dictionary or encyclopedia, and there are no papers or articles that discuss it as a term or that mention any piece in the entire history of music that uses it as a term, other than this piece. (A Google search on the term “trillo longo” returns seven results, one of them about a piece that does not in fact use the term, and all of the other six about this passage. Included in these search results is one prior column in this series.)
So if this term was not in particularly common use—even if its basic meaning is clear—why did Buxtehude (or his copyist: we can’t be sure) use it here? Was he simply observing that the printed notes constitute a “long trill”? Or was he instructing the player to execute a long trill beyond what the notes indicate? If so, is this to be accomplished by adding notes and time, or by adding notes and making them faster? Does the designation of a group of 32nd notes as a “long trill” suggest that they can or should be played freely, or given some particular grouping or shape? (For example, the 16th-note B that falls on “the ‘and’ of three” in m. 51 could be thought of as the beginning of a trill, and the 16th-note/32nd-note rhythm rendered freely, as the gradual beginning of the trill.) Or was he just reminding the player to resist the temptation to shorten or omit or simplify the trill due to its being in the pedal, and therefore tricky to execute? Here’s another possibility: perhaps Buxtehude wanted to employ some Italian language at this point to signify that the trills in question were Italian-style trills, that is, trills beginning on the main note.
I don’t know the answers to these questions, or whether any of these thoughts really apply. I throw them out there for the student—or teacher—to muse about. Meanwhile, the “long trill” continues to be important as the section goes along, especially as manifested by the (very long) trill in one of the inner voices in m. 56. In this spot, unlike in mm. 51, 53, 55, and 57, the trill is accompanied throughout by motion in other voices. This is also the measure in this passage that is in five voices—and five notes are actually sounding throughout the measure—therefore it is literally the loudest measure within this section. It has the largest number of total notes played of any measure at 32. (The following measure is second at 29.) All of this suggests that this measure might be the rhetorical climax or high point of the section. The major interpretive or performance issue in this measure concerns the trill. Should the notes that follow the pattern of a trill on E and D-sharp be played “as written,” that is, as more or less measured 32nd notes, or should they be untethered from that timing and played as a fairly free trill? The latter is, to put it plainly, harder. It requires that the trill pattern be learned and practiced so well that the fingers can execute it while the mind of the player is, in a sense, ignoring it. The player must let those notes go their own way rhythmically and concentrate on playing the other—right hand—notes in the desired rhythm, regardless of how those notes do or don’t line up with the notes of the trill. In any case, the student or player should initially practice the notes of this trill in the “as written” rhythm, learning them more and more securely while thinking about whether to try to set them free from the printed rhythm.

Pedaling
Pedalings in this passage are mostly straightforward. That is, there are easy pedaling solutions involving toes—mostly alternate toes—as would have been the norm in Buxtehude’s time. A possible pedaling—along with some fingering—is suggested in Example 8. The pedal notes marked with asterisks are (some of?) those that could very easily be played with heel if a player is so inclined, either because that happens to be more comfortable for the particular player or to avoid a disjunct articulation at those spots. (Just for the record, I believe that I have usually used the left heel on the asterisked note in m. 51, where my particular posture makes it extremely comfortable and natural to do so, but not on the one in m. 53.) The transaction that takes place between the second and third pedal notes of m. 51 (G# and F#) is interesting. The articulation created by simply using the right toe for both notes, as I have indicated it, is natural and “musical” in that it precedes a note that is on a beat, and confers a slight accent on that note.
However, if in a particular player’s conception of the passage that articulation seems jarring, then it is difficult (but probably not impossible) to figure out a way to avoid it that works. Players with very wide feet can play the G# with the extreme outside of the right toe and rotate the foot in order to play the F# with the inside of the foot—the big toe. Some players might be comfortable initially catching the F# with the left toe and quickly substituting the right toe, in order to free the left toe up to aim for the following note. It is hard to picture getting the heel involved since we are dealing with black notes. It is very possible to turn the logic of this around and say that since it is so much more natural to use a pedaling here that creates an articulation, perhaps that is how the passage was meant to be played.

Fingering
As always, the first step in creating a fingering is to figure out, where there is any possible doubt, which notes belong in which hand. I have indicated some “handing” choices in the example above, using curved lines. There are several other options. For example, it would be possible to take the 16th notes on the second beat of m. 52 in the left hand, or the B# and C# in the second beat of m. 54 in the right hand. In the third beat of m. 57, I have suggested taking the G# in the left hand. This is because I would find it extremely awkward to play the remaining upper-voice notes of that measure while holding the G#, all in the right hand. However, reaching the E/G# dyad with the left hand is indeed also tricky. It certainly involves a break immediately before those notes, and must be practiced carefully to avoid making that break sound jarring or abrupt.
I have included only a few fingerings as examples. Any of them can also be done a number of other ways. For example, changing the numerals printed above the upper staff in m. 52 from 2-3-4-5-4 to 2-3-1-4-5 would result in an also very good fingering (leaving the other fingers the same). In the right hand in m. 53 the fingering could be (instead of 4-3-1-2-1-4-3) 5-4-3-2-3-4-3 or 4-3-1-3-4-5-2 or a number of other possibilities. For that matter either or both D#’s could be taken in the left hand. Comfortable hand position is the main guiding principle, and this is something that varies from player to player, based on posture and the size and shape of the hands.
Notice, however, that in all of these (m. 53) examples I am carefully preserving the use of a different finger to repeat the D# from the one that is already holding it. The suggested fingering for the right hand in m. 56 is also designed to use different fingers on repeated notes. By and large, it is a good idea to keep the thumb off of black keys. In fact, the most physiologically comfortable use of the thumb at the keyboard is for playing white notes just before or just after another finger has played a black note. Much of my approach to fingering a passage like this—in a heavily “black note” key—is derived from this concept of the use of the thumb. This can be seen in essentially all of the fingerings that I have written in here.
The student and teacher can try some of my fingerings, but should primarily work fingerings out from scratch, bearing in mind the ideas discussed above. Then, of course, the next step is what it always is: careful and patient practice, starting with separate hands and feet—doing as much of that as turns out to be needed, better too much then too little—then putting things together at a comfortably slow tempo, speeding up gradually, keeping the hands and feet relaxed.
Next month we will return to Boëllmann, looking at the charismatic and popular Menuet Gothique.

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.