On Teaching

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

Additional practice techniques

This month and next month I will discuss a number of practice techniques that involve changing something in the music while practicing. This includes practicing in rhythms other than the true rhythm of the passage being practiced, and practicing passages with some of the notes actually omitted. (The former is the subject this month, and the latter next month.) Some of the techniques are generally quite familiar, although I may have my own twist on them. I have at least briefly alluded to some of them elsewhere, but I think that it is useful to bring them together here and to zero in on them in a bit more detail.

Any and all of the techniques that I will describe here are meant only to supplement the basic, solid way of practicing that I try never to miss a chance to describe: slow, careful repetition—with or without separating hands and feet, depending on the exact circumstances—with correct notes and correct rhythms, speeding up only gradually, in a way that is determined by the flow of the practicing itself, rather than by any predetermined schedule. This discussion of, among other things, practicing “wrong” rhythms comes the month after I talked about various ways of thinking about counting and the art of learning correct rhythms. Therefore it is important to remember that practicing in alternate rhythms is a technique that should have a well-focused purpose and that should be kept conceptually separate from playing the piece or passage as such. I will talk some about how to maintain this separation.

Alternate rhythms: dotted values

For me, the purpose of practicing in alternate rhythms is quite specific: it is a halfway point between a slow practice tempo and a faster tempo, which may be the performance tempo or may be even faster than that. When a rhythm is altered, some notes become faster and some slower. The faster notes are being practiced in isolation at a faster tempo than they would have otherwise; the slower notes, because they are slower than they would otherwise be, provide an opportunity to rest and regroup between fast notes. The classic form of this sort of practice is, therefore, to create pairs of practice rhythms, in each of which half the notes are fast and the other half slow, and between which all of the notes get a chance to be the ones that are being played (extra) fast. 

In turn, the classic form of that technique is to take a passage in which the note values are uniform and to make those note values dotted. So a passage that looks like that in Example 1 will be played first like Example 2, and then like Example 3.

The purpose of this, again, is technical. The first rhythm offers a chance to practice half of the movements from one note to the next quickly; the second offers the chance to practice the other half equally quickly. Because this kind of practice allows the player to stop and rest, in effect, after each fast gesture, it is usually possible to include and drill those fast gestures sooner in the process of learning the piece than it would be possible to boost the overall tempo to that same speed.

A modification of this technique that I think makes it even more useful is to replace the dotted rhythms (“regular” and “reverse”) with a kind of unmeasured over-dotting. So, in the above rhythmic templates, the dotted eighth-notes would all be replaced with fermata-ed notes to be held as long as you want, and the sixteenth-notes would be replaced with notes as short, quick, and light as you can make them. This approach creates an even more intense drilling of the quick gestures and an even more effective rest between those gestures. It also, by virtue of its being farther from any sort of regular pulse, has less ability to affect or possibly undermine the regular steady rhythm of the passage when the player returns to regular rhythm.

This sort of practicing can be applied very naturally to a line such as the opening of Bach’s Prelude & Fugue in G Major, BWV 541 (Example 4), which is in one voice only and in all or almost all one note-value. Practicing a line such as this in some version of dotted rhythm is most useful if you analyze what it is that you are gaining in each spot in the line. For example, when it is the on-the-beat sixteenth-notes that are held long, then going from the first beat to the second beat of the second measure (marked x) you will be practicing quickly moving the hand position in such a way as to reach the middle D reliably. 

In a passage such as Example 5—from the Vierne Divertissement (Pièces en Style Libre)—if a dotted rhythm is applied to the sixteenth-note line, the quarter-note chords will come along for the ride, and the practicing of those chords will also be affected. If the on-the-beat sixteenth-notes are being held long, then in spots like those marked with x’s the student must be fully ready to play the next chord, as well as the next sixteenth-note, before playing the (very fast) off-the-beat sixteenth-note. The actual gesture of moving from one chord to another will then be fast: probably faster than it will need to be in the piece. However, the student will have time, waiting on the “and of two,” to prepare that very fast gesture. The other half of the exercise—the reverse dotting—applied to this passage probably has less effect on the feel of the playing of the chords. In that case, moments like those marked with y’s will probably constitute the most intense and useful part of the exercise—playing wide intervals very quickly. 

In writing like Example 6—from the Bach Toccata & Fugue in F Major—these sorts of rhythms can be applied to one hand at a time and then to both hands together. Again, the student should analyze and pay attention to what exactly is being practiced at each moment in the passage. For example, going from the second beat to the third beat of the first measure of this excerpt, the left hand has a “stretch” or shift in hand position while the right hand does not; the opposite is true near the end of the fourth measure, or heading into the last measure. The use of the two complementary dotting patterns will highlight some of these technical details.

(Would it be a good idea to practice this passage or one like it using opposite dotting in the two hands? That is, first place the lengthened notes on the beats in the right hand and off the beats in the left hand, then reverse both of these. I have actually never tried that and I can’t recall a student’s doing it. The purely physical practice would be unchanged from the method described above, but the concentration required would be different—and it would probably be harder.)

Alternate rhythms: 

Groupings of notes

Another format for altering rhythms to create effective targeted practice strategies involves speeding up not one note at a time (every other note, as above) but clusters of notes. The classic way of organizing this is to play first all of the notes after each beat very fast, ending on and then holding the next beat, then to play all of the notes starting on each beat very fast, ending with the last off-the-beat note of each grouping. The template for doing this works as follows. For a set of notes written like Example 7, you would first play as shown in Example 8, with the notes under each slur played as fast as possible, and the notes under the fermatas held as long as necessary to feel ready to play the next cluster of fast notes; then Example 9.

In this case, the notes under the slurs should again be played as fast as possible. Then the last note of each grouping can be held until it feels comfortable to execute the next cluster of fast notes, or the note can be released, and the waiting can take place while not actually holding any notes: in effect a fermata in the gap between groups of notes. In the latter case, of course, it is a good idea not to let the hands or feet move too far above or away from the keys.

(As it happens, I myself have recently used the fast-cluster approach myself on this Buxtehude harpsichord passage, from the La Capricciosa Variations, which I have always found extremely hard—harder than I had originally expected [Example 10]. This measure is full of funny changes of direction and unexpected intervals. I was eventually able to get comfortable with it—and to get it to be reliable—and I believe that the fast-cluster practicing was the most important part of the process.)

How to use alternate rhythms

Practicing in “off” rhythms is, as I said above, a technical practice. The purpose is not to learn something about rhythm or any other artistic or interpretive aspect of the piece. It is to drill isolated gestures at a fast tempo in a focused way that does not demand that the fast tempo be kept up for very long. Therefore, it only makes sense to practice a passage this way (that is, in one of these ways) once the fingering and/or pedaling has been worked out and is indeed fairly well learned. If the fingering or pedaling is uncertain, then the fast moments in the rhythmic patterns are not going to work: they will be hesitant or actually fall apart. It also makes sense to practice this way only with a complete texture or with a part of the texture that involves the same fingering and pedaling as the complete texture. That is, it is fine—very useful in fact—to apply different rhythms to one hand at a time or to the feet alone, but not to separate voices extracted from a contrapuntal piece.

Since the technical purpose of this sort of practice is focused on the fast moments, the slow moments, whether they amount to every other note or to one note in a larger grouping, can be held for as long as the player wants. There does not need to be an overall tempo. Since every gesture—moving from one note to the next—takes its turn at being the fast gesture, everything gets practiced effectively regardless of how long—how slow—the held notes are. The less regular the timing of the held notes—the more the student simply waits on those notes until he or she feels ready to play the next fast gesture—the less this kind of practice will have any tendency to interfere with normal rhythm, because it will not be presenting an effective alternate rhythm.

It is easiest to apply this kind of practicing to passages in which rhythm is more or less even, as in all of the examples so far. In a passage such as Example 11, from Buxtehude’s Praeludium in C Major, BuxWV 136, the rhythm is less regular. There are beats in which the surface rhythm is two eighth-notes, in which it is four sixteenth-notes, and in which it is mixed. In the second beat of each of the first two measures of this excerpt, for example, if all of the notes within that beat are being played fast, then it would be conceivable either to try to maintain the rhythmic relationships within the beat, or just to play all of the notes as fast as possible and, therefore, as fast as one another, whether they are in fact eighth-notes or sixteenths. Either approach could be fine, as far as I can tell, and they would both amount to effective practicing. In fact, students can be encouraged to create their own short clusters of notes for very fast practicing, and to figure out how they would like to deal with rhythms within those clusters. As long as the clusters are not very long, and as long as they overlap by a note or two, the practicing should work well. 

Next month I will talk about a sort of practicing that is, in a sense, the opposite of what I have been discussing here, namely playing some notes of a passage while leaving the other notes out. The reasons for doing this are usually not technical, but rather about developing the ears’ relationship to the music in a way that enhances understanding of structure, rhythm, and pulse.

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

Rhythm and counting

The music that we as keyboard players work with on a daily basis involves time as well as pitch, timbre, and other qualities of sound. We are so used to this that it seems like something that does not need to be said. It is very close to the core of the way that we think about music. In fact, I have sometimes heard people define music as something like “sound with defined pitch organized according to regular time intervals” or words to that effect. This is, if not necessarily a valid definition of anything that could possibly be considered music, certainly a good start at defining one of the important components of the type of music that we typically hear and play. Of course, due to the nature of time and perception, whenever a sound succeeds some other sound, it has to do so on some kind of schedule, and indeed once in a while that schedule is irregular or subject to the whim (or judgment) of a player. But most of the time sounds in pieces of music follow one another at regular intervals. This phenomenon of pulse or rhythm or beat is as important as the notes (pitches) themselves, or close to it, in most musical situations.

And of course our system of notation includes indications for rhythm—that is, lengths of notes in relation to one another. It is actually hard to call to mind any standard way of notating pitch in post-medieval music that does not also notate something about rhythm. When a composer wants to suggest that, in some way, notes are not being presented as having a pre-determined set of rhythmic relationships, the composer has to borrow rhythmic notation and then somehow indicate that the usual rhythmic meaning of the notes is suspended. That is the case, for example, with the unmeasured preludes of Louis Couperin and some other seventeenth-century composers, and with passages marked “free” or “unmeasured” or “molto rubato” or something to that effect.

However, organ teachers are rarely in the position of teaching students how to read rhythmic notation from scratch, or how to read notation at all. We usually take on students who have already learned “the basics” by studying piano—this includes notation along with at least some ideas about fingering, and of course a certain amount of actual keyboard dexterity. (Of course, many of us do teach these basics in settings other than organ instruction, and occasionally we are lucky enough to find a student who wants to study organ from the very beginning!)  On the other hand, there are many students whose sense of rhythm—even at the level of their comfort with reading the rhythmic dimension of the notation—is shaky. There are students who feel that they “can’t count” or who are at least not always confident about their reading of note values, and who are often right not to be confident. As with any other problems in studying or in playing, this usually stems from something’s having been taught inadequately or (and this might actually be more common) having been taught in a way that makes the matter seem more complicated than it has to be.

What follow here are ways to help students with some aspects of reading and producing correct rhythms. This is separate from, though in the end of course related to, the business of playing with a convincing sense of rhythm and pulse. Paradoxically or not, the convincing sense of pulse often comes from departing slightly from the scientifically (i.e., metronomically) correct reading of the rhythm. I am not talking about that here—rubato, timing, using accent to create pulse: all very important, but mostly for another time. One important aspect of the relationship is this: that all of the possible subtleties in the realm of rhythm are extremely difficult to execute for anyone whose playing is burdened by a fear that the basic rhythm is shaky—whether it actually is shaky or not. 

1) If it does fall to me to teach the basic meaning of the different “note values”—that is, the way that we indicate rhythm in written music—I try to do so in as simple and colloquial way as I possibly can. None of the jargon or the ways that we habitually put these things to ourselves in our heads once we know them really well is self-evident, and some of it is unnecessary. Take, for example, the phrase “note value” or the concept of the “value” of a note. It becomes second nature that this word refers to the aspect of the note that is the length of time that it occupies, but someone who has actually not studied the notation at all will not know this. I have actually seen someone more or less flummoxed by the statement that a dot “adds half the value of the note to the note.” And why not: unless you almost already know what that statement means, it is not particularly obvious what it means. I would rather say something like: “if you put a dot immediately to the right of a note, it makes that note one-and-a-half times as long as it would otherwise have been.” There are then two ways to concoct examples of this: first, if, say, a quarter-note takes as much time as two eighth-notes, then a quarter-note with a dot next to it takes as much time as three eighth-notes; and second, if a quarter-note is going to last a day, say, then a dotted quarter-note is going to last thirty-six hours.

2) The notation is all about ratios, and my last example above is meant as a reminder that a ratio is a ratio, regardless of the absolute times involved. A student learning the rhythmic notation from scratch needs to embrace the idea that the notation is all about ratios and not about absolute time—or for that matter about beats, pulses, measures, or time signatures. It is about the notion that some notes last twice as long—or three or four times as long—as others. That’s all. A whole-note lasts twice as long as a half-note; a half-note lasts twice as long as a quarter-note, and so on. Thus, if a quarter-note is going to last a second, then a half-note is going to last two seconds, and a whole-note, in turn, four seconds. If a sixteenth-note is going to last four years, then a thirty-second note is going to last two years, plus or minus an adjustment for the stray February 29. Once the student is comfortable with the idea of ratios, then learning which symbol is which note and what the ratios are is rather easy: there aren’t that many of them. Of course, the teacher must include in the discussion not just all of the “regular” notes, but also the concept of dotted notes, the meaning of ties, and the meaning of triplet signs. These are still all about ratios, and still do not amount to very many different things to learn.

3) By the way, as far as rhythm and counting are concerned, it is probably true to say that nothing would change if all of the time signatures and all of the bar lines were magically erased from all of (at least) western classical music. The note lengths and the rhythms that arise from them are fully described by the note-heads, stems and flags. The bar lines do not change anything about that, and a time signature is—for basic rhythms—either redundant or incorrect. Sometimes a time signature suggests something about what pulses or groupings will arise out of the basic rhythm. But even with respect to that, if the groupings or pulses would not be there or would not be convincing without the time signature, then they are probably not really there with it either. I mention this partly to reinforce the idea that no one learning how to read rhythm in our common notation should be thinking about time signatures or bars or measures. This is just a distraction. Also, when a player who is past the stage of learning notation—who is presumably comfortable with the rhythm side of music reading—nonetheless has a problem reading the rhythm of a passage or with feeling secure about that reading, it is almost always a distraction to be thinking about the time signature or the phenomenon of “measures”. I have seen many students effectively prevent themselves from reading a fairly straightforward rhythm because they were not sure right off the bat how to relate that rhythm to something about the time signature or meter or the placement of bars. This leads me to the next point, an especially important one.

4) If the systematic counting of a passage is going to be useful in creating an accurate rhythm, then of course the counting must happen at a steady pace. It does not, however, need to use numbers that relate it to the measures. Often using the ordinary “one and two and three and . . . ” system for counting a passage is enough of a distraction that it hinders rather than helps. Also, sometimes a student puts so much stock in the fact that the numbers are present and in the correct order that he or she forgets to keep them absolutely steady. So we hear something like this: “one and two . . . and three . . .  andfourand.” The student believes that the passage is being practiced correctly because, again, those numbers are there, and they are the right numbers in the right order. So rather than counting a passage as in Example 1, I would suggest something like that shown in Example 2.

This starts with deciding to use the eighth-note as the steady beat. (The correct choice for the steady counting beat at the beginning of the process of drilling a rhythm is the smallest fairly common note value, unless the passage needs to be kept slow enough that that note value is too slow to follow easily: see 7) below.) Then it expresses the length of each note in the number of eighth-notes that that note value actually includes. Of course, it is still necessary to be sure that the numbers come at an even pace. But the second example zeros in on what the player needs to understand and to work on. Of course, as the passage becomes better learned and can go faster, the next step with this type of counting looks like Example 3.

5) The kind of counting described in 4) is also one of the best exercises for teaching the basics of rhythm notation, once the simple rhythmic meaning of the different note shapes has been learned. Taking a large number of fairly straightforward but not trivial rhythms—say of about the level of my example—and counting them out this way serves to drill the meaning of the different note values quite efficiently. For this purpose it is not necessary to play anything, just to count, dropping back to “1” at the beginning of each new note. At the same time, this type of counting really does work well to straighten out a tricky or recalcitrant rhythm. It is not just for beginners: I use it myself when I encounter a rhythm that I want to count out.

6) Sometimes the idea arises of practicing the rhythm of a passage completely separately from the actual notes. This usually takes the form of tapping the rhythm on a table or clapping it. This can be a good idea. It is based on the clearly sound notion that a tricky rhythm should be practiced some—initially or whenever it becomes a problem—without the distraction of worrying about fingering and hand position. It is a form of isolating and simplifying something difficult, philosophically similar to practicing hands or feet separately. I would suggest, as a modification of this, that a student can in effect practice a rhythm in isolation by playing it with random easy notes, perhaps just five adjacent notes played up and down by the five fingers: no choices to make about notes or fingering, but a sonority to hear. This seems to me to be more “true to life” and probably just more interesting for many players. It also gets around a problem that clapping and tapping both have: that they are usually carried out as “repeated note” gestures, and that fast “notes” are therefore harder than they need to be. If a student is in fact going to tap a rhythm on the table, then he or she should use two hands alternating, or two or more fingers alternating in what amounts to keyboard-playing gestures.

7) Another way to practice the rhythm of a passage with difficult notes is to slow the passage down enough that the notes become easy. This is, of course, always the pillar of good practicing, as far as I am concerned, whatever the particular circumstances. Sometimes, however, in order to make the notes of a passage easy enough that the student can afford to think about the rhythm, the tempo has to become so slow that the rhythm begins to seem even more non-intuitive or not really there: almost as if the sixteenth-notes were indeed lasting years. The way to deal with this is not to be afraid of subdivision. If the line that I used for my examples above were hard enough that it had to be practiced at eight quarter-notes per minute, for example, then the correct choice for the counting beat would probably be the thirty-second note, at sixty-four per minute. This would indeed mean that the opening whole-note would be counted (steadily!) from one to thirty-two. This might seem—or indeed be—annoying. However, there is no shortcut to practicing slowly enough, and attempting to time a note that lasts half a minute by counting only “one and two and three and four and” is not going to succeed. The numbers and the “ands” are too far apart to be meaningfully related to one another in counting them out. 

8) There is sometimes a fear of subdivision or of building rhythms up by counting out the smallest components. The fear is, I believe, that too much of this will make a performance seem choppy, make it not convincingly reflect the underlying pulse. My own experience is that this is just not a problem. Having the player’s conception of what the rhythm actually is—what the note lengths and their relationships are—be both correct and really solid is the absolute requirement for achieving a convincing pulse. Counting small beats—subdivided beats—accurately is the most sure-fire way to be certain that the rhythm being drilled is accurate. As a passage becomes solid and as the tempo is able to approach performance tempo, the player’s focus on the smaller beats will naturally melt away. The ease with which both the correct notes and the correct rhythm can be executed will free the player up to listen for the beat groupings and the underlying pulse along with any and all other artistic or rhetorical aspects of the music. Also, any rhythm that needs to be slowed down a lot and treated to a really extreme subdivision will be the exception: an especially hard passage. Every player will have the experience of playing many passages that have been learned from the beginning counting only the time-signature beats. If it is indeed easier to get a convincing overall pulse and shape in these passages—which I rather doubt—then the player can consciously transfer the feeling of playing and hearing those passages to others that have had to be taken apart more finely.

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

Continuo, Part 3

The core of this month’s column is a description of the approach that I suggest for drilling and learning the actual—improvised—creation of continuo parts at the keyboard. The fundamental reason that it is better to improvise continuo parts than to play from a part—a realization—written out in advance is that the most effective continuo accompaniment is one that is flexible. Even at the last minute, but certainly during any process of rehearsal and preparation, it is important to be able to make basic decisions about what notes to play in response to things that we hear from the other players: dynamics, accentuation, intonation, and so on. The earlier in the process the notes are fixed once and for all, the less flexible it is possible to be. So, in playing, unaltered, a continuo realization written by the editor of a published version of a piece, we are committing ourselves to having no flexibility whatsoever during the rehearsal and performance process. Most published realizations are very thick—four voices most of the time—and, in the judgment of many players and listeners, too busy, too noisy. (This is especially true when they are played on organ or harpsichord. At the piano the busy-ness can be made less of a problem by simply playing the part more quietly.) But any realization that is created beforehand, even a wonderfully musical and sensitive one, lacks this flexibility. A player who works out a continuo realization during preparation and rehearsal, and writes it down planning to play it as is, has the opportunity to make it a good realization. But in this approach, last-minute flexibility is still lacking. 

(Actual last-minute flexibility—the ability to change the notes of a continuo part in performance from what they were even a short time before in rehearsal—can be desirable for several reasons. Some of these are: a change in the room acoustics with the arrival of an audience; an unanticipated change in the way a colleague is playing his or her part; problems in performance that suggest that you must project the beat more forcefully; and—most happily!—the fact that a new and better idea occurs to you.)

It also turns out to be easier in the end to learn how to realize continuo parts at sight than either to write them out in advance or to edit existing, published realizations to make them suitable for a given occasion. (And “suitable” still doesn’t take the idea of flexibility into account.) My own reason for plunging into studying continuo realization in the first place—about twenty-five years ago—was not anything artistically significant, but rather extreme annoyance with the mechanics of writing out parts for myself: it was boring, and it took too long.

In the decades following the disappearance of continuo playing as a living art, the notation and technique of continuo realization—figured-bass realization—was borrowed to fill various roles in the teaching of theory, harmony, and counterpoint. It is routine, almost universal, nowadays that anyone who has studied music theory at the college level has spent time learning how to concoct and write out realizations of figured bass lines. Because this activity is done in order to further the learning of something other than actual continuo playing, the kind of realization that is being sought is very different from what is best in performance. Specifically, in theory class, or a similar setting, it is almost always considered necessary to realize in a certain number of contrapuntal voices—probably ideally four, or three to make it easier. The rules of voice leading of course must be followed, and perhaps it is expected that each voice will be kept mostly within a certain range. Often this kind of exercise is presented in two alternate versions: one with all of the added notes in what amounts to the right hand—say, middle C and above—and the other with the four voices more or less evenly distributed, creating a hymn-like texture. In any case, again, all of the rules must be followed. It is (mostly) the need to avoid parallel fifths and octaves that can make practitioners of this sort of exercise tear their hair out. 

It is often their experiences with figured-bass realization in such a context that leads students to believe that it is almost unimaginably hard to play continuo at sight. After all, if something is so difficult and awkward even when you have all day to puzzle over it, to try different things, and to write it out, study it, and think about it, then it must be effectively impossible to do it off the cuff while other musicians are actually playing and expecting you to keep up. This logic is good, but the facts are wrong. What you do when actually playing continuo bears very little relation to the “figured-bass as theory-learning tool” activity, and is in some ways directly opposed to it. The last thing that is desirable in a “real” continuo part is, of course, that the number of voices remain always the same. That immediately and utterly prevents us from using the realization process to influence rhythm, dynamics, texture, and so on. That is, it takes away the very reason for the existence of continuo accompaniment. 

The process of actually learning to play continuo, therefore, does not go through the kind of theory-oriented figured-bass study that I describe above. That kind of study can serve a purpose similar to the reading exercise that I included in last month’s column, that is, to bring a student to the point of knowing the meaning of the figures with real immediacy and ease. (It is overkill for that purpose, in the amount of time and effort that it takes, but it does accomplish it.) For every aspect of learning continuo playing after the meaning of the figures is well established, work on “continuo as theory/harmony/counterpoint” is actually taking us in the wrong direction.

If a student develops a strong sense—simultaneously conscious and instinctive—of what constellation of keys on the keyboard any given note/figure combination is pointing towards, and this sense directs the fingers towards those notes without the need to think much about it, then that student can play continuo at sight. That is, when the student who can already pick up the exercise from the last month’s column and “look at the first note and say ‘F’, the second note and say ‘A, C, and E’, the third note and say ‘F and C’” can play those notes rather than say them, he or she can take on continuo parts from real pieces with other players also playing.

The most effective way to develop that sense goes like this:

1) Find a bass line with some figures. It doesn’t matter very much what the bass line is, although lines from harmonically dense choral or orchestral music can be harder to deal with than is ideal at this stage. Handel chamber music is one excellent source, among many. (A public domain edition can be found at this address: <http://216.129.110.22/files/imglnks/usimg/4/4d/IMSLP05632-Handel_19_Son…;. There are appropriate bass lines on more or less every page.) The bass line can come from a slow or a fast movement. For reasons explained below, this doesn’t matter at all. It need not be a complete movement of a piece or any coherent section, just some notes and figures.

2) Put this bass line up on the music desk of a keyboard instrument. For this purpose it doesn’t matter what instrument: harpsichord, organ, piano, electronic keyboard—anything with at least about four octaves of normal keys.

3) Prepare to play the line very slowly. Because the tempo at which you play this bass line and do this exercise bears no relation to anything about performing the piece from which you have extracted the line, it doesn’t matter what the tempo of that piece might normally be. Each note of the bass line must come along very slowly, regardless of whether it is printed as a whole note or a thirty-second note or anything else. For someone beginning this process, the notes of the bass line should come at a rate of no more than ten or twelve per minute. But that is just a guideline: slower is always fine; faster is also fine if it works.

4) As you play the bass line very slowly, try, for each note of the line, to play (in the right hand) some version—any version—of the notes suggested by the bass note and its figuring. Do not think about anything other than playing something that counts as the right notes: the playing equivalent of what you thought or said in doing the exercise from last month. Specifically, do not worry about the spacing of chords, the part of the compass of the instrument, or the nature of the transition from what you play with one bass note to what you play with the next. Do not worry in the least about parallel fifths or octaves or whether notes resolve correctly. 

5) If you cannot—more or less in tempo—think of any notes to add above a given bass note, simply move on. Do not worry about this. If, the first time through, you only add ordinary triads above the “8,5,3” notes—or even only above some of them—and nothing “fancier”, do not worry about this. 

6) After you have played the bass line and whatever notes you have added in this way once, do it again. Don’t increase the tempo. Try to add some notes where you didn’t the first time. Then, of course, do it a few more times. If it feels natural to let the tempo increase a little bit that is all right, but by no means necessary. However:

7) Do not play the same line more than several times. If after a while (four or five times through) you have not succeeded in providing right hand notes for all of the bass line, don’t worry about this either. The effectiveness of this drill does not depend on “solving” the entire bass line, but rather on developing a sense of spontaneity with those spots that you do solve. If you play over it too many times in a row, that sense of spontaneity will be lost and replaced by excessive concern for getting it all right. 

8) Choose another bass line, and do all of the above again. This can be another section from the same movement or piece, or something completely different. Practice this way with as many bass line passages as possible. Never stay with one of them so long that you feel like you know it and are simply repeating something that you have already learned: move on to another one. Try to use lines in different keys, but you need not seek out anything too unusual: two sharps or flats is far enough along the circle of fifths for now. If most of what you use is in keys with one or no sharps or flats that is OK. Just don’t stick to only one key. That can become a rut.

All of the details above are important, but clearly step 4 is the essence of this exercise. Here are a few more specific thoughts about how to carry out that step.

a) It is perfectly all right for the tempo of the bass line not to be entirely steady. (This is certainly different from most types of practicing.) It doesn’t exactly need a tempo, but only be not too fast. If you need to draw one note out a little bit longer to think about what to play over that note, that is OK, as long as it is only a little bit. If you are really, in effect, stopping to figure something out, then that defeats the purpose.

b) You need not play all the notes that you add at the same time as the bass note or together with one another, though as you do more of this exercise you should discover that you can add the relevant notes with or close to the bass note more of the time. Initially it is perfectly acceptable to do something like this: set a metronome to 60; allow each bass note to last for eight metronome beats; expect to play the added notes on or near the fifth metronome beat; use the last beat or two to begin to look ahead at the next note. The numbers are arbitrary; the principle of keeping it slow and careful is crucial.

c) If you make certain kinds of mistakes about what the figuring means or what notes would be appropriate to add over a particular bass note, this doesn’t matter! One extraordinary thing about this exercise is that it usually leads a student to the right place even if it is done wrong. The most common way that this comes up has to do with un-figured notes. If you mistakenly assume that a passing tone is not a passing tone, and therefore add chords to bass notes that are not supposed to have anything added, this just constitutes more (fully useful) practice. If you interpret as a passing tone a note that really should have something added, and don’t add anything, that is a very minor wasted opportunity. It doesn’t mislead or do any harm. If you forget, for example, that “7” usually implies “7,5,3” and just play the pitch seven degrees above the bass note, that is still useful practice in developing the spontaneity that we are looking for. There is time to refine and fill in gaps in your awareness of what the figuring means and what the abbreviation conventions were later on. 

d) Likewise, leaving out things that are too complicated or unexpected—for example a figuring like “9, 7#, 4, 3b”—is not a problem. You have simply utilized one less practice note: no harm done. Reading really elaborate, complicated, counterintuitive figures can come later. In any case they are extremely rare. It is of course OK not to leave them out, but only if they are accurate and don’t slow the process up very much.

e) Of course, really fundamental mistakes—taking “6,3” to mean the notes one and four steps above the bass, for example, or anything else really egregious—will lead to trouble. Real misunderstanding at a fundamental level will be hard to eradicate later on. Therefore this exercise should come, as I said above, only after the student has comfortably learned the basic meaning of the figures.  

f) It is extremely important to resist the temptation to write anything down about a realization. The sole purpose of this drill is to develop the reading faculties as they apply to figured bass lines. Any time you write anything—a note or chord or a reminder perhaps expressed as a letter-name for a pitch—you have lost the opportunity to develop that reading, and in fact you are training yourself to be unable to do it. 

g) It is perfectly OK, though, to flesh out the figuring itself. The relative completeness of the figuring of the line that you happen to be using for practice is arbitrary. If you make it more complete before playing from it that is fine. (See, for example, the two versions of the Handel bass line that I included in last month’s column. Either of them is good material for this sort of practice.)

After doing a certain amount of this work, the student will be ready to begin thinking about how to shape an accompaniment for “real life” use, and to begin playing pieces with other musicians. This “certain amount” is often something like 25 or 30 bass lines, each eight to sixteen measures, each played five or six times. That is not a lot, but this method is extremely efficient. Some students will need or want to do more than that; some will be ready to move on to the next stage sooner.  

I will return to the subject of continuo playing and deal with approaches to entering that next stage in a future column. Not next month, however; I want to give readers a chance to digest what I have written about it so far and, if so inclined, to try out the drill suggested here or to have their students do so. I welcome both questions about that process as it unfolds, from anyone who is trying it, and any other feedback.

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

Some thoughts about substitution

Substitution in organ playing—both with fingers and with feet—is a technique that is practiced to some extent by almost every organist. This includes both those who plan it out and know that they are doing it and those who don’t plan it and nonetheless do it by chance at the last minute. It has been the subject of heated debate and disagreement—one of those subjects that can sometimes seem almost political in nature. The disagreements are usually about the relationship between substitution and various aspects of authenticity—and of course authenticity is the most political subject in the realm of performance. Indeed, it is quite certain that substitution has been more prevalent at certain times in the long history of organ music than at others, and practiced, or expected, more by some composers than by others. 

It is also a technique that can be carried out in ways that are natural and easy or in ways that are awkward and difficult. In this column I want to discuss, just briefly, the history and theory of substitution and also to suggest ways of thinking about applying the technique itself.

Before the eighteenth century

The usual succinct way of describing the history of substitution in keyboard playing is this: that it was unknown or at least very uncommon before the late Baroque, and that by the nineteenth century it had become extremely common—though more so in organ playing than in piano playing. As far as the historical record is concerned, there are no sources from before the early eighteenth century that explicitly discuss substitution or that direct a player to use it, but there are many from the nineteenth century and beyond. 

The first surviving printed or written reference to finger substitution comes from François Couperin, writing in his L’Art de toucher le clavecin—a harpsichord method published in 1716. He speaks of it as something unusual if not downright new, contrasting it to “l’ancienne manière”—“the older way [of fingering].” Couperin’s prose is concise or even cryptic, and he says very little about the thinking behind his employment of substitution, but it seems to be intended some of the time to make it easier to achieve some sort of legato, as in Example 1, or to cope with suspensions or other complicated textures, while maintaining legato as in Example 2. (Note that there are no fingerings given for the upper left-hand notes. The G in the second measure would be played with the thumb—after the substitution on the lower note is complete. But what then? A substitution to preserve strict legato in the inner voice or not?) 

There are two significant pieces of evidence that substitution was not common before the time of Couperin. They are, first of all, Couperin’s own attitude about substitution: that it was something new. Of course, he did not know everything about musical practices over the whole world and for all of the decades before his own time, but he probably kept himself rather well informed. The second piece of evidence is simply that no one mentions it prior to 1716. During the seventeenth century there was by no means as much written about keyboard playing and pedagogy as there was in later centuries. However, enough such writing has survived that it seems significant that substitution is not even hinted at in any of it. This is of course consistent with much of what else is known about keyboard playing, whether on organ or on harpsichord or clavichord: in particular, that full legato was the exception, especially over long chains of notes such as the ornamented melody in the first example above.

I however have always felt cautious about assuming that no one in the time before Couperin ever used substitution, either with fingers or with feet. My principal reason for this is that it seems to me to be a natural human thing to do—not necessarily as a result of planning or artistic decision-making, but as a tool for coping with situations that might arise. I have seen many students—beginners, with no preconceptions about fingering, to whom I had certainly not (yet) said a word about substitution—in effect re-invent the technique because they found themselves at some sort of fingering dead end. Furthermore when they do this, they usually do it—because it is not self-conscious—in a relaxed and natural way that constitutes good technique. Also, substitution is a natural thing to do by analogy with other human activities. For example, arriving at the front door recently from a trip to the grocery store, I shifted the bag of groceries from one arm to the other so that I could reach my keys. This is conceptually the same thing. If a player is holding a note with a particular finger and finds that it is inconvenient to be holding it with that finger, slipping a different finger onto the note is a natural, spontaneous human response. I put it this way only partly to make the case that players prior to the eighteenth century may well have used substitution willy-nilly, so to speak, even though it was clearly not a prominently taught technique. I also want to suggest that because it is a natural and physically obvious thing to do, when we in fact want to do it, we should remember to do it in a physically natural and comfortable way. Also, perhaps, that we should avoid it whenever it cannot feel natural and comfortable, unless there is a very strict reason for its being necessary. 

The choice about whether to use substitution in playing music that was written in the era when it was, at a minimum, clearly not being taught as a core technique is of course one for each individual player to make. It will inevitably stem in part from that player’s overall approach to questions of authenticity, and also from other things about technique and habit. Every teacher should frame this particular issue to students in whatever way is consistent with the teacher’s and students’ interactions over matters of authenticity in general. To me the bedrock caveat or concern about substitution in what we might categorize as “pre-Couperin” music is this: that if you actually need substitution to make a particular articulation or phrasing happen, then that articulation or phrasing is almost certainly not anything that the composer specifically had in mind. 

The Classic period and beyond

Substitution is referred to in printed sources only a little bit through the middle of the eighteenth century, but references to it in keyboard methods and elsewhere proliferate in the Classic era. It is interesting to note that although we organists (rightly) think of substitution as being most at home in a certain branch of organ technique, it was in early piano playing and teaching that it first caught on. This was in the era when the damper ‘pedal’ on pianos was usually either a hand stop or a knee lever but, in any case, was awkward to operate. Legato lines were by and large achieved through fingering. During the nineteenth century two developments shifted the emphasis on substitution from piano to organ: first, the invention and quick universal acceptance of the (real) damper pedal, and second, the use of a more legato style in  organ technique.

It is worth remembering that even for the relatively well-documented nineteenth century we do not in fact know how everyone did everything. Franck, for example, left no substitutions among the few fingerings that he provided for his own organ music. There are clearly many places indeed where substitution is required, especially if the goal is to create true unbroken legato. In this passage from the Prière (Example 3), there is a need for substitution in, probably, a majority of the transitions from one moment to the next—if, again, true legato is to be maintained. (It is possible to play these notes without any substitution if the full-fledged legato is abandoned.) The section of the piece from which this passage comes is under the marking “très soutenu,” which suggests legato. However, I myself cannot devise any way at all to play the last three eighth-note left-hand chords of either the second or the fourth measure truly legato, with or without substitution. There are other spots throughout the section of the piece about which I would say the same thing. Does this tell us anything about articulation? We know that Franck had large hands—much larger than mine or than those of other players whom he might have expected to play his music. We also know that most European churches, certainly including Sainte-Clotilde, have spacious acoustics in which listeners can experience the effect of legato even through subtle breaks. 

The point here is not to resolve anything in general about the articulation practices of Franck. It is rather this: that we should be ready to use substitution where it makes sense, but be cautious about assuming that legato is necessary in nineteenth or twentieth century music, simply because the possibility of substitution exists. There is a kind of circular logic that says: “This passage must be played with a lot of substitution because it has to be legato, and we know that it has to be legato because players at that time used a lot of substitution.” This doesn’t make sense. (I have certainly caught myself thinking that way, as well as students and people who have written about these things.) The more appropriate way of thinking about it something like this: “If I want this passage to be legato and that requires substitution—even a lot of substitution—that is indeed completely consistent with what the composer might have intended or expected.” 

This is the fingering, just as an example, that I myself would use for part of the left hand in the excerpt from the Prière (Example 4). The function of most of the double substitutions is clear and normal: to create the possibility of smooth legato. There are a few specific things to say about these fingerings. The 3–4 substitution on the fifth eighth-note of the first measure is really just for comfort—better hand position reaching that chord and moving away from it. That is specific to my hands: another player might play the lower note initially with 4 or hold it with 3. Holding that D# with 3 might take away the need for the lower part of the next substitution (Example 5).

I would execute these substitutions quickly and in an unmeasured fashion (more on that below), with the possible exception of the one on the chord that spans the first bar line. That one I might divide between the two beats in a measured way. The 3–4 in the second measure is—again in relation to my particular hand—an attempt to make the large jumps at that spot more comfortable and closer to legato, although, as I said above, I cannot quite reach them fully legato.

As I wrote in my column on repeated notes (January 2009), there is a relationship between the practice of playing repeated notes with different fingers and substitution, but with a difference in articulation. In playing two notes in a row with different fingers, you release the first finger before playing the second; in substitution you play the second finger before releasing the first. (It is interesting, by the way, that Couperin was an advocate of, and wrote about, both of these practices.) There is also this difference: with repeated notes you have the opportunity to get the first finger out of the way early, but with a substitution the two fingers must be able to share the key at least briefly. This can dictate the details of how the fingerings are carried out—which finger goes above or below which, and whether the finger being released is released up, sideways, or down. 

Playing substitutions

The most important thing in preparing a substitution to be comfortable and natural is working out the details of the direction in which the fingers move—the choreography of the fingering event. In the first Couperin example, the first few substitutions are all 4–3. In these cases the fourth finger must be released down (towards the player) and slightly to the right. In the 4–5 substitution at the beginning of the second line, the fourth finger must be released up (away from the player) and probably straight or slightly to the left. These shapes will prevent the fingers from interfering with one another. In double substitutions the most important part of the choreography is the order in which the chain of substitutions is carried out. There is always an order that allows the hand to contract during the process and an order that causes the hand to stretch. It is never hard to tell which is which. The former is always better; it is always possible to tell which is which: it is important to do so. 

The gesture of substitution can usually be carried out either in a way that is measured—the new finger moves onto the note at a definable time, the old finger moves away at a definable time—or in a way that is unmeasured, with the new finger simply sweeping onto the note as promptly, quickly and lightly as possible, while the old finger is swept away. The first of these is, in a way, analogous to a measured appoggiatura in the Baroque style, and the second to a quick grace note or an acciaccatura. Furthermore, whether the substitution itself is measured or quick, it can, on a longer note at least, be positioned either right at the beginning of the note or anywhere else in the lifespan of the note before the moment when the logistics require the new finger to be in place. 

On the whole, I prefer to execute suspensions quickly—the acciaccatura model—and as close to the beginning of the note as possible. I believe that I do this because I want them to have no rhythmic weight of their own. Not that they would have audible rhythmic weight since by definition they are silent. In fact, that is the point. As much as possible I like to reduce the feeling—which substitutions by their nature are inclined to create—that there is something going on physically in the playing that is not reflected by anything audible to the listener. All else being equal, I believe that a one-to-one correlation between physical gestures that we feel ourselves making and sounds that we hear our instrument producing helps to intensify our focus on the rhythmic aspect of the music and to make it more likely that we will effectively project rhythm and pulse to the listeners. In my fingering example above, I might play the substitution on the note that crosses the first bar line at the downbeat of the second measure rather than at the beginning of the note. This is because there is an implied rhythmic event there—the strong beat across which that chord is suspended. I would probably still make the gesture of the substitution a quick one, since there is only one rhythmic event going on with which the gesture might be correlated. 

The use of substitution

There are three ways in which substitution is used: 1) as part of a well worked-out fingering plan, with some specific goal in mind, usually related to achieving legato, but sometimes for comfort, reliability, or good hand position; 2) as part of an approach to fingering, even when it is not explicitly worked out in advance, but still with goals in mind, again usually having to do with creating legato; and 3) as a way of scrambling around to get notes at the last minute in a passage that has not been adequately prepared. For an observer, including a player observing him- or herself and also including a teacher observing students, these last two can be hard to tell apart. The third of these is on the one hand a useful fallback if it is needed: substitution can be a powerful way of crawling around the keys and getting notes in an emergency. However, any tendency to rely on it for that, except in the occasional emergency, has to be resisted ferociously. If a teacher believes that a student is using a facility with substitution to avoid having to think about the best fingerings, listen for what fingering does for interpretation and performance, and practice enough and well, then the teacher must step in and ask the student to pull back from that and restore substitution to its place amongst the legitimate technical tools that we have at our disposal.

Gavin Black is director of the Princeton Early Keyboard Center

Hard pieces and 

recalcitrant passages

This month I am writing about the phenomenon of pieces being difficult and the related phenomenon of specific passages being hard to learn: either difficult by any standard or surprisingly difficult—for reasons that may seem elusive—for a particular student. This is not a very systematic or methodological discussion: just a few ideas—almost just random thoughts—that I think are interesting or that may help some students or teachers. 

We all believe that some pieces are harder to learn or to perform than other pieces. This—just as a basic fact—is probably as close to uncontroversial as anything gets in the field of music and music teaching in general, or of organ-playing and organ teaching in particular. We don’t necessarily all agree as to which pieces are more difficult and which less so. Most of us, from our own experiences as players and from what we have seen with our own students or other performers, know that different pieces or sorts of pieces are more or less difficult for different players, and at different times in one player’s career.

Repertoire in order of difficulty

When I first acquired copies of one or two volumes of the Peters edition of the Bach organ music—in about 1971, at the age of about fourteen—I noticed that the separately bound Preface included a listing of all of the (non-chorale based) pieces arranged according to difficulty. I was excited about this, since it seemed both useful and authoritative. I allowed it to influence what pieces I chose to work on—though not in a logical or consistent way. Sometimes I would choose a piece because I thought it was easy enough to be within my grasp, sometimes I would spurn and reject pieces that were described as being “easy,” because I thought that working on them would be sort of embarrassing, classifying me as “not very good.” Needless to say, this was all rather silly. 

I did continue for a long time—after my studying had become at least a bit more systematic and effective—to cast sneaky glances at the list out of the corner of my eye. I would pat myself on the back just a little a bit whenever I put in some work on a piece in the top half or so of the difficulty scale. I pretty much stopped doing this when Eugene Roan, with whom I had by then started taking lessons, mentioned casually to me one day that an eminent recitalist he know thought that piece x was much more difficult than piece y—the opposite order from the Peters list. This introduced me to the idea that this whole difficulty thing could be relative, though at that point in my career I couldn’t have said how or why this might be so. 

Reger and Straube

Another way that the concept of difficulty as a kind of independent variable in pieces of music came to my attention when I was first getting interested in organ was through hearing the story of Max Reger and Karl Straube. The idea was that Reger had made his organ pieces more and more difficult in the hope of writing something that Straube, his good friend who was also the leading German organ virtuoso of the time, would be unable to play. It was also said that he never succeeded: that Straube “won.” There are a couple of interesting things about this. One is that, of course, it is trivially easy to write a piece that is unplayable, if that is really all that you want to do. All that you need to do is to write notes that are too far apart in compass to reach.  The music does not have to be particularly complex or intricate or fast. However, a piece that is really unplayable will, in fact, not be played. That is never in any composer’s interest. Not surprisingly, composers—whether they are writing for Karl Straube or not—tend to approach daringly close to that “unplayable” line, and then to decide not to cross it. This is as true of a composer like Beethoven, who stated bluntly that he didn’t care what performers could or couldn’t do, as it is of composers like Bach or Franck, whose keyboard compositions arose out of their own work as performers and improvisers. 

It is also interesting that Straube—as a student, before he had met Reger in person—was in fact drawn to Reger’s music in part because it was first presented to him as being too difficult to play. Straube’s teacher Heinrich Reimann showed him Reger’s then very recently published Suite in E Minor, op. 16, telling him that it was unplayable. This seems to have motivated Straube to learn it, which may or may not have been Reimann’s intention all along. I myself, when I was still more-or-less a student, occasionally started to work on a piece because someone had said to me that I could not learn it. (This was never, in my case, one of my own teachers.) I always learned something valuable from the attempt, although it did not necessarily result in my mastering the piece in question at that time.

Aspects of difficulty 

When we talk about a piece’s being very difficult, we are almost always talking about the learning and reliable playing of the notes: the right notes, in the right order, at a suitable tempo. That is not to say that anyone denies that other aspects of playing a piece can be difficult. In fact, performing even a simple piece in such a way that it is extraordinarily compelling, beautiful, interesting, thought-provoking, disturbing, whatever we want it to be, is probably as hard and (at least) as rarely achieved as playing a difficult piece competently. However, that is indeed a different thing. When students ask whether the Goldberg Variations or the Dupré Prelude and Fugue in G Minor is too hard for them, they are rarely inquiring about whether the teacher thinks that they can project the deepest meaning of the piece effectively. Of course, there is always this relationship between what might for the sake of simplicity be called the two types of difficulty: that the better-learned the notes of a piece can become for a given player—the closer the piece can come to feeling easy once it has been learned—the more of a chance there is that a performance can also be musically effective.

The piece that I happen to have been practicing the most in the week or so before I sat down to write this column is the “In Nomine” by John Bull that is found in volume 1 of The Fitzwilliam Virginal Book. The makers of a list like the Peters Bach organ repertoire list would probably put this piece at the easy end of “moderate” or the somewhat high end of “easy.” It is in three voices throughout, but none of the voices is very busy or intricate. For much of the piece the middle voice lies in such a way that it could be taken by either hand, so there is a fair amount of fingering flexibility. It is (though this is obviously subjective) not a piece that many people would think should go very fast: certainly not fast enough to make playing it into an athletic challenge—which some of Bull’s pieces are. This is a piece that I used to play a lot and, as best I can remember, I did indeed initially choose it because it was not too athletic. Bull’s Walsingham or King’s Hunt would have seemed beyond me many years ago. However, it occurs to me that this piece is a good illustration of the relationship between note-learning difficulty and tempo. There is—literally—a set of tempos at which this short Bull piece would be harder to play than the Reger Opus 16: that is, a mind-bendingly fast tempo for the Bull and a glacial tempo for the Reger. In order to achieve my inverting of the difficulty of these two pieces, the tempos would have to be so extreme that they would both be well outside what anyone would ever do. However, within a more realistic range of performance tempos, the Bull can become a virtuoso challenge of its own, and the Reger can move from the “impossible” all the way down to the “very hard.”

Difficult passages

Many pieces that have a reputation for being very hard are as difficult as their reputations suggest only in spots. For example, the Bach F-major Toccata is considered one of his hardest organ pieces. It earned a very high place on “the list”—maybe at the very top, certainly close. However, long stretches of the piece are really not hard at all. The opening has nothing going on in the pedal, and the two manual lines are somewhat intricate, but not remotely beyond the bounds of the “intermediate” for anyone. Then there is a pedal solo, which is also quite learnable. The following two pages are essentially a recap of this opening: carefully designed by the always pedagogically aware composer to be a bit longer and a bit trickier than the opening itself, but similar in nature. Then, beginning at about the fifth page, the hands and feet start moving together, and things get more complex. Still, however, the notes fall into place quite naturally. Most players I know who have worked on this piece report that this section yields nicely to practicing and is not more difficult than other Bach prelude-type pieces. It is the three brief passages that involve the return of the opening motif of the piece, this time in manuals and pedal together, that seem really hair-raising to many of those who work on the piece. This is not everyone’s experience, but it is a common one. Other very difficult pieces can be analyzed this way as well: perhaps most of them. In the Goldberg Variations, for another example, probably about eighty percent of the writing is no more difficult than the average for The Well-tempered Clavier or Handel harpsichord suites. That is not, by any standards, “easy.” But it is the remaining fifth or so of the work that gives it its reputation as “only for advanced players.”

One source of difficulty in working on pieces of music is unfamiliarity with a particular style or the technical tendencies of a particular type of music. Ralph Kirkpatrick, in his preface to his edition of sixty Scarlatti sonatas, first outlines a set of rigorous ideas about how to work on the sonatas, both as to analysis and as to practicing. Then he says that if a student approaches six sonatas this thoroughly he or she will not have to do the same with the next sonata or later ones. The particular shapes of a given kind of music become ingrained. I myself, as a player who has worked more on Baroque music than on anything else, find it much easier both to sight-read and to learn Baroque pieces—even complex and difficult ones—than music from a later era. To me this suggests patience. If a student is working on his or her first piece from a particular genre or style or time period, then that piece is going to be harder than the next one will be. That should not be surprising.

Practice strategies

If a student is interested in working on a piece that seems too hard, I am extremely committed to letting him or her do so and to making it work. The first step for me is to try to figure out whether the difficulty is found in a few spots or more or less throughout. This affects learning strategy. In the first instance, I will suggest to the student that we break the piece up and completely abandon any thought that it is one unified piece—just for the time being of course, but with a lack of impatience as to how long that time will be. Then the easier—more “normal”—parts can be practiced and learned in a “normal” way, systematically and carefully, along the lines that I have written about before. The extremely hard passages can be treated as intensive exercises: analyzed, taken apart, put back together and practiced to within an inch of their lives. 

A piece that is quite difficult—perhaps too difficult for the student—and of much the same difficulty throughout simply needs to be taken apart and practiced well. The key here is to make sure that the student understands what the process will feel like. Anyone can practice anything effectively if it is kept slow enough. In this context, the meaning of a piece’s being “too hard” is simply that working on it correctly will take a long time. Would the student rather work on this piece for a very long time, or postpone it, work on other pieces in the meantime, and wait to work on the proposed piece later? This is simply a matter of what the student prefers: either approach is fine for helping him or her to become a more accomplished player. 

In fact, it can be perfectly useful and helpful for a student to work on a challenging piece even if he or she never really learns it—assuming that the failure to learn it is of the right sort. If the goal is to perform a piece then, by definition, that piece must be practiced until it is learned and secure and ready to go. However, if the goal is to use the process of working on a piece to become a better player in the long run, then it doesn’t matter whether the time put in practicing that piece is followed by more time with that same piece (eventually leading to its being learned) or by practicing a new piece. The choice to practice a hard piece up to a certain point and then let it go is perfectly acceptable, assuming that the student is happy with it, and understands that it is a process, not a failure. And of course, that same piece will be there for the student to come back to later. In fact, the first round of work on the piece will leave that piece in very good shape to be picked up again later: it will probably even get better during any time that the student takes off from it. It will be sinking into the subconscious mind. The only technical requirement for this approach to be fruitful is that the work done on the piece—or any section of it—be accurate and technically sound, but below tempo. If the piece is put aside in this way, it should be put aside at a slow tempo but otherwise exactly as it should be.

Gavin Black is director of the Princeton Early Keyboard Center. He can be reached by e-mail at [email protected]. A selection of Gavin Black’s organ performances can now be heard on YouTube by searching on his name at the YouTube website.

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

Continuo, Part 2

This month I am following up on the discussion of continuo playing, offering more specifics about how to read and understand continuo parts. I will wait until next month to describe my approach to the teaching of actual continuo playing at the keyboard to students who are not yet experienced in it. A combination of the approach outlined here to understanding the notation, and the approach that I will outline next month to drilling the playing can enable a keyboard player to begin to feel comfortable playing continuo on an improvised basis after something that could be described as “several hours” of study. Of course no one is fully accomplished at it after that little work, but many students are ready to apply what they have been working on to real music in that sort of time scale.

A continuo part is, as discussed last month, a bass line that is meant both to be played, in itself, and to be supplemented by other notes. A combination of the ordinary musical notes of that bass line and the numbers and other symbols written above or below that line (the “figures” in “figured bass”) guides the player in choosing what notes to add to the written line. (It makes no difference whatsoever whether the figures are written above or below the notes. Below is much more common, and I will use that style in my examples and assume it in this discussion. But everything that I say here applies equally to a continuo part in which the figures happen to be written or printed above the notes.) The first step in learning how to play a continuo line is to learn what that combination of notes and figures means. Continuo or figured bass notation is essentially simple, but it is open to various misunderstandings, and is, like so much in music, capable of seeming more complicated or mysterious than it actually is. 

The musical notes of a continuo line are, of course, normal musical notes and, being in the tradition of tonal music, have a key signature. The figures written below any note point to the pitches—or really the pitch classes—that you find by counting up from the written note by the number of steps indicated by the figures, counting the printed note as “1”, staying within the key signature. Here are some examples:

1) If there is a key signature of no sharps and no flats (that is, what we sometimes call “no key signature”), the printed note is C, and the figure is “4”, then the additional pitch being indicated is F-natural.

2) If there is a key signature of one sharp, the printed note is C, and the figure is “4”, then the additional pitch being indicated is F-sharp.

3) If there is a key signature of three flats, the printed note is C, and the figures are “6” and “3”, then the additional pitches being indicated are E-flat and A-flat.

4) If there is a key signature of one flat, the printed note is B-flat, and the figure is “4”, then the additional pitch being indicated is E-natural.

5) If there is a key signature of two flats, the printed note is B-flat, and the figures are “4” and “5”, then the additional pitches being indicated are E-flat and F-natural.

This way of describing what is going on with the figures is accurate and straightforward. Students sometimes ask, however, why we don’t describe the same thing using the terminology of intervals: that is, by saying that the figures point to the notes that are that interval above the printed note—again within the key signature. This would also be a valid way of describing what is going on. However, it is not necessary that the interval be one that we often or normally deal with as an harmonic interval, and sometimes describing it that way is just confusing or inefficient. For example, in 4) above, the harmonic interval is a tritone, or an augmented fourth. There is certainly nothing wrong with noticing this, or with describing it that way. But in practice, experience shows that it is more direct and in the end both easier and quicker—even if it is counterintuitive to some students at the beginning—just to notice that it is four steps above the printed note. (To put it more accurately, most players use some combination of these two ways of thinking about it—“this note is four notes up from the bass” and “this note is a fourth above the bass”—but it is useful at the beginning at least to emphasize the former way of describing it. It is important not to be misled, in incorporating the concept of intervals, by a sense of what an interval should be, when that is different from what the interval is. For example, in a piece in A Major, a G# with the figure “5” under it will give rise to a diminished fifth. Some students who are looking at continuo through the lens of harmonic intervals will be at least fleetingly tempted to raise the D to a D#, since the figure “5” looks, at first glance, like it should refer to a perfect fifth.)

Along with numbers, the figuring of continuo lines will sometimes include accidentals. These are used to take the realization of the continuo part out of the constellation of notes that are in the key signature. Here are some examples:

1) If there is “no key signature”, the printed note is C, and the figure is “4#”, then the additional pitch being indicated is F-sharp.

2) If there is a key signature of two flats, the printed note is B-flat, and the figure is “4#”, then the additional pitch being indicated is E-natural.

3) If there is a key signature of two flats, the printed note is C, and the figures are “3”, “5”, and “7#”, then the additional pitches being indicated are E-flat, G-natural, and B-natural.

4) If there is a key signature of three sharps, the printed note is E-flat (achieved with an accidental, of course) and the figures are “2”, “4#”, and “6b”, then the additional pitches being indicated are F-sharp, A-sharp, and C-natural.

5) If there is a key signature of two sharps, the printed note is F-sharp, and the figures are “3#” and “5”, then the additional pitches being indicated are A-sharp and C-sharp.

In 3) and 4) above, the pitches indicated, taken together, do not add up to a normal, or common, chord. This does not matter. Of course, in most Baroque chamber or vocal music, the prevailing harmonies are—most of the time—quite normal and recognizable. However, the notation of continuo parts works completely independently of any assumptions about what harmonies do or don’t make sense. Looking at it this way saves a lot of time and worry. A note in a continuo line that looked like Example 1 would indeed be inviting you to play all of the natural pitches. It wouldn’t matter that this, in some way, doesn’t make sense. I have never quite seen anything this extreme in the repertoire, but there are examples of figuring that are almost this unexpected, the chordal nature of which is hard to figure out quickly. What chord, for example, is indicated by the flat 9 and the natural 3 in this Bach cantata bass line? (Example 2)

This might take some sophistication or even inventiveness in harmonic analysis to figure out. (It is probably part of a diminished seventh chord combined with the dominant note of the tonic towards which that dominant seventh chord wants to resolve.) However, for the purpose of continuo playing, there is no need to answer the question, and the time taken to figure it out would be wasted as far as playing the continuo part was concerned. The notation is telling you that the notes available to play along with the G on the third beat of the measure are B-natural and A-flat. That is what you need to know.

I mentioned above that we are really talking not about pitches, but about pitch classes. Thus Example 3 is directing us towards E’s and G’s, not towards any specific E or G, in particular not towards the ones that are closest to the printed note. In the following example, the printed notes and their numbers are directing us towards any of the pitches where I have placed x’s. (Example 4)

It is important to remember that nothing about the notation tells us which of all the possible notes (x notes in the above example) actually to play. The decision to play any, some, most, or all of the possible notes at any give moment in a continuo accompaniment is made on the basis of a host of interpretive considerations, including texture, volume, accent, and more. Right now we are concerned just with the reading of the notation. Reading the notation fluently, and then learning to play from it equally fluently, are the prerequisites to making those interpretive decisions.

One good way to work on becoming fluent and comfortable at reading the notation—that is, just looking at it and knowing what it means—is to take a series of random bass notes and random figures and talk out in your head what those notes and figures are telling you. Here’s a place to start (Example 5).

The idea is to look at the first note and say “F”, the second note and say “A, C, and E”, the third note and say “F and C”, and so on. It is best to do this as quickly as possible without getting any of them wrong, and not to worry about what chords are made by the notes. Anyone can write out an infinite number of exercises like this. (If you write it out quickly enough, you can then do it as an exercise yourself, because you won’t have concocted them deliberately enough to have figured out the answers.) The next step is to do the same thing with various different key signatures. The point is very simply to train the mind to know instinctively what any combination of a note and some figures means. Since we already know what the notes themselves mean, this really amounts to becoming adept at quickly counting up from the note by the amount indicated by each figure. Most students will need to do only a small or medium amount of this, but it should be done until it seems trivially easy. This approach to drilling the notation ties in directly to the way of drilling the act of playing from that notation, which will be the subject of next month’s column.

Continuo notation in real life—as it was used every day in the Baroque period—involved a very large amount of abbreviation. That is, in order to save time and ink, certain conventions grew up about what figures could be left out or assumed. It is important for a student learning continuo notation not to worry about this phenomenon at first. However, once anyone has a clear and comfortable understanding of what the notation system means, the following things should be thrown into the equation:

1) Since the ordinary triad above the bass note is the most common note picture, the figuring for that note picture—8,5,3—was usually simply omitted. Therefore, when a note has no figures associated with it, it is assumed to be “8,5,3”.

2) Since most harmonies include the third, the figure “3” is often omitted and can usually be assumed. It is only incorrect to assume “3” if “4” or “2” is present. Thus, the figure “6”, for example, usually means “6,3”.

3) As a natural extension of 2), an accidental by itself means “3” plus that accidental.

4) It is usually acceptable to double the bass note itself unless the figure “6” is present. Thus the figure “8” is rarely used, and it is clear when it can be assumed.

5) If a note in the bass line is meant to be considered a passing tone and should not have any realization associated with it, or if the prevailing harmony from the previous note is meant to continue, it is “officially” supposed to have a dash written under it. This is often omitted, leaving the identification of such a passing tone to the judgment of the player.

Here is a fragment of a Handel Flute Sonata, first with figuring from the composer’s own time, then with a version of complete figuring (Examples 6 and 7). Anyone who has learned to understand the bass line and figuring from the second of these examples will, in the normal course of working on the actual playing of continuo parts, come to feel comfortable playing from the first. The two are identical in what they suggest or imply or require in performance.

In teaching the actual playing of continuo at the keyboard—the next step once the notation is basically understood—I do not ask students to write anything out, not even as a sort of transitional stage. A written part is antithetical to the art of continuo playing, even if it is an unimpeachably good realization. The whole point of continuo is flexibility, including last-minute flexibility. And the good news is that efficient learning of the art of continuo playing actually takes place best at the keyboard and at the keyboard alone. Also, oddly enough, it is possible to practice the art of continuo playing just as effectively whether you are reading the notation correctly or wrongly, and whether or not you fully understand the conventions about abbreviation. Therefore, once a student has a basic understanding of the notation, it is time to go on to playing, and we will do so next month.