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.
