Figured Bass for Beginners

 Figured Bass for Beginners

After some study of the subject and how to wade into it, I’ve decided it would be good to attempt a treatment of the subject of Accompaniment From Thorough-Bass in a form useful for beginners. I know that when I started trying to work on Figured Bass exercises I had almost no idea how to proceed and a lot of trouble would have been saved if I had known a few little things that don’t seem to be well documented in the books I started with. So let’s begin with…

Intervals

An interval, as you may or may not know, is the difference in pitch between two notes. The two notes may be one after another, in which case it is a melodic interval, or they can occur at the same time creating a harmonic interval. The numbers in a figured bass, the figures, are simply the harmonic intervals that occur above the bass note, that when played together form the desired sound, or sonority.

As an example, here we have the bass note C.

Underneath the note, we have the figure 5-3. This means that the notes needed to complete the chord lie a fifth and a third above C. These notes, if you count up to them, are: G and E respectively. So let’s write those in.

Those of you with a little bit of theory under your belt will recognize this as the most basic three-note chord, or triad: C major chord in root position. While it is of some use to recognize this fact, it is good to keep in mind that during the time period when these figures were invented and used extensively, these terms such as ‘root-position’ or ‘chord inversions’ weren’t used. For now, let’s just acknowledge that this 5-3 figure happens to sync up with our idea of a root position triad.

So we plotted out the intervals and made a chord, but we’re not quite done. A 53 chord doesn’t have to look like the one we wrote down. That E doesn’t have to be down there, it could appear up here in the treble instead.

And we don’t have to limit ourselves to just one G or any other note of the chord. Any one of the notes described by the intervals can be doubled or duplicated. We can have as many C’s, E’s, or G’s as we want!

We can see now that while the figure is describing specific notes to us (C E and G), it isn’t telling us which C, E, or G to use, nor how many. The sonority (the C major root position triad) is being described precisely, but its disposition (how widely spaced, how many notes are duplicated, which note’s on top) is left to the discretion of the performer. If we only restrict ourselves to what is physically playable by two hands at the keyboard, we still have a LOT of different ways that we can play that one figure of 5-3.

So now we reach the first stumbling block that I found when working on this subject. Without any experience or professional discretion, how do we know what to play? There are a couple of ‘rules’ we can follow to get us started.

1.       Limit yourself to 4 voices.

Yes, 4 voices. While that may sound kind of arbitrary (Why not 5? Why not 3?) and counterintuitive (Shouldn’t we start with 1 voice and work our way up to 4?), I swear that it is the best thing to do. Here’s why:

First off, think of the chords that we are going to be playing. Triads have three unique notes per chord. Seventh chords have 4. We need to play with at least three or four voices just so that we can play complete chords without leaving anything out.

Secondly, when you play with only three voices, you will find it a little more difficult than with 4 voices because all three notes will be busy trying to form complete chords. Unless you have a great amount of skill, you will have much less freedom in your voices. (That’s part of why Bach’s trio sonatas are so miraculous, because he could create such freedom in the voices despite there being so few to create a full texture.)

When you use 4 voices, if you play a triad then one of the notes must be doubled. Choosing which note is doubled actually gives you a lot more wiggle room to make good and musical progressions.

Lastly, 4 voices fit pretty well under the hands, unlike 5 voices. One hand can accommodate 2 voices without much difficulty (with practice, of course!), but three voices in a hand leads to great difficulties in keeping all the lines separate and smooth. 4 really is the magic number when it comes to the hands, and theory.

Now we’re playing with more limitations. Keep in mind that limitations are good in the beginning because too much freedom can lead to aimlessness and confusion. We’re using a more manageable number of notes, but where should those notes be?

2.       Play in a Close Position

Let’s be clear on this one. Our four voices have four names. From highest to lowest, they are: Soprano, Alto, Tenor, and Bass. When we talk about an open or close position, we are talking about the spacing between the top three notes, the Soprano, Alto, and Tenor. Bass is exempt. If the top three notes are in a range greater than an octave, like this example….

…then they are considered in Open Position. If they are spaced in a range smaller than an octave, basically as close as they can be squeezed together…

…then they are in Close Position. This last style is the one we will be using almost exclusively at the beginning. You see, once we start putting one chord in front of another, it will suddenly matter that we follow the rules of good voice leading and avoid parallel fifths and octaves between any voices, as well as hidden fifths and octaves for that matter. It’s a lot to think about if you are a beginner. However, if we play in close position with three voices in the right hand, and the bass note in the left hand, you will find that for the most part, voice leading will just take care of itself. It’s the magical short-cut solution we’ve been searching for!

There’s one little tid-bit I should tell you before we move further. That figure we looked at before, the 53? Well, don’t expect to see it written under any of the bass notes; they’re invisible. What I mean to say is that if you see a bass note in a figured bass line that has no figure underneath it, you can take it for granted that the actual figure is 53. It’s our default chord, so to speak. You can have a whole bass line that’s made out of these root position triads. Like this one:

Now let’s take stock of how to realize this ‘figured’ bass. Using our two limiting rules, we restrict our chords to 4 voices, counting the bass, and we play them in a close position. Just so we know what’s possible, let’s jot down all the possibilities:

(Though each of these chords could be played in another octave, there are nonetheless only three unique chords...)

So….not a lot of possibilities. That’s actually a good thing at this stage. Just three chords! Now this is where we should pay attention. We want to make these three chords our friends. Each one is wonderful and unique and we need to get to know them and find out what makes them each a beautiful snowflake and how proud we are of all of them…

How to recognize a unique disposition

First, look at the shape of the three note chord being played in the right hand. We see the first one is three notes nicely stacked on top of each other, like a snowman. Easy to identify. Look at the second one; now snowman has lost his head. And the third, um… he lost his… Well, in any case, these three shapes are very recognizable and distinct from each other. Notice how each shape has a different feel to it when you play it on the keyboard. Those of you with some theory knowledge will possibly see each as a root position, first inversion, and second inversion triad respectively, but I encourage you just to see each shape as it is.

Now, this recognition of shapes doesn’t really do us any good without another piece of information: how far away from the bass is it? More specifically, which interval from the bass is represented by the soprano voice?  Well, in the snowman’s case, the top of the complete snowman is a G, which is a fifth from the bass note C (It doesn’t matter that it’s several octaves away. A fifth is still a fifth.). Now, knowing this, we can make a shortcut.

Here’s the way we realized a figured bass note in the beginning:

1.       What’s the bass note?  C

2.       What note is a third above C?   E

3.       What note is a fifth above C?  G

4.       Since I’m in four voices, I’ll have to double a note, so let’s throw in another C.

5.       Spell out C, E, and G on the keyboard and play them all together.

We were basically figuring it out from scratch every time we saw a new bass note. Here’s the new way.

1.       What’s the bass note? C, and I know a chord shaped like a snowman that goes a 5^th above C

2.       Put a snowman shaped chord with it’s head a fifth above C and play them all together.

Suddenly, we’re not building the wheel every time; we’re using our already discovered knowledge of relationships to cut straight to the answer. It’s totally cheating! In the same way that memorizing your multiplication tables before a math exam is cheating.

Moving on, we see that the snowman-sans-head is placed with his missing head an octave (or multiple octaves) above the bass. And finally, the third is placed with the top a 3^rd above the bass.

So suddenly we’ve reduced the multitude down to three simple chord shapes and an interval for each to make sure it’s placed correctly. For convenience, we will call this chord-shape-plus-interval amalgamation a  disposition.  Now we can use this knowledge to realize that bass line. Start by just picking one of our three dispositions, whichever one is your favorite, and plugging it onto the first bass note. I’ll go with this one:

Now, where do we go? Well, we know that we have three basic possibilities:

A simple rule will guide you well: leave a note unchanged whenever possible. By this we also mean to say that it is usually best to move to the chord that is the closest to the one you just played. There are reasons to jump around, but not at this early stage. We find that the closest choice we have is this one:

 

Now we’re cookin’ with gas! And we use the same simple rules to get us all the way through the bass line. Just one more simple rule for the ending: end with the soprano either one the octave, or the third above the bass, but not the fifth. In the interest of building sensitivity, let’s be sensitive to this old bias that a cadence should not be ended on the fifth.

 

You can see now that there’s no one right answer. A given bass line can be realized in multiple ways, some better than others. Sometimes there is a realization that is clearly the best, and sometimes you just have to let your sensitivity guide you. Try realizing a given bass line in as many different ways as you can. This would be agonizingly tedious on paper, but at the keyboard it’s quick and easy.

So we’ve gone this far and can now realize a simple bass line with the simplest of figures. We now know the basic process of realizing a figured bass but where do we go from here?

Building a Vocabulary

Well, when I said we just had three dispositions for our basic invisible figure? I might have been lying just a little bit. You see, each of those three dispositions have something in common with the others, they are all doubling the bass. If C is the bass, then you can bet there is another C in the chord in each of those dispositions. We don’t have to double the bass; we could double the third instead. There are two shapes that appear if we do this and keep it within the span of one hand:

The first has two of the exact same note, which is totally acceptable in chorale or instrumental writing but a bit silly on the keyboard. Instead of four voices, we effectively have only three. For that reason, the other chord shape is the better one for the keyboard. We see that it’s a an octave wide and the soprano lies a third above the bass. Great! A new shape with a placement interval. What’s the point?

This particular shape is a good one because it can get you out of a little problem you might run into. Say you have this bass line and have played these chords:

 

What comes next? Well, you should always be wary when the bass moves up or down by step because that’s a great way to run into some parallel fifths or octaves. The easiest solution is to move the right hand in the opposite direction of the bass line. If the bass steps up, the right hand disposition moves to one that is down from where it was. It’s really very easy if you just look one chord ahead while you’re playing. However, we have a problem here because the top note of the right hand happens to be the leading tone and it really really wants to move up to that C. If you follow that impulse and move your chord shape up, then you will get parallel 5ths and parallel octaves. Your theory teacher will stop putting ice in their drinks. If you go the other direction, you get a frustrated leading tone in the soprano which is deeply unsettling for our musician nerves. So…

We try a different chord shape and it saves us! Hooray, it has a practical use!

So we have three different dispositions where the root is doubled and they’re good for normal busy-work, we have one where the third is doubled which gets us out of some hairy deceptive cadences, do we have any with a doubled fifth?

There’s a couple, and it’s the last one that’s keyboard friendly again. I’m sure we can find a use for it.

And that there is the point of what we should be doing. We should be building a vocabulary of dispositions for a given figure and finding out how they can be used to good effect. We must begin by becoming acquainted with the 7 fundamental figures : the Triad and its 2 inversions, and the Seventh Chord with its three inversions. (Those figures are 53, 63, 64, 753, 653, 643, and 642. They are abbreviated as: (blank), 6, 64, 7, 65, 43, and 42 respectively.)  For our explorations of these figures, we should be armed with this plan of attack:

1.       Hey, a new figure! What intervals and notes are implied by the figure?

2.       If I squeeze the soprano, alto, and tenor together, what different chord shapes can I make that fit within one hand. (For triads, some note will have to be doubled so start with doubling the bass.)

3.       I see new shapes and old shapes. What intervals link the top of them to the bass?

4.       Now what shapes can I find if I double the other notes, instead of the bass?

5.       Now that I know all the different ways I can play this figure, which ones are useful for normal situations? How about special situations?

Hopefully after enough study and experimentation we will know how to handle that particular figure whenever it pops up. In this manner, we are building a vocabulary of chords. Our hands will eventually build a muscle memory of the sensation of the proper chord to fit over a figured bass note. As time goes by, more exotic figures can be found and assimilated in the same manner. Eventually it would be well to examine the usefulness of open position dispositions.

To practice these new-found dispositions, one should put them in some sort of context. Play cadences and sequences that incorporate these chords in every key and you will quickly learn the physical sensation and build the mental associations necessary. For cadences and sequences, I would say that you can write your own, but it would probably help to find a book on figured bass that has that sort of thing already written out. I like Figured Harmony at the Keyboard: Part 1 by R.O Morris. He treats each figure with its own chapter and at the beginning presents varied cadences and sequences using the figure, before moving on to exercises resembling proper bass lines. He also writes in a preferred soprano line so all you have to do is fill in the inner voices. This affords one good practice at knowing just what disposition to use, since often only one or two will fit. If you have this book or one like it then I have a suggested plan of attack.

In Going Forward…

… it is my belief that one should as quickly as possible, write down all of the practical dispositions available to all of the fundamental figures. Use this list to aid you in working out the cadences and sequences that involve them. Once you can play the cadences and sequences without difficulty, exercises can be worked involving the figures already learned.

One goal is to take each of those cadences and sequences and write them out in all playable dispositions (e.g. Beginning with the soprano a third above the bass, or a fifth above, or an octave above) and then practice each one in all 24 major and minor keys. This is great exercise for the mind and body. Practicing one of these every day means that it will take a lot of time, over a month for just the root position chords.

A further suggestion is not to wait for that to be completed before moving on to the next section! If you work at that snail’s pace, you will master cadences and sequences but will be getting no experience in that other important sphere of study: Realizing Figured Basses! Therefore, I suggest doing both concurrently. Make your slow but steady progress up Parnassus mountain by practicing all dispositions of cadences and sequences in all keys as it will aid you in the studies of harmonization, improvisation, and composition; continue at the same time with practicing playing from figured basses as soon as you can play the cadences and sequences involving a particular figure with some proficiency. Don’t wait for your slow practice to catch up; keep each study separate and unaffected by the other.

As you go through each figure, you will discover (from the book hopefully) that there are certain preferences for doublings and usage that will reveal many of the rules of harmony as you go. Be open to the reason and method behind the music and I feel confident you will find a deeper connection to the music you hear and the music you create.

Happy studies!