Grade Six Music Theory - Harmony Lesson 8: Figured Bass
What is Figured Bass?
Figured bass might look a bit mysterious if you've never seen it before. Even if you have heard of it, you might think it's rather strange. Let's find out what figured bass is all about.
This is what it looks like - the figured bass is the little numbers written underneath the lower stave:
Figured bass is a shorthand method of composing. It was invented during the Baroque period (about 1600-1750). In those days, composers only wrote out a melody and a bass line (and not any of the middle parts). The melody was played (or sung) by a soloist, and the bass line was usually played on a keyboard instrument, such as the harpsichord or organ.
Obviously, the keyboard player needed to do a bit more than just play the bass line with his or her left hand, but where was the rest of the music? Well, he or she had to improvise! The composer added small numbers underneath the bass line, like a kind of code, which told the player which chords to play. However, this code (which is the "figured bass") didn't tell the player exactly how to play the chords - for example, they could choose to play them as solid chords, broken chords or could weave them into heavily decorated individual voice lines.
In fact, keyboard players in those days were judged on their ability to create amazing improvisations from a figured bass - and of course, the same piece of music would be played in totally different ways by different musicians. Don't worry though - in grade six theory you only need to write out the chords in their most basic forms - you don't need to add melodic decoration or anything fancy!
In the modern world, you can find a similar kind of thing in sheet music for pop songs. Have you ever seen a tune written out with chord markings for piano or guitar? The accompanist uses the suggested chords, but plays them in whatever way they feel like. Figured bass is just the same, except that there are a few rules you have to obey - the rules of harmony.
Figured bass is hardly ever used today except in music theory exams, or in early music groups. So why is it tested? Well, it's been part of the study of music theory for hundreds of years and it's an excellent way to test your knowledge of harmony. Although no one composes using figured bass any more, it's still a useful way of referring to chords and chord progressions quickly. Figured bass is a compulsory part of Grade Six Theory, and actually it's quite simple to get the hang of, you'll be pleased to know! So let's get started!
Understanding Figured Bass
Figured bass is written underneath the bass line. (Sometimes a bass line with figures is called a "continuo".) The numbers in figured bass tell you what chord to build up from the bass note, and in which inversion.
The single most important thing to remember about figured bass is that the bass line shows you the lowest note, and that you must build a chord upwards from that note. Never, ever write a chord note which is lower than the bass note.
Each number tells you the interval above the bass note which you need to write, in order to create a chord. We will write all our chords as 4-note chords, creating 4 independent voices – soprano, alto, tenor and bass.
(Note, although figured bass is really all about playing and improvising, rather than writing, we will talk about writing here because we are training you for an exam, after all!)
In Grade 6, there are three figures which you need to know; we call them “5-3”, “6-3” and “6-4”.
5-3 means root position. From the bass note, write the note a third higher, and then the note a fifth higher.
Remember that the exact position of the notes of the chord are up to the performer. Only the bass note is fixed. But, it doesn't matter at all what order we write the notes of the chord, or in which octave. For example, we could write either of these two chords:
We have written a four-note chord, so one of the notes is doubled. In both these examples, we have doubled the B (there are two Bs in each chord). B is the root of the chord, (the “root” is the lowest note of the triad). In a 5-3 chord, the root is the most common note to double, but you are also allowed to double the 5th. It’s better not to double the 3rd in most cases. (See Rule 3a – Doubling for more details about this.)
Because root position chords are so very common, sometimes the 5-3 figure is left out. If you see a bass note without any numbers at all, it means it's a 5-3 or root position chord. (It does not mean that you can write any chord you want!)
A 6-3 chord is a first inversion chord. The notes we need to write are a third and a sixth above the bass note.
Here the bass note is C. The figured bass tells us to add the notes E (a third above C) and A (a sixth above C). Our chord notes are C-E-A, which is A minor in the first inversion.
Some examples of 6-3 chords:
In a 6-3 chord, you are allowed to double any of the chord notes to make a 4-note chord.
We can talk about the chord notes as if they are triads, (e.g. A-C-E), or as they are written on the stave (C-E-A). A triad has a root, 3rd and 5th. The notes on the stave are the bass note, the 6 and the 3. In the first example, the “root” or “6” (A) is doubled). In the second example, the “3rd” or “bass note” (C) is doubled. You could also double the “5th” or “3” (E).
Because 6-3 chords are also very common, sometimes they are just written as 6 instead of 6-3. The figure 6 means first inversion.
A 6-4 chord is a second inversion chord. The notes we need to write are a fourth and a sixth higher than the bass note.
Here the bass note is C. The figured bass tells us to add F (a fourth above C) and A (a sixth above C). The chord notes are C-F-A, which is F major in second inversion.
In a 6-4 chord you should always double the bass note (5th) of the chord. The rules of doubling are very important and need to be learned. More information can be found in Rule 3a – Doubling.
You can add sharps and flats to figured bass. The accidental is written next to the number which it affects.
If the accidental is not next to a number, but just appears on its own, then it refers to the 3rd of the chord.
= sharpen the 3rd. The chord notes will be F#, A# and C#.
= sharpen the 6th. The chord notes will be C#, F# and A#.
Chromatic alteration is very common in minor keys, where the dominant chord has a sharpened third which does not appear in the key signature. For example in A minor, the dominant chord is E major, with a G sharp accidental.
Horizontal lines in figured bass mean that the same harmony applies to two or more notes. It means "don't change the chord!".
First Realization of Figured Bass
Here’s one bar of figured bass which uses everything we’ve learned so far. We’ll go through it step by step. Each note is numbered (1-5), so you can easily see what we’re talking about. Look at each note and try to work out which three other chord notes you would need to write down. (Don’t worry about their exact positions on the stave for now!) Then check your answers below.
1. No numbers = 5-3, root position chord. B - D - F#.
2. No numbers = 5-3, root position chord with a sharpened third.. F# - A# - C#.
3. Line = hold the previous chord.
4. 6 = 6-3, first inversion chord. D - B - F#.
5. 6-4 = second inversion chord. F# - B - D.
The Cadential 6-4
When we use the chords Ic-Va-Ia, and notate them in figured bass, they are written as 6-4, 5-3, 5-3. This is also known as the "6-4 - 5-3 progression" or cadential 6-4. This is one of the very few chord progressions where you are allowed to use a second inversion chord.
Cadential 6-4s work really well at the end of a piece, because there is a very strong emphasis on the dominant note in the bass for two chords (Ic and Va) instead of just one (e.g. V7). When the final Ia chord is finally reached, our ears and brains feel very satisfied, because we've had to wait just a tiny bit longer to hear the tonic.
Let's add a bar to the previous example, to finish off with a cadential 6-4:
Notice how the chord notes move: in the 6-4 chord, the B falls to A# in the 5-3 chord (tenor line). The D in the 6-4 chord moves to C# in the 5-3 chord (soprano line). In a cadential 6-4, the 6 ALWAYS moves to 5, and the 4 ALWAYS moves to 3.
You can easily spot a cadential 6-4, because the bass note is the same for both chords (F# in this case), and the second chord is always notated "5-3" instead of being left blank.
The Passing 6-4
If you see a 6-4 chord notated, but the bass note of the following chord is different, it will be a passing 6-4. The bass will move by step.
The rules for voice-leading in a passing 6-4 just follow the normal rules of harmony. There are many variants.
You can spot a passing 6-4 because the chord following the 6-4 will not be notated "5-3", but will be left blank if it's a root position chord. (It could also be a first inversion chord, notated in the normal way with "6").
Here's an example of a passing 6-4 notated in figured bass: