Grade Six Music Theory - Harmony Lesson 8: Introduction to 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!
Most theory students find that having a teacher to help with figured bass is essential. MyMusicTheory also offers a teacher-led harmony course which covers figured bass and harmonising a melody in a step-by-step way, with plenty of guided practice exercises. Please click here for more information about our tutored harmony course.
So, let's find out what figured bass is all about.
This is what it looks like - the figured bass is the little numbers and accidentals 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 anything fancy (except perhaps a passing note or two!)
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.
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 given 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”, pronounced "five-three" and so on.
Talking about Chords, Triads and Inversions
Many students get confused about what is the "root", "bass", "third", "three" and so on in chords and triads. It is essential to have a clear understanding of how the parts of chords and triads are named, before continuing!
Triads: Triads are chords in their simplest, closest pattern. Triads contain three different notes, and each is a third apart.
The C major triad contains the notes C-E-G, in that order, for example.
In any triad, the first note is the root. The next note is the third (because it's a third higher than the root), and the last note is the fifth (a fifth higher than the root). All triads contain a root, third and fifth.
Chords: We are studying 4-part harmony, so all our chords will have four notes in them. The four notes are referred to by voice. Starting from the bottom, the four voices are bass, tenor, alto and soprano.
Each voice can theoretically sing any note from the triad. Therefore, the bass voice can sing the third of the triad, or the alto voice can sing the root of the triad, and so on. Chords are very flexible!
Chords usually contain the three triad notes plus one of them doubled, for example C-E-G-C (doubled root), G-E-C-G (doubled fifth) or E-C-G-E (doubled third).
Chords can also sometimes contain other combinations of notes from the triad, for example C-C-E-C (root tripled, fifth omitted).
Inversions: The inversion of a chord is decided by the bass note only.
- Bass note=root of triad> the chord is in root position.
- Bass note=third of triad> the chord is in first inversion.
- Bass note=fifth of triad> the chords is in second inversion.
5-3 means root position chord.
Look at the bass note (B). Add a note which is a fifth higher (F#) and another which is a third higher (D). This makes a root position chord: B-D-F#.
The F# and D can occur in any octave, and because this is four-part harmony, one of the notes will need to be repeated.
In this example chord, the B (root) is repeated in the tenor part, and the F# and D are on the treble stave, built as compound intervals (more than an octave) from the bass note.
The bass = the root of the triad
The tenor = the root of the triad (doubled bass note)
The alto = the fifth of the triad AND the five of the figure
The soprano = the third of the triad AND the three of the figure
Here is another example of the same figure interpreted in a different way. This time the root B is doubled in the soprano part, and the F# and D occur in the middle parts, the alto and tenor.
Because root position chords are so common, the "5-3" figuring is usually 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 is a bass note C. We need to add a note a sixth higher (A) and another a third higher than the bass (E). This gives us the chord notes C-A-E, with C in the bass. It is an A minor chord in first inversion, with a doubled root.
Bass = third of triad (A-C-E)
Tenor = root of triad (A-C-E), or six of the figure (a 6th above the bass)
Alto = fifth of triad (A-C-E), three of the figure (a third above the bass)
Soprano = root of triad or six of the figure
Here is a different interpretation of the same figured bass. This time the third of the triad has been doubled (A-C-E)
Because 6-3 chords are also very common, they are usually just written as a lone 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.
Bass = fifth of triad (F-A-C)
Tenor = third of triad (F-A-C) or six of the figure (a 6th above the bass)
Alto = root of triad (F-A-C) or four of the figure (a 4th above the bass)
Soprano = fifth of triad (doubled bass note)
Here is another interpretation of the same figured bass note.
6-4 chords are always figured in full - they are not missed out or abbreviated like the 5-3 and 6-3 figures.
Figured bass sometimes includes sharps, flats or naturals. The accidental is written next to the figure which it affects.
If the accidental is not next to a figure, but just appears on its own, then it always refers to the 3rd of the chord.
= sharpen the 3rd. The chord notes will be F# (key sig), A# (accidental) and C# (key sig).
= 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!".