Realizing a Figured Bass

Baroque scores, roughly 1600 to 1750, preserve a curious way of writing music.

Only the bass line appears, with numbers underneath it. The three upper voices are simply not written. Harpsichordists and organists read those numbers and assembled the chords on the spot as they played. The practice is called basso continuo, and its notation is figured bass.

The idea is close to modern chord symbols, with one decisive difference: a chord symbol specifies a chord, while figured bass specifies intervals above the bass.

This lesson builds four parts from a given bass and figures. Unit 3 supplied the meaning of the symbols and this unit has supplied the voice leading, so both now come into play.

Figures are intervals above the bass

To review: the numbers give intervals counted up from the bass note. They do not name a chord quality.

Figure	Meaning	Note in the bass
(none)	root position; 5⁄3 left unwritten	root
6	first inversion	third
6⁄4	second inversion	fifth
7	seventh chord, root position	root
6⁄5	seventh chord, first inversion	third
4⁄3	seventh chord, second inversion	fifth
4⁄2	seventh chord, third inversion	seventh

A bass note with no figure at all is in root position. The convention is that nothing written means ordinary, and figured bass records only what is not ordinary.

Identifying a chord from the figures

Given a bass note and a figure, first work out the root of the chord.

• no figure → the bass is the root
• 6 → the bass is the third; the root lies a sixth above
• 6⁄4 → the bass is the fifth; the root lies a fourth above

Suppose the bass is F in C major with the figure 6. The bass is the third, so the root is a sixth above F, which is D. The chord on D in C major is Dm, making this ii6.

Check

In C major the bass is B with the figure 6. What chord is this?

I in first inversionV in first inversionvii° in root positioniii in second inversion

Check answer

The realization procedure

Once the chord is known, add the upper three voices. The procedure from the previous lesson applies unchanged.

1. the bass is given, so it cannot be moved
2. write the soprano as a melody (small leaps, inside the range)
3. fill the inner voices: hold common tones, and where there are none, move contrary to the bass

Having the bass fixed in advance leaves less freedom than writing from scratch. That constraint is precisely what makes it a good exercise.

Here is one worked through. Take the following bass and figures in C major.

Reading the figures:

• C3 (no figure) → C in root position = I
• F2 (6) → the bass is the third, so the root is D = ii6
• G2 (no figure) → G in root position = V
• C3 (no figure) → I

So the progression is I – ii6 – V – I. From here it is only a matter of distributing four voices.

Look at the soprano: E – D – D – E, barely moving at all. A realization does not call for a striking melody; the objective is to support the bass without breaking any rules.

The completed exercise

▶The realization▶With ii in root position

Check: Over a bass moving C–F–G–C, the upper three voices sit almost still. The sonority shifts only where the bass drops to F. That chord is ii6, with the third in the bass. Comparing it against root-position ii (bass on D) shows how much more smoothly the inversion connects.

I – ii6 – V – I

Figures can also call for alterations

Figures carry more than intervals; they can carry accidentals too.

• a ♯ or ♭ beside a number alters the note at that interval
• a ♯ standing alone, with no number, raises the note a third above the bass

That last form appears constantly in minor keys. The dominant in minor needs its seventh degree raised to supply a leading tone, and a lone sharp is the instruction to do it.

Which means the dominant chord in a minor key almost always carries a sharp. Miss it and you write something like Gm, with no leading tone, and the chord stops functioning as a dominant at all.

The cadential 6-4 seen through the figures

Unit 4 introduced the cadential 6-4. Here it is again from the figured-bass side.

The bass holds G across both chords while only the figures change, from 6⁄4 to 5⁄3.

What that notation reveals is that the 6⁄4 is not an independent chord. Since the bass never moves, no fundamental substitution has occurred — the upper voices have simply gone from ornament to substance over the same dominant.

Written as a Roman numeral, I64 looks like a tonic chord. Written as figured bass, its status as an ornament above G is visible in the notation itself. The same phenomenon, and different notations reveal different things about it.

Check

What does figured bass show more clearly than Roman numerals?

Whether a modulation occurredA chord's function within the keyWhether the bass movedA chord's root

Check answer

Realization gets easier as constraints increase

Figured-bass realization feels cramped at first. The bass is fixed, the chords are fixed, and rules apply. There is hardly any freedom.

But the more constraints there are, the narrower the path to a correct answer becomes. Hold common tones, move the rest contrary to the bass, and respect the destinations of the leading tone and the seventh. Apply those four in order and the options usually collapse to one or two.

It is easier than writing freely — that is the nature of realization, and it is why training in harmony begins here.

▶ Practice realization in the part-writing checker Choosing a degree and an inversion fixes the bass. Place the upper three voices yourself and look for an arrangement that produces zero warnings. That search is the exercise SATB Part-Writing Checker → ▶ Review the figures in the inversion trainer The real bottleneck in realization is whether the inversion comes to mind the instant you see a figure. Run the 'name the figure' mode until the answer is reflexive Inversion & Figured Bass Trainer →

That completes Unit 5. You can now distribute a chord correctly across four voices, connect chords without breaking the rules, and build a texture from a given bass.

The next unit deals with notes that do not belong to the chord. Everything so far has kept all four voices on chord tones; real music colors its melodies with notes that belong to no chord at all. Classifying those is the subject of non-chord tones.