Figured Bass

In a lot of old music, especially from the 1600s and 1700s, the composer wrote out the melody but gave the keyboard player only the bass line, with little numbers under the notes. Those numbers are a code telling the keyboard player which other notes to stack on top of each bass note. The system is called figured bass.

The idea is a shortcut. Rather than writing every note of every chord, the composer trusted the player to read the bass and the numbers and fill in the rest. A number like 6 under a bass note says "add notes at these distances above me," and the player builds the chord from there.

Imagine a bass note with a small 6 beneath it. That 6 is an instruction: play a note a sixth above this bass note as part of the chord.

Figured bass began as a performing musician's tool. In a baroque ensemble the continuo player, at a keyboard or lute, accompanied by reading the bass line and filling in the harmony on the spot, and the figures gave the minimum information needed to do that while playing. The notation is a set of instructions for real-time realization.

Measuring everything from the bass reflects what the player saw under the hands. The bass note was given, and the figures said how far above it to reach, so the harmony was specified as a stack of intervals over that bass. This bass-first reading is older than the root-based chord theory that Jean-Philippe Rameau set out in 1722.

For plain three-note chords, figured bass uses just three patterns. A root-position chord, with the root in the bass, usually gets no numbers at all: the player sees a bare bass note and knows to build an ordinary chord on it. So most of the time, no figure means a simple root-position triad.

When the chord is inverted, a number appears. A 6 under the bass means a first-inversion chord, with the third in the bass. A 6 and a 4 together mean a second-inversion chord, with the fifth in the bass. So blank means root position, 6 means first inversion, and 6/4 means second inversion.

Match each to its inversion: no number is root position, 6 is first inversion, 6/4 is second inversion.

The triad figures are the origin of the inversion labels used throughout harmony. Players named 6 and 6/4 straight from the intervals they saw above the bass, and later theory carried those same figures into analysis as the marks for first and second inversion.

Leaving root position blank shows what the notation treats as normal. The unmarked case is the plain chord over its root, so figures appear only where the harmony departs from it. Among the triad figures, a bare bass note means root position, and a 6 or a 6/4 means an inversion.

Four-note seventh chords need their own figures, and there are four of them, one for each position. A plain 7 under the bass means a seventh chord in root position. The three inversions get their own number groups: 6/5, then 4/3, then 4/2.

You do not need to memorize why each set of numbers is what it is yet. The useful thing to recognize is that a 7 on its own means a seventh chord, and that 6/5, 4/3, and 4/2, each written with one number on top of the other, are its inversions, in order. Spotting a 7 or one of those pairs tells you a four-note chord is in play.

Line up the four figures for a seventh chord in order: 7 for root position, then 6/5, 4/3, and 4/2 for the three inversions.

Each seventh-chord figure keeps only the numbers that tell it apart from the others. A full root-position seventh chord is 7/5/3, but the fifth and third are assumed, so 7 stands for it; 6/5, 4/3, and 4/2 each carry the intervals unique to first, second, and third inversion in turn. A player reads the distinguishing figure and fills in the understood tones from the key.

Context removes the ambiguity when the same interval turns up in more than one figure. Read against the bass note and the key, a figure like 4/3 points to one chord in one position, and the player supplies the rest of its notes.

Sometimes a note in the chord needs to be sharp or flat, and figured bass shows this with accidental signs mixed in with the numbers. A sharp or flat written next to a number raises or lowers that particular note. So a sharp beside a 6 means the note a sixth above the bass should be sharp.

Here is one shortcut: an accidental sitting alone, with no number next to it, always refers to the third above the bass. Since the third above the bass is often the note that makes a chord major or minor, composers needed a quick way to adjust it, and a lone sharp or flat does exactly that.

Picture a bass note with a lone sharp under it. That sharp raises the third above the bass, brightening the chord toward major.

The accidental conventions concentrate on the third because of what the third does. The third above the bass usually carries the chord's quality, and in dominant harmony it is the leading tone that drives a cadence, so it is often the note that needs altering. Giving it the lone-accidental slot means that change needs no number at all.

A slash through a figure, or a plus beside it, raises that note a half step without a written sharp or flat. A continuo player could catch a stroked figure at a glance and sharpen the tone, which mattered when the leading tone had to be raised again and again in minor keys.

Turning a figured bass into actual music is called realizing it. The player reads each bass note and its figures, works out which notes go above, and plays full chords, choosing how to space and arrange them. Two players realizing the same figured bass might voice the chords a little differently while playing the same harmony.

This was how a huge amount of baroque music was performed. A cello or bassoon played the bass line, and a harpsichord or organ player read the same line with its figures and filled in the chords live, choosing exactly how to play them. The figured bass gave the harmony; the player brought it to life in the moment.

Take a bass note with the figure 6 and realize it in your head: a chord with a sixth and a third above that bass note, a first-inversion triad.

In realization the figures fix the chords, and the player chooses the voicing. A baroque continuo part is a set of harmonic instructions completed anew in each performance, so the written page and the sounding music were different by design.

The practice faded as composers wrote out inner voices and left performers less to supply. What survives is the interval-from-the-bass thinking: it became the standard way to describe inversions, so a small 6 beside a numeral today is a baroque keyboard player's shorthand. Those inversion figures are the part of the system that analysis uses every day, and continuo players still read full figured basses.