Figured bass

Figured bass is a kind of musical notation used to indicate chords in relation to a bass note. Which octave each note of the chords are played in, and what, if any, embellishments are to be added, is left to be improvised by the performer, but the indicated chords must be played.

Figured bass is most often found in basso continuo parts in Baroque music, where the harpsichordist, lutenist or whoever is playing the chords in the continuo part, will employ it. It is also sometimes used by classical musicians as a shorthand way of indicating chords (though it is not used in modern musical compositions).

Although the exact figurations played above the indicated bass-line were originally improvised by the performer, in most modern editions of music with figured bass parts a fully written-out version of the figured bass is provided, eliminating the need for improvisation.

A part notated with figured bass consists of a bass-line notated in the normal western manner (with notes on a musical staff) plus added numbers and accidentals beneath the staff to indicate at what intervals above the bass notes should be played, and therefore which inversions of which chords are to be played.

The numbers indicate the number of notes above the given bass-line that a note should be played. For example:

Here, the bass note is a C, and the numbers 4 and 6 indicate that notes a fourth and a sixth above it should be played, that is an F and an A. In other words, the second inversion of an F major chord is to be played.

In cases where the numbers 3 or 5 would normally be indicated, these are usually (though not always) left out, owing to the frequency these intervals occur. For example:

In this sequence, the first note has no numbers accompanying it - both the 3 and the 5 have been omitted. This means that notes a third above and a fifth above should be played - in other words, a root position chord. The next note has a 6, indicating a note a sixth above it should be played; the 3 has been omitted - in other words, this chord is a first inversion. The note has only a 7 accompanying it; here, as in the first note, both the 3 and the 5 have been omitted - the seven indicates the chord is a seventh chord. The whole sequence is equivalent to:

except, as already stated, the performer may choose himself which octave to play the notes in and will normally elaborate them in some way rather than play straight chords.

Sometimes, other numbers are omitted: a 4 on its own indicates 64; a 2 on its own or 42 indicate 642; and a 9 on its own or 97 indicate 9753.

Sometimes the figured bass changes but the bass note itself does not. In these cases the new figures are written wherever in the bar they are meant to occur. In the following example, the top line is supposed to be a melody instrument and is given merely to indicate the rhythm (it is not part of the figured bass itself):

When the bass note changes but the notes in the chord above it are to be held, a line is drawn next to the figure or figures to indicate this:

The line extends for as long as the chord is to be held.

Accidentals

When an accidental is shown on its own without a number, it applies to the third of the chord; otherwise it applies to whichever note it is shown next to. For example, this:

is equivalent to this:

Sometimes the accidental is placed after the number rather than before it.

Alternatively, a cross placed next to a number indicates that the pitch of that note should be raised by a semitone (so that if it is normally a flat it becomes a natural, and if it is normally a natural it becomes a sharp). A different way to indicate this is to draw a bar though the number itself. The following three notations, therefore, all indicate the same thing: