Figured bass, and the numbers that describe what sounds above the bass

In the Baroque, the harpsichordist or the lutenist did not receive the chords written out: they received the bass line, with numbers under it, and realised the harmony on the spot. Those numbers are figured bass, the first abbreviated notation for chords, and it survives in harmony lessons because it describes something the modern chart does not: the intervals above the bass.

What the numbers say

Each number is an interval counted from the bass note upwards, in scale degrees. A 6 says "play a sixth above the bass"; a 4, a fourth. The exact notes follow the key signature, and an accidental beside a number alters the corresponding note.

C/E

An E in the bass with a 6 underneath: a sixth above E is C, a third above is G, and the chord is C major in first inversion, with the notes G and C over the E.

The figures that get abbreviated

Writing out every interval would be tiring, and the tradition abbreviates by the commonest figures:

• Nothing, or 5/3 — root position: third and fifth above the bass.
• 6, or 6/3 — first inversion: third and sixth above the bass.
• 6/4 — second inversion: fourth and sixth above the bass.
• 7 — seventh chord in root position.
• 6/5 — seventh chord in first inversion.
• 4/3 — seventh chord in second inversion.
• 4/2, or 2 — seventh chord in third inversion, with the seventh in the bass.

The same chords, C major in all three positions, which the modern chart writes C, C/E and C/G, and which figured bass writes as nothing, 6 and 6/4 under the bass notes C, E and G.

Accidentals

A sharp, flat or natural on its own under the bass alters the third above it; beside a number, it alters that number's note. A stroke through a number is the abbreviation for "raised". So a G in the bass with a sharp underneath is G with a B natural… or with a B sharp, depending on the key signature; the reading is always relative to the key.

Dm7ii7SubdominantG7V7DominantCITonic

In C major, that sequence in figured bass would be D with 7, G with 7, C with nothing: the sevenths indicated, the chords deduced from the scale.

It is not analysis by degree

Here is the point that separates whoever understood. Figured bass describes intervals above the bass; Roman numeral analysis describes the function of the chord in the key. A 6 under an E says there is a sixth above it, not that the chord is the I in first inversion; to know that you need to know the key. The two notations combine, and classical analysis writes the Roman numeral with the figured-bass figure beside it: I6 for the tonic in first inversion, V6/5 for the dominant seventh in first inversion.

What it is for today

For playing the Baroque repertoire from the original, which is how it was written. For reading classical analyses, which inherited the numbers. And for an exercise that remains excellent: realising a figured bass in four voices is learning voice leading with an exact brief, because the numbers say which notes to use and the leading decides how.

What to take from here

Figured bass writes harmony as intervals over the bass, in numbers the tradition abbreviated: nothing for root position, 6 for first inversion, 6/4 for second, and 7, 6/5, 4/3 and 4/2 for seventh chords. It does not say the function; analysis by degree does, and the two together are the notation of classical harmony. The inversion numbers everybody uses were born here.