Figured Bass: Reading Intervals Above the Bass Line
Figures name intervals above the bass, not chords. What each shorthand means, how accidentals override the key, and what the player decides.
A figured bass is a bass line with numerals underneath it, and the numerals are not chord symbols. Each one names an interval above the note it sits under, counted from that note. The player supplies the rest. Understanding what is written and what is deliberately left unwritten is most of the skill.
The figures are intervals, not chords
A 6 under a bass note means that a sixth above that note sounds in the chord. Put the figure under E in C major and the sixth above E is C, so the chord is E, G, C — C major in first inversion. Put a 6/4 under G in the same key and the intervals above the bass are E and C, so the chord is G, C, E — the same C major triad, this time in second inversion. The figure follows the interval above the bass, and the bass note decides which inversion the ear hears.
That relativity is the point of the notation. A chord symbol names an entire simultaneity, including its root and its quality. A figure names one or two intervals above a given note, and leaves the quality, the root and the doubling to be inferred from the key and the idiom. What the notation records with great precision is inversion, which is exactly the information a chord symbol struggles to express.
Both figures describe the same triad in different inversions. A bare 6 marks C major over E, its first inversion; a 6/4 marks the same chord over G, its second inversion. The note named by the 6 is C in the first case and E in the second, because the numeral always counts upwards from whatever the bass is doing.
The standard shorthand
The default is a root-position triad, intervals of a fifth and a third above the bass, and it is left unfigured. Figures appear only where the intervals differ from that default, which is why a continuo part has long stretches of empty space under the staff.
| Figure | Intervals above the bass | Chord | Example in C major |
|---|---|---|---|
| 5/3, often unfigured | fifth, third | root-position triad | C: C–E–G |
| 6 or 6/3 | sixth, third | first-inversion triad | C/E: E–G–C |
| 6/4 | sixth, fourth | second-inversion triad | C/G: G–C–E |
| 7 | seventh, fifth, third | root-position seventh chord | G7: G–B–D–F |
| 6/5 | sixth, fifth, third | first-inversion seventh chord | G7/B: B–D–F–G |
| 4/3 | fourth, third, sixth implied | second-inversion seventh chord | G7/D: D–F–G–B |
| 4/2 or 2 | fourth, second, sixth implied | third-inversion seventh chord | G7/F: F–G–B–D |
The abbreviations are conventions rather than abbreviations of arithmetic. A bare 6 means 6/3 with the third taken for granted. A bare 2 means 4/2. A bare 4 in certain cadential contexts is understood as 6/4. The player who reads numerals literally, as instructions to place a second above the bass and nothing else, will produce four-note chords where two were intended and thin chords where a full triad was wanted.
Accidentals in the figures
A sharp, flat or natural attached to a numeral alters that interval above the bass, and it does so regardless of the key signature. The figure 6 with a sharp under a bass note in C major raises the sixth above that note, which is how a continuo part asks for a chromatic note the key does not contain. An accidental with no numeral applies to the third, so a lone sharp alone means a raised third.
Two subtleties follow. The first is that the figures override the key signature rather than adding to it, so a natural sign can be as informative as a sharp: it cancels an accidental that the key signature would otherwise supply. The second is that a slash through a sharp or flat raises that note by a further semitone, which is how the notation writes a raised leading tone in minor, a chromatic passing tone, or any other inflection that the key signature does not already supply.
What the figures never state is register. A 6 above the bass can be placed in any octave, and a realisation in which every sixth sits immediately above the bass will sound cramped in a way the notation did not ask for.
What the notation leaves to the player
Everything about the upper voices that is not an interval is a decision. Spacing, doubling, which voice moves where, whether the chord is played in three parts or four, whether the keyboard doubles the bass at the octave, and how long each chord is held: none of that is written, and all of it is heard.
This is why a realisation is a small act of composition rather than an act of decoding. The figures give the harmonic skeleton, and the player builds the texture. A continuo part played by one hand in the middle of the keyboard and one in the bass produces a very different result from four independent voices, and both are correct readings of the same figures.
Three conventions narrow the field. A bass player and a keyboard player divide the labour: the melodic instrument states the line as written, and the keyboard fills in above it, usually keeping the right hand below the melody so that the texture does not double. The marking tasto solo instructs the keyboard player to lay out for a passage and leave the bass line unaccompanied, which is used where the texture needs thinning or where the harmony is deliberately bare. And where upper parts exist, the keyboard avoids doubling the notated melody, since two instruments on the same line at the same octave is a colour, not a texture.
Reading a line in practice
Take a short progression in C major: bass A, then F, then G, then C, with the figures 5/3, 6, 7 and 5/3.
| Bass | Figure | Intervals above | Chord | Function |
|---|---|---|---|---|
| A | unfigured, 5/3 | C, E | A minor | vi |
| F | 6 | A, D | D minor in first inversion | ii6 |
| G | 7 | B, D, F | G dominant seventh | V7 |
| C | unfigured, 5/3 | E, G | C major | I |
The line descends by step from A to F to G, and the harmony is a tonic expansion followed by a cadence. Nothing in the figures is unusual: the bare 6 marks the first inversion, the 7 marks the seventh chord, and the two unfigured notes are the plain triads at the ends. A player would add a third above the bass in the first chord, place the sixth above the F in the second, resolve the F of the seventh chord down to the E of the final triad, and lead the leading tone B up to C. All of that is idiomatic knowledge, and none of it is in the figures.
Why the notation is still taught
Figured bass survived as a working notation for something like two centuries after it appeared with the basso continuo in the early seventeenth century, and it is still taught for reasons that have little to do with performing old music.
It records inversion and function in the same symbol, which no chord symbol does as clearly. It forces the student to think in intervals above a given note rather than in memorised shapes on an instrument. And it makes voice leading unavoidable, because the player has to decide what the inner voices do while the bass moves, which is exactly the decision that part-writing exercises formalise and that performance demands in real time.
The voice-leading article covers the constraints a realisation has to satisfy. Those constraints are what turned a notation for accompanists into a training method, and they are why a continuo exercise is still one of the fastest ways to find out whether the harmony in a passage has been understood or merely labelled.
The virtual piano is a practical place to work through a realisation at the keyboard: play the bass line with the left hand as written, and add the intervals above it with the right.
