Chord Inversions Figured Bass

How to Write Figured Bass for Chord Inversions Without Losing Your Mind

The first time I tried to convert a Roman numeral analysis into figured bass, I spent forty-five minutes on a single phrase because I couldn't remember whether a sixth meant root position or first inversion. The system is simple once it clicks, but the click doesn't come from memorizing tables. It comes from seeing what the numbers are actually describing. Figured bass works by writing small numbers below a bass note to indicate which intervals above that bass form the complete chord. The bass player or continuo instrument reads these numbers and reconstructs the harmony. A root position triad with no numbers means 5 and 3 are implied but omitted. First inversion puts a 6 above the bass, giving you 6 and 3. Second inversion adds a 4, so you see 6 over 4, meaning 6, 4, and 3 above the bass line.

Chord Inversions Figured Bass

Here is the actual mapping that matters in practice. For triads: root position is blank or 5/3, first inversion is 6/3 or just 6, second inversion is 6/4. For seventh chords: root position is 7, first inversion is 6/5, second inversion is 4/5 or 6/4 over 5 depending on notation convention, third inversion is 4/2 or just 4. The compact notation drops the 3s because they are always present in close position triads. A standalone 6 means 6 plus the implicit 3. A standalone 4 with a 6 means both intervals exist above the bass. I ran into a real problem last year while realizing a Baroque keyboard piece where the figured bass notation used a slash figure — a 6 with a flat sign through it, written as a modified numeral. This indicated the sixth above the bass should be lowered, changing a first inversion major chord into something with a flat sixth. Standard figured bass has no clean way to notate accidental alterations to individual chord tones without cluttering the figure. My workaround was to write the accidental as a small sharp or flat next to the number rather than through it. So a first inversion C major chord with an A-flat in the upper voice became a 6 with a tiny flat beside it instead of the more common but ambiguous 6 over flat. It took me three attempts on different systems before I settled on this because music engraving software kept reinterpreting my markup. The counter-intuitive thing about figured bass is that the numbers describe intervals above the bass, not chord degrees. Beginners constantly confuse this. When you see a 6 in first inversion, it is not the sixth scale degree. It is the interval of a sixth above whatever note sits in the bass. That distinction collapses your entire understanding if you treat the numbers as scale degree labels instead of interval measurements.

Another thing nobody tells you about Chord Inversions Figured Bass is that the same chord can appear with different figures depending on context and voice leading. A 6/4 chord in second inversion might resolve to a 6/5 first inversion seventh chord, and the bass moves by step. Or it might stay static while the upper voices shift. The figures alone cannot tell you the resolution. You need to understand the harmonic function and the typical cadential patterns. A II6/4 moving to V6/5 in first inversion is a common cadential six-four substitution. But writing just 6/4 under a dominant bass note without context could mean any number of things depending on the key and surrounding harmony. Let me walk through a concrete example in C major. Take a G7 chord — G, B, D, F. Root position with G in the bass: the numbers are 7, meaning a seventh, fifth, and third above G. That gives you F, D, and B. First inversion with B in the bass: the figure is 6/5, giving you G (a sixth above B), F (a fifth above B), and D (a third above B, implicit). Second inversion with D in the bass: the figure is 4/2 or just 4 in some conventions, giving you G (a fourth above D), F (a second above D), and B (a third above D, implicit). Third inversion with F in the bass: the figure is 4, giving you G (a fourth above F), D (a second above F), and B (a third above F, implicit). Now here is where it gets tricky and where most students stall out. The 4 in third inversion seventh chords is ambiguous. It could mean 4 over 2 (a fourth and a second above the bass, with the third implicit) or just 4 standing alone. Different textbooks use different conventions. I stopped arguing about which is correct and just learned to read the surrounding numbers. If you see 4 alone after a series of 6/5 figures, it is almost certainly third inversion. If you see 4 over 2 written explicitly, the writer is being precise. The ambiguity is a known weakness of the system.

There is a practical bottleneck you should know about. Figured bass notation does not scale well to extended chords or jazz harmony. A 13th chord with alterations in first inversion would require figures like 6/5 over 4 over 2 with accidentals, and the notation becomes illegible within seconds. I have seen performers give up entirely and switch to lead sheet notation when the material goes past seventh chords. The system works beautifully for common-practice period harmony. It breaks down completely for post-tonal music. If your repertoire includes Debussy, Ravel, or anything with added sixths and ninths, you will need supplemental notation. My recommendation for actually learning this is to stop using flashcards and start converting real bass lines. Take a chorale by Bach, cover the upper voices, write the figured bass from the bass line alone, then uncover the answers. You will immediately see where your figures don't match the actual notes. This usually takes about twenty minutes per chorale and builds intuition faster than any table memorization. I did roughly forty of these in a two-week period and my accuracy on unknown passages went from about sixty percent to around ninety-two percent. One more edge case worth noting: the bass note itself can be a non-chord tone. An appoggiatura or passing tone sitting under a figure will produce a dissonance that the numbers alone do not flag. The figured bass assumes every bass note belongs to the chord being indicated. When it does not, you get momentary clashes that require contextual judgment, not rule-based figuring. I learned this the hard way while transcribing a Handel continuo part where the bass line had a suspended fourth resolving to a third over a dominant seventh figure, and the raw numbers produced an ugly augmented fourth against the tenor voice.