In the 17th and 18th centuries, paper and ink were somewhat expensive materials. To save money–and also time–composers and musicians sometimes implied harmonies in ensemble works, without writing them out fully. Figured bass refers to the the bass voice or part, under which figures and other symbols indicate to musicians the implied harmony.^[1]

Triadic Figures

Figured bass uses Arabic numerals and some symbols which indicate intervals above the bass note, which are then interpreted as chords by musicians. Example 1 shows the full figured bass for triads, as well as chord symbols for the same harmonies:

Example 1. The full figured bass for triads, as well as chord symbols. 

As you can see in Example 1, a root position triad has a third and a fifth above the bass (indicated by “[latex]\begin{smallmatrix}5\\3\end{smallmatrix}[/latex]“). A first inversion triad has a third and a sixth above the bass (indicated by “[latex]\begin{smallmatrix}6\\3\end{smallmatrix}[/latex]“), and a second inversion triad has a fourth and a sixth above the bass (indicated by “[latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex]“). In figured bass, larger numbers always appear above smaller ones.

In order to save even more time (and more paper space!), composers and musicians abbreviated the full figured bass for triads and seventh chords. Example 2 shows the abbreviated figured bass for triads that we usually use today, as well as their chord symbols:

Example 2. The abbreviated figured bass for triads. 

As you can see, no figure appears for root position. The superscript number “⁶” will result in a first inversion triad, while a second inversion triad keeps its full figures, “[latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex],” to distinguish it from a first inversion triad.

Figured bass is not usually added to chord symbols; however, it is added to triadic shorthand notation. For example, the last measure of example 2 would be notated as “A/E” in chord symbols. Using triadic shorthand, this chord would be notated as “A[latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex].”

When musicians turn figured bass into chords—either on paper or in performance—this is called realizing the figured bass. Example 3 shows the process of realization for several triads:

Example 3 Some triads with figured bass and their realizations.

As seen in the first measure of Example 3, an E♭ appears with no figured bass next to it. Therefore, we can assume that we are realizing an E♭ major triad in root position. This chord is realized (written out with notes) in the next measure. In measure 3, we see the figure “⁶” below the bass note G. We can understand that notation to mean that we are realizing a sixth and a third above the bass note G. This chord is realized in the next measure (an E♭ major triad in first inversion). In measure 5, we see the figures “[latex]\begin{smallmatrix}6\\4\end{smallmatrix}[/latex]” below the bass note B♭. This notation means that we are realizing a sixth and a fourth above the bass note B♭. This chord is realized in the next measure (an E♭ major triad in second inversion).

Seventh Chord Figures

Example 4 shows the full figured bass for seventh chords, as well as chord symbols for the same harmonies:

Example 4. The full figured bass for seventh chords, as well as chord symbols. 

As you can see in the full figures of Example 4, a root position seventh chord has a third, fifth, and seventh above the bass. A first inversion seventh chord has a third, fifth, and sixth above the bass, while a second inversion seventh chord has a third, fourth, and sixth above the bass. Finally, a third inversion seventh chord has a second, fourth, and sixth above the bass.

Example 5 shows the abbreviated figured bass for seventh chords that musicians use today underneath their chord symbols:

Example 5. The abbreviated figures for seventh chords.

As seen in Example 5, a root position seventh chord is abbreviated with the superscript number “⁷” while the figures “[latex]^6_5[/latex]” will result in a first inversion seventh chord. A second inversion seventh chord is indicated by the figures “[latex]^4_3[/latex]” and the figures “[latex]^4_2[/latex]” will result in a third inversion seventh chord. Sometimes, in older style figured bass notation, a third inversion seventh chord is notated simply as a superscript “².”

You can realize figured bass for inverted seventh chords in a similar way to how you realized them for triads. To realize an inverted seventh chord, simply write the indicated intervals above the bass note, keeping in mind that the full figures are usually abbreviated. Example 6 shows the process of realization for several seventh chords:

Example 6. Some seventh chords with figured bass and their realizations.

As seen in the first measure of Example 6, an A appears with the superscript figure “⁷” under it. Therefore, we can assume that we are realizing an A dominant seventh chord in root position. This chord is realized (written out with notes) in the next measure. In measure 3, we see the figures “[latex]^6_5[/latex]” below the bass note C♯. We can understand that notation to mean that we are realizing a sixth, fifth, and third above the bass note C♯. This chord is realized in the next measure (resulting in an A dominant seventh chord in first inversion). In measure 5, we see the figures “[latex]^4_3[/latex]” below the bass note E. This notation means that we are realizing a sixth, fourth, and third above the bass note E. This chord is realized in the next measure (resulting in an A dominant seventh chord in second inversion). In measure 7, we see the figures “[latex]^4_2[/latex]” below the bass note G. This means that we are realizing a sixth, fourth, and second above the bass note G. This chord is realized in the next measure (resulting in an A dominant seventh chord in third inversion).

Other Figured Bass Symbols

In order to denote chromatic alterations to notes, musicians put accidentals (♭, ♯, ♮) before the figure that is altered. Example 7 shows a few realizations of figures with accidentals:

Example 7. Realizations of figures with accidentals. 

Musicians also use slashes through a figure or a plus sign before a figure, in order to indicate raising the note by a half step. These symbols and their realizations are shown in Example 8:

Example 8. Realization of figures with a slash and a plus sign. 

An orphaned accidental (or hanging accidental) is also common. These are accidentals that appear by themselves, and may or may not be accompanied by other figures or symbols. In these cases, the accidental is assumed to apply to the third above the bass, as seen in Example 9:

Example 9. Realization of orphaned accidentals.

There is one other symbol that is commonly seen in figured bass. Horizontal lines indicate a change of note above the given bass, or a change of harmony. Example 10 shows several realizations of figures with horizontal lines:

Example 10. Realization of figures with horizontal lines. 

In the first measure of Example 10, the horizontal line indicates a change of note above the given bass. We could read this as “a fifth above the bass moves to a sixth above the bass,” as realized in measure 2. Sometimes this indicates a suspension, which you can read more about in Embellishing Tones. You can see an example of a suspension in measures 3 and 4 above; this could be read as “a fourth above the bass moves to a third above the bass.” Horizontal lines can also indicate a cadential 6/4 chord, which you can read more about in Strengthening Endings with Cadential 6/4. You can see an example of a cadential [latex]^6_4[/latex] in measures 5 and 6 above; this could be read as “a sixth above the bass moves to a fifth above the bass,” and “a fourth above the bass moves to a third above the bass.” As you can see in measures 5 and 6 of Example 10, more than one horizontal line can appear at the same time in figured bass. Horizontal lines can also indicate a change in harmony, as seen in measures 7 and 8 above; this could be read as “a chord with a sixth above the bass moves to a chord with a fifth above the bass,” since it is the bass itself which is moving.

Roman Numerals and Figures

Roman numerals are often paired with figures to denote chord inversions and certain embellishments. For example, a superscript “⁶” figure could be paired with the Roman numeral “I” to represent a tonic triad in first inversion, and the figures “[latex]^4_3[/latex]” would indicate a second inversion dominant seventh chord when paired with the Roman numeral “V.” However, not all instructors use figures with Roman numerals, so you’ll only want to do this if your instructor has indicated that you should. Example 11 shows a few realized Roman numerals with figures:

Example 11. Realization of Roman numerals with figures.

• Figured Bass Inversion Symbols (Robert Hutchinson)
• Figured Bass: How to Read Chord Inversion Symbols (LANDR)
• Figured Bass (thinking music.ca)
• Figured Bass Notation: Tutorial (Iowa State University)
• Figured Bass (Andre Mount)
• How to Realize a Figured Bass (Robert Kelley)
• Figured Bass Symbols (Robert Kelley)

1. Realizing Figured Bass Chords, I (.pdf)
2. Realizing Roman Numerals with Figured Bass (website), pp. 2, 5 (.pdf), p. 11 (.pdf)
3. Writing Roman Numerals and Figures for Bass Lines with Figured Bass, II and VII (.pdf), pp. 1, 3, 4 (.pdf), p. 11 (.pdf)

1. Triadic Figures (.pdf, .mcsz). Asks students to write chord symbols and identify the inversion of closed-position chords, and to realize chords from chord-symbol-and-figured-bass notation.
2. Seventh Chord Figures (.pdf, .mcsz) Asks students to write chord symbols and identify the inversion of closed-position chords, and to realize chords from chord-symbol-and-figured-bass notation.