FIGURED BASS

A figured bass was used a lot during the Baroque period, especially for keyboard instruments. It allowed writing music in a way that left an opportunity for a performer to improvise. The melody was written in the upper staff of the grand staff. The bass line was written in the lower staff of the grand staff and it was annotated with the figured bass. The performer used the bass line and the figured bass to decode missing notes above the bass line. 

The idea of the figured bass is to use numerals which describe interval numbers over the bass line. Please note that only interval numbers are given and interval qualities are not. Thus, the numeral specifies the number of staff positions between the added note above the bass note and the bass note itself (including the staff positions of both notes). If there is no accidental before the numeral, the added note corresponds to the key signature. If there is an accidental before the numeral, the accidental is applied to the added note. The next figure shows an example.

Figure: Using figured bass to decode missing notes above the bass line

In the figured bass, some combinations of numerals are abbreviated. For instance, the numerals 6 and 3 are abbreviated as the single numeral 6. This is illustrated in the next figure.

Figure: The numerals 6 and 3 are abbreviated as the single numeral 6

The most extreme of all the abbreviations is when there are no numerals at all. This is the abbreviation for the numerals 5 and 3. The next figure illustrates this. 

Figure: The numerals 5 and 3 are abbreviated as no numerals at all

If you wonder is it possible to annotate a solo bass line using the figured bass, the answer is: to do that, you must include the expression “Tasto solo” above the lower staff of the grand staff so that a performer can understand that the bass notes should be played as written, without adding any notes above them. “Tasto solo” in English means “single key”.

Multiple realizations of the same figured bass do exist. Actually, a bass line and figured bass define only bass notes and note names. A performer can choose octaves of the notes above the bass note and which note names will be doubled i.e. used simultaneously in more than one octave. Thus a performer may improvise. The next figure illustrates this. It shows a few possible realizations of the same figured bass. The figured bass defines only note names C, E and A together with the bass note C3 and a performer can choose between different possible realizations. However, a performer may not change all the explicitly written elements: the melody (in the upper staff), the bass line and the note names that should be added above the bass line.

Figure: Two possible realizations of the same figured bass

The next figure shows an example of the figured bass and its possible realization. The realization contains only triad chords in the close position. In the next chapter, we shall see how seventh chords can be annotated using the figured bass.

Figure: An example of the figured bass and its possible realization

Annotating positions of triad and seventh chords using figured bass

The next table shows how we can annotate positions of the triad and seventh chords using the figured bass. It is easiest to imagine the close positions. Thus, they are shown in the table. However, open positions would be annotated in the same way since the nature of the figured bass is such that a performer can choose any open or the close position while realizing the figured bass. The abbreviations that are used omit often the numerals 3 and 5 but there are exceptions to this rule. Since in the normal usage, only abbreviations appear, they should be memorized.  

The previous table shows only the C major triad chord and the G dominant seventh chord. If you wonder what would happen if we used some other triad or seventh chord, the answer is: the figured bass would not change much. The next figure illustrates this. All the triad chords in the figure are in the second inversion and they have different chord qualities. We see that they can be built using the same interval numbers: the fourth and sixth, above the bass note. However, the interval qualities are different. For instance, the minor triad chord and the augmented triad chord contain the minor sixth, while the diminished triad chord contains the major sixth. Thus, they all can be annotated with the same figured bass numerals 6 and 4, only accidentals are somewhat different.    

Figure: The interval numbers above the bass note stay the same when the chord quality changes 

From the figures in chapter Chord inversions in close position, we can see that any close position of any triad or seventh chord can be built by using certain interval numbers, above the bass note. This interval numbers depend only on the position and not on the chord quality. Thus, we can speak about the characteristic interval numbers of close positions.

This is the reason why figured bass symbols given in the previous table are used for annotating positions of all the triad and seventh chords. They are used for annotating the closed and open positions, root positions and inversions. The same table can also be used for naming the positions of chords. For instance, instead of saying the triad chord in the first inversion, we can say the six chord. Instead of saying the triad chord in the second inversion, we can say the six-four chord.