Figured bass, also known as thoroughbass, was a notational practice of the Baroque era (1600—1750) but continues to be taught today because of its relevance for understanding tonal harmony. Historically, the practice served as a guide to the keyboard player (organ or harpsichord) who played the basso continuo part in a musical performance. Basso continuo, as the name implies, was the universal style of Baroque composition in which a bassline and its implied harmony was sounded continuously throughout a composition. A keyboardist would have on the music rack the bassline for the composition, which was usually played by a double bass player and a cellist or gamba player. Underneath the bassline was a series of figures which indicated the flow of the harmony by listing the intervals to be played above the bassline. While the practice varied widely during the period, modern notation has standardized the practice to a significant degree.
This style was originally used for vocal music to accompany a singer, a soloist, or a group of instrumentalists, conceptually identical to a jazz context today, where a bassist and pianist back up a singer or sax player in a jazz trio. Only the style of the music (and the lack of improvisation on the part of the instrumentalists) is different. In later Baroque music, the keyboardist is called upon to fill out harmonies even in larger ensembles when all the notes of the chords are already written into the upper parts of, most commonly, the string section. Over time, as composers wrote increasingly complex music for instruments, imitating the complexity of a capella vocal writing, the necessity for the keyboardist to flesh out harmonies fell away and the practice largely disappeared by the end of the 18th Century, although it maintained its relevance in the opera house pit, when the harpsichordist in the operas of the Classical period (Mozart, Haydn, Gluck) played from figured bass when accompanying the singer during recitatives (sung conversational dialogues which moved the plot forward).
While figured bass is largely of theoretical interest to most musicians, specialists in Baroque performance practice continue to work with figured bass notation, and all keyboard and classical guitar players can benefit from learning to improvise harmonies based on the figured bass.
The basic concept of figured bass is simple. When presented with a bass note on a beat, play the third and fifth above the note to form a diatonic triad above the bass, unless the figures suggest otherwise. The default is always to play a triad, and it is up to the skill and experience of the keyboardist to voice the chord in a musical manner. Thus the keyboardist, when presented with the following passage, might perform it with the following realization:
This is a very straightfoward passage, where the notes of the bassline are also the roots of the chords. The right hand plays the triad of the bass note, voiced in a manner that allows for smooth movement of the fingers.
Of course, not all harmonies appear with the root of the chord in the bass. (If they did, the bass line would be very spiky and unmusical). A good bass line must flow and have melodic shape and interest, no less in jazz or rock music than in Baroque music. Thus the bass line will as often as not play other notes of the implied harmony while the upper voices fill in the remaining pitches. We have already seen this practice in the Bach chorale we looked at in a previous page, where we indicated which degree of the chord was in the bass.
Figured bass is similar in concept, although the figurations are different. When the bass line does not play the root of the chord, with the implied third and fifth, the note is figured to indicate the proper intervals above the bass. It is up to the keyboardist to voice the chord in a proper manner, which of course takes training and also a knowledge of the particular musical context.
Root position triads
If there is nothing indicated, the third and fifth are implied and thus the chord is in root position. A major triad could be written as in the first measure, but much more commonly it is just left blank. Notice that the right hand chord double the root, then adds the third and fifth above.
Chords of the Sixth and First Inversion Triads
The appearance of the 6 below a bassline is a most important and fundamental figure, and has relevance for all subsequent harmony that we will study. The 6 means that the implied "3" is still present, but the "5" has been substituted for a "6." When you see a 6 above a bassline, always interpret it as a "6-3" harmony, with the third implied. Thus above the bass note, play the third above the bass and also the sixth above the bass. (Also, double the root).
Note the subtle shift here. While the same notes remain in the bass, the chords have shifted mode from major to minor. In older harmonic thought, this was often thought of as the "chord of the sixth" because of its particular sound quality. Let's investigate this a little further.
As we begin to explore harmonic progression, it is important that you focus on the special case of the chord of the sixth, which we can also think of as a first inversion triad.
I make this distinction because a triad that maintains its bass note while the fifth of the chord changes to the sixth is a special harmonic movement that you should appreciate early on in your study.
In the first example, there is a clear change from the tonic triad to the relative tonic (or submediant) triad, because the bass note has changed. In the second example, the bassline holds while the upper voices substitutes the A for the G.
These are of course both "A minor triads." However, the second example, which is in first inversion, has a particular sound quality, with the third in the bass. This voicing is so distinctive that it is important to view this chord in two ways:
- As a "chord of the sixth," which is triad with its fifth shifted to a sixth. The relevant sound is the sixth above the bass, along with the implied and ever-present third. In a major key, it is quite common for the tonic and subdominant triads to appear in this form, which shifts the sound from major to minor.
- As a "minor triad in first inversion," which is a minor triad with the third in the bass. This is a common voicing for the submediant and supertonic triads, also known as the relative tonic and the relative submediant. These labels show the inter-relationship between all of these harmonies.
Here how the harmony moves from C major to A minor, F major to D minor and G major to E minor. This is the sound of the shift from the tonic, subdominant and dominant triads to their respective relative tonics, relative subdominants and relative dominants, voiced in first inversion. This can also be heard as the shift from the tonic root position triad to the "chord of the sixth."
Please memorize this important point: a "chord of the sixth" is identical to a first inversion triad. This chord has a dual nature: it can be heard as a triad whose fifth has shifted to a sixth, creating at the same time a shift in mode. It can also be thought of as a triad in first inversion, with the third of the chord in the bass. We will return to this point when we begin to consider the expressive qualities of harmonic progression and chord voicings.
Other Standard Figured Basses
Figured bass can potentially be used to express extremely complex harmonies. For the point of our study, however, it is necessary only to understand basic harmonic structure and progression.
Being with the basic principle: the third and fifth above the triad is always implied, unless the figure calls for a subsitution. We have already seen how the '6' replaces the fifth in the chord of the sixth, also known as the first inversion triad. Simlarly, the '3' is always implied unless a '4' appears to replace it. This occurs most commonly in the six-four chord and in the four-three suspension:
The six-four chord
Rather like the chord of the sixth, the six-four chord is related to the root position triad. A common musical cliche is for the tonic bass note to sustain while the upper two voices of the triad move down one scale degree and then fall back into the triad.
This is a common occurance at a cadence point, when a statement comes to a temporary or final conclusion. The bassnote holds the dominant while the upper voices sound the fourth and sixth above the bass. This looks like a tonic triad in second inversion, which of course it is, but if functions as a dominant triad with two notes that fall into the third and fifth from above.
In modern usage we continue to call this the six-four cadence. So common is this progression that it is important to view the "one six-four chord," when it occurs at a cadence point, as a dominant triad (a V chord) with a double appogiatura. That is, we view it from the standpoint of figured bass, where the notes that are a sixth and a fourth above the bass note are seen as variants of, or substitutions for, the fifth and the third that are the default harmonization of a bass note. There is a strong feeling of tension and resolution here, especially regarding the movement of the fourth falling to the third. Memorize the sound and feeling of the effect of six-four falling into the dominant triad and then resolving back to the tonic chord.
You will recall, when we studied beginning modal counterpoint, that the fourth was considered a dissonance within the style. This is one of the reasons—in tonal music, the fourth has a strong tendency to fall into the consonance of the third.
The four-three suspension
We can see from the example of the six-four chord that figured bass is well configured to indicate suspensions and resolutions. We practiced the seven-six and four-three suspension when we studied fourth-species counterpoint. Within the context of four-part tonal harmony, the suspension of four on the strong beat resolving to three on the weak beat is shown be the appearance of a '4' as a figure above a bass note, most often resolving to three 3 in a 'space' when there isn't a new bass note to figure.
In standard practice, you can assume that a third is always implied over a bass note unless there is a '4', which replaces the third temporarily. In almost all instances in Baroque music, that four will resolve on a weak beat into the third.
The four-three suspension is one of the great musical cliches, especially in vocal music. Even in modern four-part tonal writing, you will hear this sound evoked—it is a fundamentally satisfiying musical effect.
As an aside: Modern guitarists and pianists often use the fourth chords as a consonance, avoiding the third above the bass in favor of the fourth. This "fourthy" sound gains its effect within the context of the resolved third, even if in fact the chord never resolves. It's open quality is due to the avoidance of the more rooted feeling of the third. Of course, to our modern ears, we've become used to the sound of the fourth chord and it no longer feels strange; nevertheless, there is a fundamental sense of subtle, unresolved tension within the chord that provides it with its appealing, expressive quality.
The '7' is common figure in figured bass. When it appears by itself, as it will often do over a dominant bass note, it creates the dominant seventh chord since the third and fifth are always implied.
Notice how the '7' above a dominant triad is identical to the fourth degree of the scale. This note usually resolves downward to the third of the tonic triad.
'7' can also appear above other diatonic notes, most commonly the triads appearing above the supertonic, mediant and submediant notes. In Baroque practice, these sevenths are almost always "prepared" in the previous harmony. We will explore this point in detail when we study part writing.
This figure is most often abbreviated to just the '2' because it is a commonplace harmonization of a bass note. It is derived from the following harmonic motion:
Note that the bass note has moved down a scale step, but the overal harmony has not changed. The bass note has moved downward from being the root of the dominant seventh chord, becoming now the seventh of the chord. Above the seventh, the '2' then becomes the chord root, the '4' represents the third of the chord and the '6' actually represents the fifth! This is a little confusing at first, due to the fact that the figures no longer represent the actual notes of the chord but indicate only the intervals above the bass.
Since the interval of the second above the bass almost always implies this type of harmony—a seventh chord with the seventh in the bass—you will most often see this as represented just by the '2', with the '4' and the '6' implied. This may seem like a contradiction to the basic rule, and in fact it is! Figured bass is an art not a science. Just remember: a 2 in the bass in figured bass means a seventh chord in third inversion, with the seventh of the chord in the bass.
What is important here is to grasp this sound—a triad with an added seventh in the bass rather than stacked above. You will recall that this is also an excellent expression of harmonic polarity, since the seventh above a triad is also the subdominant of the subdominant, helping to pull the harmony towards the central tonic triad.
6-5 and 4-3
When considering the triad, there were only two possible variants: the chord of the sixth and the six-four triad, corresponding to the triad in first and second inversions.
When considering seventh chords, there are two additional variants to the '2' chord (the third inversion seventh chord). When a chord of the sixth (or a first inversion triad) has a seventh added to it within the harmony, we create a harmony with a sixth, a fifth and a third above the bass note. Since the third is always implied, this is usually shortened to a '6-5.'
This voicing is identical to the seventh chord in second inversion, with the third of the chord in the bass.
When a seventh chord is voiced with the fifth in the bass—a relatively unstable voicing that is usually reserved for passing chords on weak beats—we create a chord with a sixth, a fourth and a third above the bass. In this instance,rather than indicate it with '6-4-3,' this is typically abbreviated to '4-3.' Why? Because the important interval is the presence of the fourth and the third simultaneously above the bass note. Typically the fouth cancels out the third and vice-versa. The existence of the fourth and the third implies the 'crunch' of the root and seventh together within the harmony. Since this 'crunch' is so indicative of the seventh chord with the fifth in bass, it is enough figuration to confirm this harmony:
Just recall that in a 4-3 figuration, the sixth above the root is implied.
Accidentals and Secondary (Chromatic) Harmonies
Figures in figured bass always mean the interval above the bass note within the context of the prevailing diatonic harmony or key. When an accidental is required, most commonly in the creation of a secondary dominant chord or diminished seventh chord, an accidental is used before the figure, unless the note to be altered is the third of the chord, in which case the accidental simply appears by itself, implying an altered third.
Here are some examples of figured basses for the diminished seventh, secondary dominant, and modally altered chords that we have already studied, here expressed in the key of C major:
The V7 of IV (a tonic triad with a lowered seventh), the V of ii, the V of V, and the V of vi, each resolving properly:
The sharp by itself indicates the sharped third, turning the usually minor triads into seconday dominants.
The same chords, but expressed as secondary dominant sevenths:
Here's how you would figure the vii dimished seventh chord and the iv minor triad in the key of C major.
Finally, here is a standard passage of figured bass, with the right hand worked out in a realization. This is from the basso continuo part of the Concerto Grosso Number 12 by George Frederic Handel.
Figured Bass and Jazz
It is often remarked that there is an interesting similarity between Baroque practice and Jazz practice, especially as regards the work of the keyboardist and bass player. In both styles, the active player is given a "chart" that only suggests harmonic flow, leaving it up the keyboardist or guitar/lute player to improvise the proper harmony. We will look at some examples of these types in class.
Figured Bass and Harmonic Polarity
Since this first book of A Feeling for Harmony has oriented itself around the concept of Harmonic Polarity, it is worth looking at figured bass from within the concept of Harmonic Polarity.
Harmonic Polarity implies that at a philosophical or intuitive level, minor harmonies seem to the be the polar opposites of major harmonies due to their being derived from a downward, inward motion of the reverse harmonic series, or reciprocal series. However, figured bass always indicates harmony as being built from the bottom up, rather than from the top down. This system seems to contradict the ideas contained within harmonic polarity.
About that, this can be said: Figured bass grew out of a practical necessity, which was to give a keyboardist a bare outline of a harmonic motion for the purposes of improvisation and to support a musical performance. It is a shorthand for building harmonies quickly above a bass line. It was never intended to make a philosophical statement about the origins of harmonic thought. It is quite a simple matter to build a minor triad from a bass note, but to still hear it inwardly as descending from its top note. The one approach is practical, the other intuitive and philosophical. I have found it useful to keep these two systems alive when I work with harmony, and we will continue to discuss these two approaches as we learn the details of part-writing and harmonic analysis in the next book, during the second semester of this course.
Figured bass and the basso continuo form the basis for all study of harmony. By understanding the basics of this system, we can understand a great deal about the function of tonal harmony:
- Figured bass implies the existence of a continual flow of harmonies based that are described in relationship to a bass note.
- The default voicing for any bass note is the third and fifth above the bass.
- Alterations to this default position allow for chords that are voiced with fourths, sixths and sevenths above the bass.
- Chromatic notes are easily indicated by the addition of accidentals within the figuarations.
- Suspensions, appogiaturas and other "non-harmonic" or "embellishing" tones can be indicated when necessary.
- Figured bass is a practical system for the realization of harmony; deeper considerations of the expressive and intuitive quality of harmonic expression is left to more elaborate systems of explantaion, such as that of harmonic polarity.
The final step in this process is to see how figured bass work with Roman numerals when analyzing chord inversions.