Introduction to Figured Bass by Matthew C. Saunders, DMA
[This essay is intended for students in the first semester
of music theory to more fully explain the history and usage of figured bass as
a supplement to Tonal Harmony, 5th edition, by Stefan Kotska
& Dorothy Payne.]
Figured bass is a
technique developed in conjunction with the practice of basso continuo at the end of the Renaissance (around 1560 or
so). In basso continuo, two performers helped to fill in the texture of a
composition while one or more performers provided the melody. A single-line, bass instrument such as
cello, bassoon or trombone would play the bass line. At the same time, a chordal
instrument such as harpsichord, lute or organ would also play the bass line and
provide middle range pitches that would fill in the harmonies implied by that
bass line.
Initially, basso continuo players would look at just the bass line, with no
additional information. The
keyboard player’s choice of notes was left up to good taste and his or
her understanding of the musical language and context of the piece. As tonal music became more complex, it
became common to provide more information by including figures, that is, numbers and musical symbols, below the bass
line. This was also a sign of a
shift in emphasis from counterpoint to a more chordal
conception of harmony. However,
through most of the Baroque era, keyboard players were expected to be able to realize unfigured
bass-lines just as well as those with figures. One estimate is that about seventy
percent of the bass lines from the seventeenth and eighteenth centuries did not include figures.
The importance of figured bass,
however, lies in its role in the shift from contrapuntal to harmonic
thinking. The concept of a chord
having a root was not developed until
the very end of the seventeenth century, and not popularized until the
mid-eighteenth century. But any
musician can see that a group of pitches has a lowest note, or bass note. If a musician plays enough bass lines,
it isn’t very long before patterns within a style start to arise. Figured-bass theory was the first
comprehensive theory of tonal harmony, and as such, it has made important
contributions to our thinking today.
How Figured Bass Works
To a keyboard player of the seventeenth
century, the bass note was the most important note of the chord. Figured bass notation is a shorthand
system telling which notes are to be placed above that bass note at any time. Because it is shorthand, it
doesn’t give all the information, and some things are left up to the
performer. There is almost always
more than one correct realization of a figured bass line.
We begin with several assumptions:
- Octave
equivalence: A pitch has the
same meaning as other pitches with the same name in higher octaves. That is, if we need a C, it
doesn’t matter if it is C3, C4 or C5, as long as it is placed above
the bass note.
- Unless
told otherwise, we stay within the key signature.
- Numbers
written beneath (or occasionally above) a bass note represent generic
intervals to be played above that note.
- In
general, we will realize three notes above every bass note. This is an assumption for this
class only. The actual number
of notes above the bass in performance will depend on the whim (and
ability) of the keyboardist.
Now the rules:
- Given a bass note with no figures, it is assumed that the third
and fifth within the key are played above it, along with their octave
transpositions.
Notice
that any C, E or G above the bass
note will work, not necessarily the closest ones, and not necessarily in stacks
of thirds The
notes should be chosen around the idea of what I call the lazy harpsichordist: the fingers should be moved as little as
possible, with as little expansion of the hand as possible, while avoiding
objectionable parallels. In
realizing figured bass, you should make the smoothest possible connections
between chords.
- A “7” written below a bass note adds a seventh
above the bass to the chord without affecting other notes.
- A “6” written below the bass note changes the fifth
to a sixth above the bass and leaves the third alone, creating a first
inversion triad.
- If both a sixth and a fifth are desired, both numbers must
appear. The third remains,
creating a first inversion seventh chord.
- A “4” written below the bass note changes the third
to a fourth above the bass.
This is usually seen in conjunction with a “6”,
creating a second inversion triad.
- If both a fourth and a third are desired, both numbers must
appear. This is usually seen,
again, with a “6”, creating a second inversion seventh chord.
- A “2” written below the bass note adds a second
above the bass to the chord without affecting other notes. This is often seen with a
“4” and a “6” to create a third inversion seventh
chord.
The most frequent figures are
nothing, to indicate a root position triad, and a “6” to indicate a
first inversion triad.
Other symbols frequently
encountered help to deal with accidentals.
- A natural, sharp or flat next to a numeral below a bass note
means that that accidental should be applied to that interval above the
bass.
- A natural, sharp or flat by itself below a bass note means that
that accidental should be applied to the note a third above the bass.
- A slash through a numeral indicates that that interval above
the bass should be raised by a half step.
- A dash below a bass note indicates that the bass note has
changed, but the notes above it should not.
Figured Bass and Inversion
Symbols
Our modern inversion symbols come
from figured bass notation. Thus, a
root position triad has no inversion symbol. We could use the symbol 6-3 for a first
inversion triad, but the 3 is assumed to be there already. For seventh chords, all three inversions
have a sixth above the bass, so the only one that needs the “6” is
first inversion, since it has both a sixth and a fifth.
Remember that inversion symbols
indicate the intervals above the lowest note, with a few assumptions about what
notes will be played. See the table
on page 47 in Tonal Harmony, 5th
ed. for a quick reference.
Realizing Figured Bass
The best way to realize figured
bass is to assume “lazy fingers” on the part of the
keyboardist. When moving from one
chord to the next, move each finger the shortest distance possible so that all
the needed pitches are played.
But—the rules of counterpoint still apply, so avoid parallel
fifths and parallel octaves. The
result should be smooth lines that make the harmony clear and don’t interfere
with the melody. It is typical to
have three pitches in the right hand against the given bass line in the left
hand. The practice of basso continuo, of which figured bass is
a part, had a strong influence on tonal music of the Common Practice Era, and
on later music derived from the styles of that era. In essence, it is possible to think
about much of this music as having a “melody space” in the treble
clef, a “bass space” at the bottom of the texture, and a
“voice-leading space” in between, hovering around the middle of the
keyboard. In this
“voice-leading space,” the interest inherent in the lines is less
important than their making smooth connections between chords. Anyone who has sung alto or tenor,
played viola or French horn, or “comped”
the piano part in a jazz combo has spent lots of time in this middle
space. When one analyzes music in
these Common Practice styles, the first thing that should leap out is the
division between these three spaces.
