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Basso Continuo


provided just enough information to extemporise an accompaniment but without making the
just bare block chords.

In figured bass notation, an F written on the bass clef automatically "implies" the harmonies
shown here on the treble clef. The normal harmony was a perfect diatonic triad built on the
bass note, as shown here in the first measure. Numerical figures indicate alterations of the
normal triad: a "6" meant that the fifth interval above the root would be replaced by the sixth.
(See measure 2.) Adding a "4" to this figuration meant that the third interval (C) should be
replaced by the fourth (D). (See measure 3.) Chromatic alterations could be indicated by
adding marks such as a slash through the upper portion of a "6" to show that the sixth interval
was to be raised by a half step.
That's the system, in a nutshell, but what is amazing is the complexity of the instantaneous
compositions that musicians could create over this simple framework. One can get a pretty
clear idea of the art's complexities by viewing the next few multimedia pages. They show (and
play aloud) famous examples of thorough-bass accompaniment drawn from Johann David
Heinichen's Der General-Bass in der Composition [Thorough-Bass in Composition]
(1728). Heinichen illustrates the development of a thorough-bass accompaniment from a bass
line to final improvisation or to use the technical term, "realization" of a written thorough-
bass. First, on the next page, see how the music looks to the improvising harpsichord

Hi, Gustave;
I hope this finds you well, and in great spirits.
This lesson is going to address one of the
questions you brought up earlier:
. . . you can try some of
Pistons exercises. . .
I would love to, but I
dont understand how
Pistons figured bass
works. I can easily and
spontaneously create
chord voicings (open and
closed) from jazz chord
charts, but I must be
missing something here
I might have to go
back to some basics.
Aldwell has some information on figured bass,
and there are some decent explanations from
other texts, as well. I'll scan and paste them
here, and go over them with you. Before referring
to them, though, I would like to make a few
important points:
Figured bass also known as thorough bass
was a practice used for certain accompanying,
chordal instruments (mainly keyboards and
various precursors to the guitar) during the
Baroque period (ca. 1600 - 1750). (In fact, some
figured bass was also occasionally used by Mozart
and his contemporaries.)
It was a specific kind of musical shorthand
analogous, in some ways, to today's jazz fake
sheets that made life a little easier for the
composer, and allowed for some creative
improvisation on the part of the performer.
(Improvisation was far more prevalent in Baroque
practices especially in melodic and rhythmic
ornamentation than was the case in classical
music from that time until the 1960s). In brief
the texts will explain it in more detail a bass
line was given, with accompanying figures ie,
numbers written below each note. These
numbers stood for intervals specifically, the
intervals to be found above the written bass note.
Usually, the intervals given would correspond to
those found in a typical triad or 7th chord. Since
the intervals in a root position triad (one in
which the root is in the bass) are a 3rd and a 5th
both measured from the bass (this is always
the practice) the figures 3 and 5 would be
written below the bass note which, in this case,
would be the root of the triad like this:
. . . and would mean this:
. . . or any other voicing of this chord eg, with
open spacing, doubling, etc. so long as it has
its root as bass note.
The standard figured bass notation has the
figures stacked, one above the other, as shown.
Because were using word-processing programs,
and typingthese lessons, however, we can ease
up on tradition, and write our figures as for
example 5/3.
In figured bass (as well as in harmonic analysis),
the interval indicated by a given figure can be
either a simple interval ie, any interval up to
an octave in size or its compound equivalent.
For example, the figured bass 3 can mean a
3rd, or a 10th or a 17th, etc. the choice is up
to the player. The same is true in reverse: if you
wish to write a figured bass for a given chord, a
3rd, 10th, or 17th within that chord
are all written as 3.
Since any chord can be inverted one, two or three
times (first inversionmeans that the 3rd of the
chord is in the bass; second inversion means that
the 5th of the chord is in the bass; third
inversion means that the 7th of the chord is in
the bass), the corresponding intervals change
accordingly. For example, the intervals in a first
inversion chord measured from the bass, again
are a 3rd and a 6th. The figured bass is
therefore written:
. . . which means this:
The intervals in a second inversion triad are a 4th
and a 6th:
. . . which means this:
The figured bass for 7th chords and their
inversions is a little more complicated, but is
addressed in Aldwell (if not in the material that
I'll paste here).
Since figured bass was used all the time, during
the Baroque period, composers and musicians
developed a further simplification for it: since
everyone knew that the intervals in a root
position triad are always a 3rd and a 5th, the
simplification was to write no figure at all under a
root position bass note. For example, in figured
bass, this:
. . . means:
So, a bass note with no figure beneath it means
that that bass note is the root of a chord.
Along the same lines, the first inversion chord
was figured as 6 instead of 6/3. Therefore,
a bass note with a 6 beneath it automatically
means that that bass note represents the third of
a chord, and that there will be two notes one
at an interval of a 3rd, and one at an interval of a
6th above it.
(Please note that these numbers refer
to intervals, and not to chord members. In the
case of a first inversion chord, we see a bass note
which represents the third of the chord. The
first figure the 6 means that the next note
is an interval of a 6th above that bass note it
doesn't mean that it's some kind of 6 chord!. It
turns out that that note will be the rootof the
chord since the root, in a first inversion chord,
is found at an interval of a 6th above the bass.)
The figures for a second inversion chord are
always written in full:
Figures can also refer to notes that do not belong
to a triad or 7th chord they can also
indicate suspensions, anticipations, passing
notes, etc. For example: let's say you want to
write a Dsus, followed by an ordinary D major
chord. In a non-simplified figured bass, this would
be written as:
The dotted line simply means the 5th is held
while the 4th resolves to the 3rd:
In simplified form (which is the usual form), the
above would be written
4 3 , since the 5th is understood.
In a way, a performer could read and play a
figured bass without knowing the name or
inversion of the chord being played he could
simply read the figures a kind of paint-by-
numbers. Of course, we also want to know
everything about the chord -- not just its figures!
In both your harmony books and in the material
that I'll paste here, you will have to distinguish
between two different things: figured bass as
used during the Baroque and the combination
of figured bass and roman numerals that is used
in typical harmonic analysis. True figured bass
does not involve the use of roman numerals it
simply uses the figures, as described above.
However, almost all harmony text books utilize
roman numerals along with figured bass, to show
not only the scale degree upon which the chord is
built (eg, ii, IV, etc), but also the inversion that is
being used.
Okay, on to the different texts. First, from Basic
Harmony, by David Cameron:
Here is another perspective on the same thing,
from our second text Harmonic Practice in Tonal
Music, by Robert Gauldin:
Why not try what the author next suggests and
then email me your results:
Now we get to Aldwell page 53 in my version
from chapter 4 (Triads and Seventh Chords).
Here Aldwell goes over specific procedures
pertaining to writing figured bass. Note that in
illustration 4-9, Aldwell intends that you
understand that he means the performer would
be playing both clefs:
All of this is, of course, a brief summary.
Here are the steps I would suggest you take, in
order to begin to assimilate figured bass:
1. Memorize both the full and simplified
figures used for root position, first inversion
and second inversion chords. If you would
like to make up some exercises eg, write
a chord progression in full, then re-write it
as figured bass please go ahead, and
then email me the results, so that I can
check it.
2. Study and memorize the full and simplified
figures used for seventh chords go to
Aldwell (same chapter), paragraph 14:
Inversions of seventh chords. If you
have any questions about any of it, please
ask me!
3. When you think you've assimilated the
basics, try the following exercises:
a. Exercises A and B, by
Gauldin (above).
b. Try to realize the
following figured bass, by
1. Notes:
i. the circled notes in the
figured bass
are not meant to be
realized they
are non-harmonic
tones passing notes,
appoggiaturas, etc.
ii. Ive entered a few
figures in
parentheses that
would not have been
necessary during
Handels day, but that
may make your task a
little easier. (Ill explain
the thinking behind the
original practice, in the
Send me your work when you've completed it.
And please feel free to ask me any questions as
you go along.
Last, here's a figured bass from one of the most
beautiful pieces of music in existence it's from
the opening of Bach's St. Matthew Passion. The
cello and organ play the figured bass its on the
lowest staff, with figures highlighted in yellow
but all the other instruments (and voices) realize
it on their own, too. You can try to realize the
figured bass, and then see if you're correct, by
examining what everyone else is playing.
Note: the entire passage involves the use of a
tonic pedal read about it in Piston and
Aldwell, and ask me about it if necessary.
Please dont hesitate to email any questions you
may have. . .
indicate intervals, chords, andnon-chord tones, in relation to a bass note. Figured bass is
closely associated with basso continuo, anaccompaniment used in almost all genres of music
in the Baroque period, though rarely in modern music.
Other systems for denoting or representing chords include:
plain staff notation, used
macro symbols,
sometimes used in modernmusicology, and various names and symbols used
in jazz and popular music.
Figured bass notation
staff plus added numbers and accidentals beneath the staff to indicate what intervals above the
intervals such as 10, 11, and 15.
Contemporary Figured Bass as taught at university level, may be summarized as follows, for
For diatonic triads:
root position = blank or 5/3
1st Inversion = 6 or 6/3
2nd Inversion = 6/4
For 7th chords:
root position = 7
1st Inversion = 6/5
2nd Inversion = 4/3
3rd Inversion = 4/2
be played. For example:

major chord is to be played.

In this sequence, the first note has no numbers accompanying itboth the 3 and the 5 have
been omitted. This means that notes a third above and a fifth above should be playedin other
played; the 3 has been omittedin other words, this chord is in first inversion. The third note
omittedthe seven indicates the chord is a seventh chord. The whole sequence is equivalent


next to the figure or figures to indicate this:

the accidental affects the said interval. For example, this:

is equivalent to this:
