- Hi.
Now we've learnt roughly
how figured bass works,
we're going to try an exercise,
first of all
that's on lines of the kind
of thing you're asked to do
in grade six theory.
And on the board, you can
see that I've got a melody.
And underneath I've
started to write a bassline
and there's some figuring
in the bass as well.
Then underneath the stave
we've got a whole series of asterisks.
So the task that we're going
to try and complete now
which you might be ask to do
in a grade six theory exam,
is to complete the bassline
and also to come up with any figures
that you think might be
needed to figure the bassline
and indicate which chords
we're going to use.
So the first thing we might just notice
is what's the material that we've got.
Well, we're in B-flat major
and if we're not in B-flat
major we must be in G minor.
But as I look through the piece
I can't see any accidentals at all.
There's B-flat at the end as
well which is another pointer.
That's probably confirming
that we're in B-flat major.
We've also got two, four bar phrases.
And that implies something important,
which is that a phrase wants
to finish with a cadence.
So we're going to need to think about
what the cadence is here
and what the cadence is at the end.
And the temptation with
this kind of exercise
is just to get to work
on the very next note
that needs a bass note and a figure
and see if somehow we can get to the end
but actually there's a lot of sense
in planning the cadences.
Just before we do that,
let's have a look at
the given couple of bars
to see if we can work out
what's going on there.
So here's our melodic line.
Here's the bassline that goes with it.
You'll notice things
like in the second bar,
there's contrary motion
between the top and the bottom.
You know, the given line is going up,
the bottom line is coming down.
That's often a good way
to write a bassline.
If you have too much of the bassline
going in the same direction
as the melody line,
you'll soon bump into problems.
And we have another session
which is outlining the basic
rules of writing harmony,
of writing chords and in that,
you'll discover all sorts of information
about consecutive fifths and
consecutive octaves and so on.
If we've got the bassline
going as the same direction
as the melody all the time,
we're much more likely
to have problems with consecutive fifths
and consecutive octaves.
Now you can't always write
it in contrary motion
but if there's a sense of
that going on during the piece
it's probably quite helpful.
And you can already see it
happening in that second bar.
Even in the first bar
you can see there's a
bits of contrary motion
looking at the two notes
at the end of the bar.
From the first note to the second note
the melody going down by
step but the bass is leaping.
So if the the one part's going by step
and the other part's leaping
that's also going to get
you away from the problem
that you might have
with consecutive fifths
and consecutive octaves.
Now if the figuring is blank,
we've already discovered that,
that means 5-3 is the chord.
In other words, a root position chord.
So we've got a root
position chord here, a 5-3.
A root position chord here another 5-3.
A root potion chord here, another 5-3.
So if you wanted to think
about this in roman numerals,
you can see that
because we've got B-flat
in the bassline here
and it's a 5-3 chord, it's
a root position chord.
So B-flat must be at
the bottom of the chord.
So it's B-flat, D, and F.
And you can see that this D in the melody
is in fact one of those notes.
So that's a 5-3 chord
that we might in roman
numerals also call, chord I.
The next chord is another 5-3 chord.
It's a root position chord built on F.
So that should be F, A, C.
You can see the C is there in the melody.
So we could call that in
roman numerals, chord V.
The F, A, C, is chord V.
It's also a 5-3 chord built on F.
The next chord is another 5-3 chord
built on G this time.
So this chord is G, B-flat,
because B-flat's in the
key signature, and D.
So here's the G in the bass.
We've got a B-flat in the melody.
And of course it would be
down to the continuo player,
the harpsichordist, or the organist,
to insert the missing note.
So if we've got a G there,
then the continuo player
would be playing a G
but would also be looking for a B-flat
and a D to complete this chord.
When we get to bar two,
you'll notice we've started to move away
from the 5-3 chords.
And remember that 6 is an abbreviation.
It's a abbreviation of 6-3.
And 6-3 is always a first inversion chord.
So in other words this E-flat in the bass,
if this is a first inversion chord,
this E-flat must be
the third of the triad.
So the triad must be C, E-flat, G.
And you can see the C is
there in the melody part.
So in B-flat major,
C, E-flat, G would be chord II.
But because the E-flat's in the bass
the third of that chord's in the bass,
in roman numerals we'd
call that chord IIb.
First inversion chord in
figured bass is a 6-3 chord
but were abbreviating 6-3 to 6.
Now, the dash that comes after the 6
is telling us to carry
on using this chord.
Even though the bassline
has moved to another note
and the melody's off
somewhere else as well,
we're going to hang on to the same chord.
Now it's up to the continuo
player at the keyboard
to decide whether just
to put down a chord here
and sustain it while
the next note is played
or whether just to rearrange
the notes of this chord
as we move on to the next one.
That's entirely up to
the player to decide.
So that's what's going on there.
Then we've got another 5-3 chord
at the end of the bar.
So it's built on C.
C, E-flat, G.
Known in roman numerals as
chord II in B-flat major.
C, the E-flat's in the top there,
the continuo player would
be looking to supply the G
as well, probably.
So that's what we got so far
and it gives us the lie of the land.
And now we've got to go on
and decide what we're
going to do in the bassline
for the rest of it
and make sure we've got figures
for each of these asterisk
down below.
Well you might want to start
with the very final cadence
right at the end
because this B-flat if
we're in B-flat major,
there's a very good chance
we're going to finish on chord I.
On the tonic chord.
So the tonic chord in B-flat major
will be B-flat, D, F.
So it's probably fairly safe
to put a B-flat in the bassline.
So let's do that.
Don't forget that anything we write,
you can always change later
if we think of a good reason
to come up with something else.
Which is why it's a very good idea
to do these answers in pencil
so you have a rubber at hand
to modify things as you go.
Well, if it's finishing on a chord I
with B-flat in the bass,
this means that we've only
got two possible cadences
because there are only two cadences
that finish on the tonic chord.
It could be a perfect cadence
or it could be a a plagal cadence.
Well if it's a plagal cadence
going IV followed by I,
the notes of chord IV in B-flat major
are E-flat, G, B-flat.
Well we've got A in the melody.
It doesn't seem to belong
to E-flat, G, B-flat at all.
So, I don't think it's
going to be plagal cadence.
Let's look at chord V.
In B-flat major, chord V
is going to be F, A, C.
Ah, now then.
We've got A in the melody.
So this is looking very possible isn't it?
So, it could be that we're
looking for an F there
and that we're looking
for another 5-3 chord.
So we've already got the
last two chords in place.
Now the F could be here, it
could be an octave higher.
We can keep an open mind on that
for the time being if we want to.
Now when your putting in a cadence,
once you've got the cadence
secure as we have now,
you might just want to
think about the chord
that comes before the cadence.
It's what we call the approach chord.
It's the chord approaching the cadence.
B-flat in the melody.
Well we've already discovered haven't we
that B-flat's at the end and
so it's implying a chord I.
But remember that any note you have
signals three possible chords.
Because any given note
is the root of one chord,
it's the third of another chord,
and it's the fifth of another chord.
Let's have a little think about this.
We've got B-flat.
So B-flat is the root of chord I.
It's also the middle,
the third of chord VI.
And it's also the top,
or the fifth of a chord IV.
So we could go I, V, I.
But maybe that's going to
be a little bit you know,
I, V, and come back to I.
We could go IV, V, I.
That would be quite strong wouldn't it?
We could go VI, V, I.
All three are perfectly possible.
If you go VI, V, I,
you're going to have the bassline
moving in the same
direction as the melody.
Sometimes that's perfectly okay
but bear in mind what we said earlier.
Once we are moving in the same direction
and by the same interval,
there's a good chance we'll end up
with some consecutive troubles
somewhere down the line.
So, we might decide
that we're not going to go
for that particular option.
Another possibility however,
is that we could use chord
I in a different inversion
and I'm just going to
suggest this possibility.
It's not the only possibility
but have a think about this one.
And if I put 6-4 under here,
you'll remember from our earlier lesson
that 6-4 means second inversion.
So let's have a little look
at what we've now written.
We've got F in the bass but 6-4 telling us
that this is a second inversion chord.
So F, is the fifth of the chord.
So we've got F in the bass,
the third then must be D,
and the root must be B-flat.
So hopefully you can see
that B-flat, D, F is chord I
but by putting the F in the bass,
we've turned our chord I
into a second inversion of chord I.
It's a Ic chord.
And in fact the progression
that we've now got at the end
is a very common progression.
Ic,
V,
I.
And it makes for a nice strong cadence.
There's nothing to stop
you going IV, V, I.
So if you were happier to
do that, that would be fine.
That great thing about these
kind of exercises at this level
is that there isn't one
single right answer.
There are various possibilities.
So as long as we come on
one that works well for us,
all is fine.
But this sort of bass, what I
call the "Hot cross bun" bass.
♪ Hot, cross, buns ♪
That's goes dominant, dominant, tonic.
And that's a 6-4, 5-3, 5-3.
So see how that works it's chord Ic,
chord V, followed by chord I.
So that gives us the last three chords.
Now maybe this is a good time
to have a look at the cadence
at the end of the first phrase.
See if we can get some notes in here.
But all the time we're
looking at the melody,
just have a look and see
what you think is going on.
We're asked to put a chord
in the last beat of this bar.
It's the last minim beat of the bar
because were in 3/2.
So, we've got two crotchets here
and it's worth just thinking
about what's going on there.
The D is on the beat, the
C comes after the beat
and it anticipates the following note.
So this C, the last crotchet of the bar,
is an anticipatory note.
In other words, it's one
of those inessential notes.
It doesn't belong to this chord
having sounded this chord,
the C anticipates the C
that comes in the next bar.
So we're not going to
worry about finding a chord
that fits with this C because
it's an inessential note.
We're going to find a
chord that fits with this D
and then a chord that fits with this C.
Maybe it's easier to start with the C
because that's going to help us discover
what kind of cadence we're dealing with.
Well, if it was going to be
a perfect or a plagal cadence
then we'd need this note
to fit with chord I.
chord I is B-flat, D, F,
and there's no C in it.
So it can't possibly be perfect or plagal.
Which means that it must be
imperfect or interrupted.
If it's imperfect we're
going to need a chord V here,
if it's interrupted we're
going to need a chord VI.
Let's look at chord VI first
Now in B-flat major
chord VI is G, B-flat, D.
No sign of C so it can't be that.
Chord V however in B-flat major
is F, A, C.
Ah ha.
C, that's useful.
So this can only be a chord
V because it's a cadence
and we now know that
it's going to have to be
an imperfect cadence.
So, I'm going to an F in the bassline
as it's the cadence point,
we don't want the music
to be charging around,
we just want it to settle at that point.
And if it's an F, A, C chord,
chord V in root position,
then obviously we don't need any figures
because it's 5-3 chord.
Now then, let's step back
because now we know this
is an imperfect cadence.
We know the chord before it
will have to be I, or II, or IV
because that's the pattern
for an imperfect cadence.
Well let's explore those possibilities.
D is the given note.
That's the harmony note.
If we have chord II in B-flat major
that will throw up C, E-flat, and G.
Well there's no D in that,
so that's not going to work.
If we're going to have chord IV
that would be E-flat, G, B-flat.
Well there's no D in that is there?
We could conceivably think
that if we had a chord IV,
the D could make it a IV7 chord.
So that's not beyond the
bounds of possibility
but it's not the most obvious
solution at the moment.
However, chord I has
B-flat, D, and F in it.
So it's looking likely that
this is going to be a chord I.
So let's see what happens
if I put a B-flat in there.
That's going to take up the
last minim beat of that bar.
That's going to give me
chord I in root position.
So I've got chord I followed by chord V.
Because this is root position
and that's root position,
we don't need to worry
about putting any figures
because they're both 5-3 chords.
Now this means that we're very close
to completing the first phrase.
And I've done something
that I'm going to
demonstrate here on purpose.
I've said try to get contrary motion
between the top and
bottom whenever you can
and you could carry on
getting contrary motion there.
Be quite easy to do something like this
to have a D in the bass there
and then to have an
E-flat in the bass there
and if we did that
then we'd have to think
about what this chord is.
It's going to be a chord
of B-flat major, chord I.
B-flat, D, F because remember
we need a chord that has F in it.
But this D, puts that chord
in it's first inversion.
So we'd have to call that a 6.
6 abbreviating 6-3.
If you want to consider
the other possibilities,
we've talked about chord I because F
is the fifth of a chord I.
F is also the third of a chord III.
Well remember chord III is possible
but it's one of the less
likely chords to be used.
Or it could be something to
do with the root of chord V.
So those are all possibilities.
The reason why I wouldn't
choose a chord V there is this.
If I had a chord V,
I'd have F in the bass
followed by E-flat in the bass.
F, E-flat is also in the tune.
So if we want F in the tune
and E-flat in the bass,
we would have blatant consecutive octaves.
So V just really can't be used
if we're going to have
that chord after it.
III is a bit unlikely.
So, I feels good
and to have a mixture
of root position chords
and first inversion chords works well.
So we could do that.
When it comes to this note,
this is keeping a bit of
contrary motion going.
I've got E-flat in the tune
and I've decided at the moment
to treat that as the root
position chord on E-flat.
E-flat, G, B-flat,
which gives me chord IV in B-flat major.
I could've gone for a chord II
because E-flat is the third in chord II.
I could've gone for a chord VII
because E-flat is the fifth in a chord VII
but chord VII doesn't always
work brilliantly does it?
So we have to be a little
careful with chord VII.
So in fact chord IV in root position
would work fairly well.
So if I do that I'm going
to leave it as a 5-3.
The only other possibility that
you might just consider here
is to put a C in the bass.
That's a slightly more risky possibility
but here it comes as a possibility anyway.
And I'm going to put a 6 there.
Now let's see what this actually means.
If see is being used as
first inversion chord,
then C must be the middle of a triad.
So that's the third of a triad.
So the triad must be A, C, E-flat.
Now didn't I just say that
that could be chord VII
and chord VII is a chord we want to avoid?
That's true.
However, chord VII does
works particularly well
in first inversion.
It doesn't work very well in root position
but it works well in first inversion.
So you could have chord
VII in first inversion
if you want to.
Slightly risky, because
we're going down by step
and we're going down by step here
so we've always got the risk
of those consecutives looming
but if you feeling ready to take that risk
there's a possibility.
If you'd rather play it safer,
move up to the E-flat and
call that a 5-3 chord.
Okay.
Moving on to the next pair of bars.
You might notice there's a sequence.
Do you see these three notes,
are repeat it a third lower?
So it could be that
whatever pattern of chords
we've got in this bar,
it might just repeat in the next bar.
Well have a little think
about that in a moment.
B-flat is the next note.
B-flat's the root of a chord I,
it's the third of a chord VI,
and it's the fifth of a chord IV.
I'm going to suggest that
we go for the chord VI.
Not the only possibility.
We could easily use one
of the other possibilities
but it'd be quite nice at
this point to have chord VI.
Chord VI is a minor chord.
We've just had two major chords
and rather than go back to chord I
because we just had chord I there,
it just makes life a little
bit more interesting.
Why have we not got an asterisk
on the second beat of the bar
but we've got one on the third?
Because this C is passing note.
So it could just sit on a G I suppose
because G, B-flat, and D,
well there's B-flat and there's D.
But that would make the harmonic
rhythm a little bit slow.
Wouldn't it?
So, we've got an asterisk anyway
that's telling us to change the chord.
So we've already got to
change at the end of the bar
just because of the asterisk
but also just to keep the harmonic rhythm.
It's changing on nearly
every minim beat isn't it?
We've had two beats on this
so we probably need to
shift on the third beat.
I'm going to suggest
that we put an F in there
and you might wonder
why I've gone for an F.
Well, let's have a think about it.
We've got D and we've got F.
So those two notes are either the third
and the fifth of a chord I
or there they're the root and
the third of that chord III.
Slightly unusual chord.
I didn't say we couldn't use it
but we going to use it rarely.
However if the F is in the bass
then it's a chord IIIb.
So that is a first inversion chord.
Again not the only possibility.
There are other things you could do
but let's put it in first inversion.
So we'll write a 6
which is telling us it's
a abbreviation for 6-3,
first inversion.
Now, we said this might be a
sequence so if that works there
and this is a third below that,
what happens if I put this
bar here a third lower?
Let's just see if it works.
Let's test it out.
That was 5-3, followed by a 6-3.
Well, 5-3 here.
E-flat, G, B-flat.
Oh that's handy, isn't it?
E-flat, G.
That fits.
Passing note.
What happens if we then
call that D in the bass a 6,
a first inversion?
Well, that's going to tell us that D
is the third of a triad that
contains B-flat at the bottom
and F at the top.
It fits with the B-flat doesn't it?
So 5-3, 6-3.
5-3, 6-3.
Just keeping our sequence
going there, isn't it?
And then we've just got
one note left to put in
and we've got C in the tune.
So if we've got C.
C is the root of chord II.
C is also the third of a chord VII.
And C is the fifth of a chord V.
So really we've got chord
V or we've got chord II.
I'm sort of thinking
about avoiding chord V
because chord V it just about to appear
around the corner.
So how about we go for a chord II.
We could either go for
a II in root position
if I put a C in there
that would give me II in root position
or we can have a IIb chord
with an E-flat in the bass.
Maybe well go for that.
There's an E-flat in the bass
and we'll put it in first inversion.
So that's one possible working
of this kind of exercise.
Let's hear what it sounds like
if I play the top and the bottom
and insert the missing
notes of the chords.
That seems fairly satisfying to me.
Not the only possibility
but at least it gives you an idea
how to work this kind of exercise.
