- Hi, I'm Gareth Green,
and in this video we're going to work out
how to realise a more advanced figured bass.
Now, when I say more advanced,
it's simply that we've done another video out there,
which was how to realise a simple figured bass.
So this is not ultra advanced,
but it's more advanced than simple, if that makes sense.
So if figured bass is a relatively new thing to you,
or the idea of realising a figured bass is new to you,
you might want to look at that other video
on how to realise a simple figured bass
and then come back to this one.
But let's move on for now.
And what I've got up here
is a summary of the basic diatonic chords.
So any chord that's inside the key,
so if I'm in C major,
chord I, II, III, IV, V, VI, VII,
those are my seven diatonic chords.
If I have a root position,
that's known in figured bass as a 5-3 chord.
Just to recap why that is,
if I have C in the bass,
three means play a third above the C,
so C, upper third is E,
and five means play of fifth above C, which is G.
So my chord is C, E, G,
which you can see is a root position chord.
Once I've got those notes,
I can distribute them in any way I want to.
So as long as I keep C in the bass,
and I'm using E and G because they're five and three,
I can organise that chord in any way
that takes my fancy.
And when we use a 5-3 chord in figured bass,
actually we leave it blank.
So if you see no number at all underneath the note,
then you know it's a 5-3 chord, a root position chord.
So looking at this example,
the very first note is E and it's blank, no numbers.
So it's a 5-3 chord.
So it's a root position chord on that first note E
so it will be E, G, B.
So it's giving me a root position of an E minor chord,
so I can organise that in any way that I want to.
Okay.
If I want a chord in first inversion,
it works out to be a 6-3 chord.
And in figured bass, we abbreviate that as a 6.
So let's look at the second note of this example.
You can see I've got D-sharp in the bass.
So 6 is abbreviating 6-3,
and I'm expecting to see and hear a first inversion chord.
Let's see how that works out.
Well, three above D-sharp is F-sharp.
It's F-sharp because that's in the key signature.
Six above the D-sharp is B.
So there's my 6-3 chord,
And you can see it's a B major chord
in first inversion, or in the key of E minor,
which this piece is in,
it's chord V in first inversion.
So again, if I use those notes,
D-sharp, F-sharp, B,
I can use them in any order I want to,
as long as D-sharp is in the bass.
Okay, so that's how that works.
If I have a second inversion chord,
that will work out to be 6-4.
I haven't got any examples in this particular extract,
but that's fine.
I've done that on purpose,
because you don't get every chord
in every few bars of a piece of music.
But if I had say, that first note E,
and it said 6-4, well the forth above E is A,
the six above E is C,
so that's my 6-4.
And of course, it gives me an A minor chord
in second inversion.
So in the key of E minor, its chord IV
in second inversion.
So you see how these things work.
Root position is always 5-3.
First inversion is always 6-3.
Second inversion is always 6-4.
5-3 we abbreviate to blank.
6-3 we abbreviate to 6.
6-4 we write out in full,
because that's the least common presentation.
There are many more root positions
than there are first inversions.
There are many more first inversions
than there are second inversions.
Okay, now that's fundamentally what you need to know,
but we also need to know about seventh chords.
So I'm going to talk about seventh chords for a moment.
Okay, so let's just then add to our list
seventh chords.
Okay, and I'm going to talk about
each of the positions here.
So if I've got a seventh chord in root position,
what might that look like?
We're in the key of E minor,
So let me take a dominant seventh.
That's the most common seventh chord
that you're going to have in Baroque music, certainly.
So if the dominant note is B
and the dominant chord is B, D-sharp, F-sharp,
if I make that a seventh,
I'm going to put A on the top of it.
So what are my numbers then?
Well, the D-sharp is three, the F-sharp is five,
and the A is a seventh.
So any seventh chord in root position
is going to be a 7-5-3.
Okay?
Fine.
Let's talk about seventh chords in first inversion.
So if I take the same seventh chord
and put it in first inversion, I've now got.
D-sharp, F-sharp, A, B.
Can you see what I've now got?
I've got a six, a five and a three.
So that's going to be 6-5-3.
If I go into second inversion,
let's see what we end up with this time.
So now I've got F-sharp, A, B, D-sharp.
So what have I got?
I've got 6-4-3.
Okay, so that becomes 6-4-3.
Okay, and of course, because it's a seventh chord,
it has an extra inversion.
So we also have a third inversion.
Okay, and let's see what happens
when we put it in its last inversion.
We've got A, B, D-sharp, F-sharp.
So what's this?
It's 6-4-2.
Okay, so 6-4-2.
Sorry that's a slight squeeze on the board, isn't it?
But there we are.
Now that gives you all the inversions of any seventh chord.
It doesn't have to be a chord V7,
could be a II7, could be any other seventh for that matter.
And we also have abbreviations.
So the root position is a 7-5-3
and we abbreviate it 7.
What's the logic of that?
Well, we said that 5-3 abbreviates to blank.
So we blank out the 5-3,
all that's new is seven.
So that's kind of logical, isn't it?
First inversion is a 6-5-3,
and that's going to abbreviate to 6-5.
Well, what's the logic of that?
We can't abbreviate to 5-3,
because that means an ordinary chord in root position.
We can't abbreviate to 6-3,
because that's a diatonic chord in first inversion.
6-5 is the only abbreviation you can use,
so there's a kind of logic in this.
Okay, second aversion is a 6-4-3.
Well, we abbreviate that to 4-3.
Again, think of the logic.
You can't abbreviate 6-4,
because that looks like a second inversion triad.
You can't abbreviate 6-3,
because that looks like a first inversion triad.
So the only thing you can do is 4-3.
And the third inversion, 6-4-2
abbreviates to 4-2.
So that gives you all the abbreviations of seventh chords.
And really, if you want to realise figured bass,
so you either writing harmony from figured bass,
or if you're playing this as a keyboard player,
just by reading the figured bass,
that's essentially what you need to know about your chords.
What are the triads and a key in root position,
first inversion, second inversion?
How do the seventh chords work out in root position
and in first, second and third inversion.
That's basically what you need to know.
Other things you might need to know about are these.
Well, you might notice occasionally
you have an accidental next to a number.
So if you look in bar five of this particular piece,
you'll see I've got #4-2.
Well, 4-2 is here.
It's an abbreviation of 6-4-2,
so it's the third inversion of a seventh chord.
But because it says sharp four, it's just saying, well,
what's the fourth degree of the scale above the bass note?
Sorry, the fourth above the bass note
is a clearer way of expressing that.
When you come to the fourth above the bass note,
sharpen it.
In this case, raise it a semitone.
So I've got A in the bass,
and I've got four is the D, two is the B,
but I want that D to be sharp.
So it's going to be a D-sharp.
So you see if you have an accidental next to a number
it's telling you about that particular note.
If you have an accidental sitting on its own
without reference to any number at all,
it always refers to the third.
So if you look at the last two chords of this extract,
you can see that I've just got a B followed by an E,
and underneath the B there's a sharp sign.
Underneath E there's a sharp sign.
So it's the third, so these are 5-3 chords,
because they're blank, aren't they?
But the third is sharp.
So when I've got B in the bass,
I'm going to have a D-sharp as the third,
and F-sharp as the fifth.
F-sharp because of the key signature.
When I come to the last chord, I've got E.
It's a 5-3.
The third above it is G, but it's going to be G-sharp,
and the fifth is going to be B.
So this whole piece of music is in the key of E minor,
but because I've got that little sharp under the last note,
it's really making the last chord E major.
So it's in E minor.
You might expect it to finish on an E minor chord,
but it's actually a finishing on an E major chord.
It's what we call Tierce de Picardie
and there's another video on Tierce de Picardie
on the channel if you want to find out about
Tierce de Picardie.
But it's essentially when you're in a minor key,
you just want to finish on the tonic major chord.
So you can begin to see how some of this
greater detail of figured bass works out.
Sometimes in figured bass,
you get numbers that tell you about melodic movement.
So for example, if you have a look at the end of bar three,
you can see I've got A in the bass,
and we've got 6 dash 5.
So it's not six above five.
So it's not telling us this,
a first inversion of a seventh.
It's 6 dash 5, so it's telling us something melodic.
And what it says is in any of the parts above the bassline,
you can go to a six followed by a fifth,
but keep that in the same part.
So for example, if I decide in the soprano part,
I'm going to go 6 dash 5, I'm going to go F-sharp, E,
but I'm not going to go F-sharp in the soprano
then E in the tenor part, or something like that.
It's going to be in the same part.
But if I wanted to do it in a middle part, I can do that.
For example, where I've gone F-sharp, E
in the middle part, and I've got
another note of the chord sitting above it.
So figured bass normally tells you about chords.
Sometimes it tells you about melodic movement.
What this doesn't cover is things like suspensions,
but they would look like that, 6 dash 5.
But we'll come back to suspensions on another occasion.
So when we're talking about realising a figured bass,
there'll be people out there who
are just wanting to understand figured bass
and how it works.
Hopefully this helps to explain that.
There'll be people who've got to
kind of realise some figured bass for an exam
where they've got to do it on paper
and come up with the right chords.
So if you're going to do that,
well, the figured bass tells you about
these intervals above the bassline,
and I hope information shared here
is really going to help you to do that.
But I think it's really good to sort of
translate that to Roman numerals a little bit as well
so you can see where the cadences are.
You can think about how one chord
progresses to another and so on.
But the real joy of working with figured bass
is to be able to sit down at a keyboard instrument
and play it from the score that you see.
And that's what these Baroque players did
and Baroque composers did
who were directing often from the keyboard.
They were just realising, just playing the figured bass.
The wonderful thing about figured bass
is it's really logical
and it covers all sorts of things.
You might think, "Well, how do they cover modulation
"and how do they cover this?"
Well, the numbers take care of everything.
So for example, I've slipped in something
just to sort of show you this.
If we look at the end of bar six,
you can see in the bass there's a G-sharp
and you might be thinking,
"Well, why is there a G-sharp
"if I'm in the key of E minor?"
Well, that G-sharp is temporarily taking us to A minor.
So if we kind of convert this into Roman numeral thinking,
the G-sharp looks as if it might be something
to do with chord Vb in A minor.
And the first note of bar seven
could be chord I in A minor.
So if we're going V-I in A minor.
In this case, we're going V7b to I in A minor,
because that's what the 6-5 is telling us.
Well, if I gain some kind of V-I in a different key,
that looks like it might be a secondary dominant
when we go V-I temporarily in another key,
and then we carry on and the original key.
That's kind of what's happening here.
So even things like that,
you can show how a secondary dominant would function
in figured bass.
So the thing then is just to get fluent
in finding your way around these chords
so that you can go through
and actually realise this at the keyboard.
So it might come together as something like this.
That's a way of putting it in
fairly straightforward block chords.
And that might be a very appropriate way
to play figured bass if you were in a very
kind of chordal environment say,
accompanying a choir that's singing something
like a chorale going from chord to chord,
that would be a good way to do it.
You might want to be doing something
with some figuration,
but it was still involve the same chords.
Something like that, you know.
You can just use some inessential notes
to make it a bit more decorative, a bit more figurative.
Depends on the style and mood of the piece.
One thing I should just point out is what these lines mean.
Do you see in bar two, for example,
we've got this continuous line?
Well, what that means is
the first note of bar two is a 5-3 chord.
So above E I've got a G and a B,
so I'm putting down that chord,
and the line says just hold onto that chord
while the bass moves to the next thing,
and then when you see a new number,
okay, move on to that chord.
So the F-sharp in the bass there is actually a passing note.
So we don't want to have a new chord on the passing note.
It just wants to pass between those harmony notes.
So the continuous line says hold onto this chord
and then change.
You don't have to sustain the chord.
You could move the chord to some other formation
of that chord as long as it's the same chord.
But I'm changing to a different chord, that's the point.
And then you'll notice of, course, in bar five,
we've got the sharp 4-2
with these continuation lines as well.
Well the reason for that is the bass
is just leaping an octave
but the chord is the same.
So you can sustain the chord,
or you can think I'll keep the same chord,
but I'll move to a new position in the right octave.
You could even put a passing note in
just to spruce it up a bit.
And of course, when you're realising figured bass,
you probably want to put some inessential notes in
just to make it slightly more interesting.
So I hope that progresses the journey
of learning to understand figured bass,
realising that one could write a bit
of written harmony from figured bass,
and most importantly, could realise this at the keyboard.
If you found this something that's really engaging you,
and you want to know more about it,
or feel that your knowledge needs reinforcing,
have a look at our Advanced Theory course
at www.mmcourses.co.uk.
And that will really tell you much more about it.
You could also look at our Keyboard Harmony course,
that would get you more fluent at
doing this under your fingers.
If you're wanting to hear all this stuff
with greater facility,
have a look at our Aural Dictation course.
Lots of different causes out there,
but those would be perhaps of particular interest.
And while you're on the website,
on the homepage, you'll see one of the links
takes you to Maestros,
and you might be interested in Maestros,
because it gives you discounts on courses,
and it gives you all sorts of other perks,
including access to our monthly livestreams,
where we study music together,
we give individual feedback
on compositions and performances and so on.
So that may be something that's also of interest to you.