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Figured Bass Lesson 6: Modulation

Grade 7 Music Theory Figured Bass 6: Modulation

At grade 7, it’s very likely that the figured bass exercise you are given in the ABRSM exam contains some modulation, or passes through different keys.

  • A true modulation occurs when the music changes from one tonal centre to another, and stays there for some time. For example, a piece could start in A minor, modulate to E major and then continue in that key for a while. It’s usually relatively easy to spot a modulation and work out which keys are involved.

  • When a piece of music passes through various keys, it can sometimes take a little bit more detective work to figure out what’s going on. When music passes through a key, that key might only last a very short while – even perhaps just one chord. And it’s possible to move through several keys in quick succession.

 

Related Keys

Music from this era (late Baroque/early Classical) usually moves to a closely related key, whether as a modulation, or just passing through.

The most closely related keys are the dominant and subdominant, the relative major/minor, and the parallel key. (“Parallel” keys are C major and C minor, for example. Any of the closely related keys can be used in its parallel form too.)

For example, if the piece begins in C major, then the most closely related keys are these:

  • C minor (parallel key)
  • A minor (relative minor)
  • F major (subdominant)
  • G major (dominant)

But, as soon as the key passes from C major to one of these related keys, it might either return to the original key, another closely related key or pass through the next level of related keys.

Let’s say C major passes through A minor. From this point, the next key to pass though could be related to C major again, or to A minor:

  • A major (parallel key)
  • C major (relative major)
  • D minor (subdominant)
  • E major (dominant)

And so on. So as you can see, you can move from C major to E major very quickly, although they are not closely related to each other.

It’s also worth remembering that the dominant chord is occasionally used in its minor form (parallel), in a minor key. For example, in A minor, we would normally expect the dominant chord to be E major, and a modulation would be to the major key. But you could equally modulate from the key of A minor to E minor.

 

Spotting Key Changes in a Figured Bass Exercise

Usually you will easily be able to see where a key change is happening – there will be accidentals in the music which do not fit the current key. If the piece begins in C major and you see an F#, that is a good sign that the music is modulating to G major. Don’t forget though, that accidentals can be used simply because the piece is in a minor key, or as chromatic melodic decoration.

There may be no visible accidentals, however, when the music modulates between the relative major and minor, since they share a key signature.

 

Working Out Key Changes in Figured Bass

Once you have identified the place where a key change (or changes) is happening in a figured bass exercise, you’ll need to work out what that key is, so that the correct chord can be figured.

It’s essential to remember that at this period, most modulations were created with the use of chord V or V7 in the new key. (An exception is when the music moves into the parallel key: when C minor moves immediately to C major, for example.)

Don’t forget that chord vii° is considered to be a V7 substitute. The chord notes F#-A-C, for example, make up chord vii° in G major. V7 in G major is D-F#-A-C – it’s the same as vii° with a missing root. In the following paragraphs, chord vii° also works wherever you see V7.

Important: When used as a tool for modulation, the dominant chord will always be in its major form.

 

Let’s go back to the list of closely related keys, and examine the chords which would be expected at those modulations.

  • C major > F major: via C (C-E-G) or C7 (C-E-G-Bb)
  • C major > G major: via D (D-F#-A) or D7 (D-F#-A-C)
  • C major > A minor: via E (E-G#-B) or E7 (E-G#-B-D)

In order to know which is the correct chord to figure at a modulation, follow these steps:

  1. Work out the key up to this point, and list the closely related keys. This narrows down the possibilities!
  2. Look at the bass and melody lines, and work out which dominant/tonic chords would fit, always remembering to think through the added 7th chords too.
    For example, a C/F# would fit D7, and B/G# would fit E or E7.
    In most cases, an added 7th chord is preferable when the key is changing, as it fixes the new key more strongly. This is particularly important when the key is changing rapidly.
  3. Jot down the chord notes, paying attention to any accidentals which will be necessary to add to the figure.
  4. Look at the next chord for confirmation. Usually, it will be chord I (or i) in the new key. But, there may be another key change to another closely related key instead.

 

An Example from Bach

This is the beginning of Bach’s chorale no. 200, “Christus ist erstanden, hat überwunden”. It starts in C major – this is apparent from the key signature and opening tonic chord.

Bach Chorale 200

 

Chord 2 is G major (V) in first inversion.

Chord 3 contains a suspension. The G is not a “member” of this chord – it’s a hanger-on from chord 2.

Chord 3 contains the notes A-C-F#, which is chord vii° in G major, so at this point the music is passing though G major.

Chord 4 is G major (I). But it includes an F natural passing note, making G-B-D-F, or V7 in the key of C major.

Chord 5 is C major (I), but again the passing note Bb then creates C-E-G-Bb, or C7 in F major.

Chord 6 is F major (I).

Chord 7 is C major, with a suspension. At this point, whether you name this as V in F major or I in C major is a matter of individual perception! After moving through so many keys so quickly, the original tonal centre (key) is lost, and the final chord has some ambiguity about it.

 

Now take a closer look at the bass and soprano lines – in fact, these parts don’t include any of those added accidentals. If you were given this piece as an exercise, you could do it without any key changes at all. However, it’s worth playing it through, to notice how Bach effectively changes key rapidly, and the effect of the added 7th chords. Play it through without the accidentals as well, and compare the results. It sounds fine, but it’s much less interesting aurally.

Bach Chorale 200 unmodulated

 

Occasionally Bach changes to a less closely related key, e.g. in chorale 199 he moves from a chord of F7 immediately to G7. However, you’re not likely to find such a progression in the grade 7 exam figured bass question.

 

Example Figured Bass Exercises

Now let’s take a look at some typical figured bass exercises where a modulation is not optional.

These two bars are taken from the middle of Bach’s chorale no. 215, “Verleih’ uns Frieden gnädiglich”. The key is G minor at the start of the extract.

Bach Chorale 215

 

Notice the C sharp, and also the F (natural) at the end of the second bar. These are clues that the key is changing.

Now find the most likely chord/key for each numbered chord.

Chord 1 is V(7) in G minor (figured 6 or 6-5).

Chord 2 is i in G minor (5-3).

Chord 3 is V(7) in G minor (5-3# or 7#).

Chord 4 is i in G minor (cadence) (5-3). (G major would also work here).

Chord 5, with two G’s, is i again (5-3). (Think through the alternatives and pick the most “usual” chord).

Chord 6 has C# and G, which are both in V7 in the key of D (dominant key). So this is V7 in D (6-5-♮).

Chord 7 has D and F natural, which confirms the modulation to D minor. This is i in D minor (5-3).

Chord 8 with Bb and G is open to interpretation. Look at the next chord for some clues.

Chord 9 with F and C will be an F major chord (5-3). We could then interpret the G/Bb in the previous chord as V7 (6♮-4-3-) or vii° (6♮) in F major – the relative major key. (In fact, Bach uses vii° and the chorale stays in F major for a few more beats.)

 

It can be helpful to try and assume the “most likely scenario”, when you are faced with chords that could be interpreted in different ways. Chords 8 and 9 are a good example of this. The G/Bb in chord 8 could be interpreted as G minor, E° or C7. Chord 9 could be F major or minor. How do you choose the most likely combination?

Firstly, F major is more closely related to the previous key of D minor, than F minor is. F major is the relative key.

Having chosen F major for chord 9, which progression is more common: V7-I, vii°-I or ii-I? Either of the first two progressions is fine, but ii-I is relatively unusual, so choose V7 or vii°.

 

This is the opening of Bach’s chorale no.206, “So gibst du nun, mein Jesu, gute Nacht”.

Bach Chorale 206

 

The key signature is two flats, and the F# in bar 1 should lead you to G minor as the opening key.

The first cadence, at chord 4, is clearly V7-i.

The F natural at the end of bar 1 is a diatonic note in G minor, because it’s part of the melodic minor scale. By itself, it’s not enough to signify a key change.
Take a look at chord 10 though – the pause symbol means this is another cadence (you can also look for longer note values, don’t forget). But the two notes we have to work with are both Bb’s. At a cadence, in the final chord we’d normally expect:

  • A root position chord
  • A doubled root

Which means that chord 10 should be a chord of Bb major.

Chord 9 has the notes A and C – which fit with chord V in Bb major (F major). However, the C in the bass would make Vc, but a second inversion chord would not be acceptable in this position. We should therefore make this a V7c chord. (7th chords can be used freely in second inversion).

 

 

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