Techniques of Modulation

The four preceding lessons used notes from outside the scale while keeping the key. Secondary dominants, borrowed chords, the Neapolitan, and augmented sixths all end up back on the tonic of the original key.

This lesson does not go back. It moves the key itself.

Modulation and transposition are different things

First, separating the terms.

• Modulation — the key changes partway through a piece, and the listener perceives the change
• Transposition — the entire piece is rewritten at another pitch level, and the listener perceives only the same piece

Transposition is a practical operation, for finding a comfortable range to sing in or accommodating an instrument. Modulation is a compositional technique for building structure. The words resemble each other and nothing else about them does.

Measuring closeness — three axes

Any key can be reached, but some are nearer than others, and closeness has three measures.

Direction	From C major	Difference in signature
Adjacent on the circle	G major (dominant), F major (subdominant)	1
Relative	A minor	0
Parallel	C minor	3

Keys reachable by combining these directions — the relative of the dominant, the relative of the subdominant, and so on — are generally counted as closely related keys. From C major that means roughly G, F, Am, Em, and Dm.

The difference in the number of accidentals is the clearest measure of distance. Going from C major (none) to F-sharp major (six sharps) is a difference of six with few shared notes, which makes it a distant modulation.

Bridging on a common chord

The smoothest method is to find a chord belonging to both keys and switch its meaning there. That is a pivot chord.

Setting the diatonic triads of C major and G major side by side:

Chord	In C major	In G major
C	I	IV
Em	iii	vi
G	V	I
Am	vi	ii
Dm	ii	(absent; G major has D)
F	IV	(absent; G major has F#dim)
Bdim	vii°	(absent; G major has Bm)

Four are shared. Each of them carries two meanings at once, so passing through one gives you the opportunity to switch the listener’s interpretation.

In Fig. 1 the C chord does not change meaning as it sounds. At the moment it is played it is still I in C major. Only when the D7 arrives and the F# sounds does the listener retroactively reinterpret it: “that C was IV.”

That retroactive shift is what makes modulation interesting. Nothing whatever happens to the pivot chord itself.

Modulating through a pivot, and modulating abruptly

▶Through a common chord▶Direct

Check: Both end on the tonic of G major. The first slips in through the C chord as a bridge, and it should be hard to say exactly where the boundary was. The second throws the dominant seventh of G major immediately after a C major chord, so the switch is plainly visible. It is a choice between smoothness and surprise.

C – F – C(=IV) – D7 – G

Check

How many diatonic triads do C major and A minor share? Treat A minor with harmonic minor, as harmonic practice requires.

5all 724

Check answer

Forcing entry with a dominant seventh

The other basic method is to place the dominant seventh of the new key outright. It can be seen as an extension of the secondary dominants of the earlier lessons.

A secondary dominant relocates the tonic temporarily and returns immediately. Stay instead of returning and it is a modulation. The only boundary between them is how long the music remains in the new key; the chords themselves are no different.

The decisive element in Fig. 2 is the G#. That note exists neither in C major nor in A natural minor. It appears only as the leading tone of harmonic minor, so the moment it sounds, arrival in A minor is unambiguous.

From which the condition for a modulation to register follows.

The music must pass through a dominant-to-tonic motion in the new key, sounding that key’s leading tone.

Without it, a listener hears only that a borrowed chord went by. That is exactly the difference from a secondary dominant.

Rereading one sonority through another spelling

The technique touched on at the end of the previous lesson pays off here. A German sixth and a dominant seventh sound exactly alike.

The German sixth in C minor is Ab C Eb F#. Rewrite the F# as Gb and it becomes Ab C Eb Gb, which is Ab7. And Ab7 is the dominant seventh of D-flat major, so it can resolve to Db.

Reading	Chord	Destination
Ab C Eb F#	Ger6 in C	G (the dominant of C)
Ab C Eb Gb	V7 in D-flat major	Db (the tonic of D-flat major)

Not one sounding note changes. Only the notation changes, and with it the destination switches to another key. This is enharmonic modulation.

C and D-flat major are distant on the circle of fifths. Being able to join them with a single chord depends on the augmented sixth’s property of admitting two readings of the same set of pitches.

One chord with two destinations

▶Resolving as an augmented sixth▶Resolving as a dominant seventh

Check: The first three chords are identical across both variants. Only the fourth differs. The first proceeds to the dominant of C minor, the second to the tonic of D-flat major. You are hearing the same chord, and what follows it changes the answer to the question of what it was. Reinterpretation is precisely the act of defeating the listener's prediction.

… → Ger6 → V (staying in C minor)

Check

Why is enharmonic modulation useful for jumping to a distant key in one move?

One sonority carries different functions in two keys, so it can join them regardless of distance on the circle of fifthsThe key signature does not have to changeIt avoids using a dominantIt avoids using a common chord

Check answer

What modulation is for

Formally, modulation is a device for creating contrast. That is why the B section of a ternary form in Unit 7, and the second theme of a sonata form, are presented in another key.

And returning is assumed. The further the music travels, the greater the reassurance on coming home. The principle from Unit 7 — that return converts memory into reward — operates at the level of key as well.

▶ Check closely related keys on the circle of fifths Tapping a key shows its diatonic chords. Move to an adjacent key and count how many chords are shared. Neighbors share four; two steps apart drops that to two Circle of Fifths →

That completes chromatic harmony. This unit covered using notes from outside the scale while keeping the key — secondary dominants, borrowing, the Neapolitan, augmented sixths — and moving the key itself, through modulation.

The next unit looks at music from after these rules stopped being rules: twentieth-century harmony and popular music.