Modulation

Modulation is the act of changing the tonal centre of a piece — moving from one key to another mid-flow. It is the single most important large-scale tool in tonal composition. Without it a piece would stay in one key for its entire duration, which is acceptable for a hymn but disastrous for a sonata. With it, a composer can build entire architectures of contrast and return that audiences feel as drama, even when they cannot name what is happening.

There are four main techniques: the common-chord (pivot) modulation, the common-tone modulation, the chromatic modulation, and the enharmonic modulation. They differ in how smoothly the new key is introduced and in how far the new key sits from the old one on the circle of fifths. Each has a characteristic sound and a characteristic use.

A piece that stays in one key for fifteen minutes is exhausting; the ear gets used to the tonal palette and stops listening. Modulation refreshes attention. The classical sonata exposition typically modulates from the tonic to the dominant; the development wanders through several keys; the recapitulation returns home. The whole architecture is a journey of departure and return, and the cadences of each modulation are the milestones along the way.

The common-chord modulation pivots through a chord that exists in both the old and the new key. C major and G major share four diatonic triads (C, Em, G, Am); any of those four can serve as a pivot. Approach the pivot in the old key, leave it as the new key, and the modulation feels seamless. The listener hears the change but does not hear a join.

C major:  I    →  IV   →  ii  =  vi   →  ii  →  V  →  I
G major:                       =  ii  →  V   →  I  ← key arrives here

A common-tone modulation pivots on a single note rather than a whole chord. Hold the note across the boundary and use it to mean something different in the new key. The note that was the third of C major (E) becomes the root of E major; the bass drops away and the new key is established by what follows. Schubert was a master of this, often using common-tone modulations to slip into chromatic third relationships that the common-chord technique cannot reach.

Common-tone modulations sound more dramatic than common-chord modulations because the harmonic context of the held note changes audibly. The listener hears the same note as something different — what was a stable third becomes an unstable root, or vice versa. The technique is the bridge between common-practice tonality and the more chromatic harmony of the late nineteenth century.

The chromatic modulation jumps directly from a chord in the old key to a dominant seventh in the new key, with the chromatic motion of one or more voices smoothing the join. There is no diatonic pivot — the modulation is essentially a sudden announcement of the new key. Beethoven used chromatic modulations for surprise; Wagner extended them so far that the home key sometimes vanishes for hundreds of bars at a time.

Chromatic modulations work because the ear can follow stepwise voice leading more readily than it can follow leaps. Even when the harmony jumps a great distance on the circle of fifths, if every voice moves by a semitone the modulation lands. This is the trick behind almost every late-Romantic harmonic surprise — the surface motion is small even when the structural motion is large.

An enharmonic modulation reinterprets the spelling of a chord — typically a German sixth or a fully diminished seventh — to land in a key remote from the original. A German augmented sixth in C major (A-flat, C, E-flat, F-sharp) sounds identical to a dominant seventh in D-flat major (A-flat, C, E-flat, G-flat). Spell it the second way, follow it with a tonic D-flat, and the modulation has happened.

Diminished sevenths are even more flexible. Because the chord is symmetrical and divides the octave into four equal parts, every inversion sounds like another root position, and any of its four notes can act as the leading tone in a different key. The same diminished seventh can resolve to four different keys depending on how it is spelled and approached. Mozart, Beethoven, Schubert, and Chopin all use this trick for sudden modulations to remote keys.

Modulations to keys one step away on the circle of fifths sound smooth and almost imperceptible. Modulations of two or three steps sound fresh and noticeable but graceful. Modulations of four or more steps feel remote; the listener registers a definite shift of colour. Modulation by tritone — six steps, the maximum distance — is the most dramatic harmonic move available in tonal music, often used as the climactic gesture of a development section.

• Closely related (one step): use a common-chord pivot.
• Two or three steps: pivot still works, or common-tone for variety.
• Four or five steps: chromatic or enharmonic modulation begins to suit better.
• Six steps (tritone): enharmonic with a diminished seventh is the classic move.

What goes out must come back. A piece that modulates and never returns to its tonic is a piece that fails structurally — though composers from Mahler onwards have made structural use of refusing to return. In classical and Romantic forms the return is part of the meaning, and the recapitulation is itself a kind of cadence at the level of the whole movement. Listening for the moment of return is one of the great pleasures of long-form music.