The Mechanics of Modulation

Introduction: Changing the Home Base

Up to now, every progression you've written has stayed in one key from start to finish. Real music rarely does. A sonata movement, a hymn tune, a pop bridge, a Bach chorale: almost all of them travel to at least one new key and (usually) come home again. Changing the tonal center is called modulation.

Modulation is what gives longer pieces their sense of journey. The home key feels like the ground floor; moving to a new key is like climbing to a new level of the building, with a different view. And just as with a building, the easiest way up is the one that's built right in: a shared floor between the two levels. In harmony, that shared floor is the pivot chord.

Click any example to hear it.

Tonicization or Modulation?

Not every chromatic note means a new key. When a chord briefly borrows the dominant of another degree (V/V, for example) and the music returns right away, that's a tonicization: the new tonic is decorated, not established. A modulation is a real change of key. The test is the cadence: a modulation is confirmed when the music reaches a cadence, usually a perfect authentic cadence, in the new key.

Closely Related Keys

Most modulations go to a closely related key: a key whose signature differs from the home key's by no more than one sharp or flat. Every key has exactly five closely related keys:

• its relative major or minor (same signature)
• the key one sharp more (one flat fewer), and that key's relative
• the key one flat more (one sharp fewer), and that key's relative

Here's a shortcut that's easy to remember: the closely related keys are exactly the keys whose tonic chords are the major and minor triads of the home key. In C major, those triads are ii, iii, IV, V, and vi, so the closely related keys are d minor, e minor, F major, G major, and a minor. (The diminished vii° can't be a tonic, so it doesn't count.)

The most common destinations by far are the dominant key (V) from a major home key, and the relative major (III) from a minor home key. Nearly every Classical sonata exposition and Baroque binary movement does one or the other.

Shared Chords: The Pivot

Because closely related keys share all but one of their pitches, they also share several triads. C major and G major share four:

A pivot chord is one of these shared chords, heard first as a chord in the old key and then reinterpreted as a chord in the new key. The modulation sounds smooth because nothing about the pivot itself is surprising; only what follows it tells you the key has changed.

We show the double meaning with two lines of Roman numerals: the old key on top, the new key underneath, overlapping at the pivot. Some teachers draw a bracket around the pivot; others write the two names stacked.

Choosing a Good Pivot

• The best pivots are predominants in the new key. A pivot that becomes ii or IV in the new key (iv or VI in a minor key) leads naturally to the new dominant and then the cadence.
• Avoid the new key's V as a pivot. The new dominant should be the first chord that clearly belongs only to the new key, so it shouldn't also be the pivot.
• The pivot comes right before the first chromatic chord. To find a pivot when analyzing, locate the first chord with the new key's accidental, then step back one chord: if that chord makes sense in both keys, it's your pivot.
• Confirm with a cadence. Follow the pivot with the new key's dominant and a PAC. Without a cadence, you've only tonicized.

Three Common Modulations

Major to the dominant key. The new key's leading tone is the raised 4̂ of the old key (F♯ in C, C♯ in G). This is the move in almost every Classical exposition.

Minor to the relative major. No new accidental appears; instead, the old key's raised leading tone simply stops appearing. In A minor, G♯ disappears and G♮ becomes the 5th of C major's V.

Major to the relative minor. The new leading tone is the raised 5̂ of the old key: G♯ when C major moves to A minor, A♯ when D major moves to B minor.

How to Analyze a Modulation

1. Play or scan to the end of the passage. Where does the final cadence point? That's your destination key.
2. Find the first accidental (or the first missing one) that belongs to the new key. It's usually the new leading tone, inside the new V.
3. Step back to the chord just before it. If it's diatonic in both keys, it's the pivot. Label it in both keys.
4. Analyze everything before the pivot in the old key and everything after it in the new key.

Direct (Phrase) Modulation

Sometimes there is no pivot at all. A phrase ends with a cadence in one key, and the next phrase simply starts in the new key. This direct or phrase modulation is common in hymns, marches, and popular songs (think of the final-chorus key change a half step or whole step up). Because there's no shared chord, it sounds more abrupt, which is often the point. Later, in Chapter 23, you'll also meet chromatic pivots, which open the door to keys that aren't closely related.

Try It: The Pivot Finder

Summary

• A modulation establishes a new tonic with a cadence; a tonicization only borrows it briefly.
• Closely related keys differ by at most one accidental: the relative, the dominant and subdominant keys, and their relatives. Their tonics are the major and minor triads of the home key.
• A pivot chord belongs to both keys. Label it twice, with the old key on top and the new key below.
• The best pivot becomes a predominant in the new key; the new dominant comes next, then a cadence.
• To analyze: find the destination cadence, find the first new accidental, and step back one chord to the pivot.

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