Music Theory for the 21st-Century Classroom

Studying modulation will require us to distinguish between tonicization, which we studied recently, and modulation. Tonicization, involving secondary chords, can be as short as two chords (\(\left.\text{V}\middle/\text{V}\right.\) to \(\left.\text{V}\right.\), for example) but can sometimes encompass several measures as in the following example.

Below is a reduction showing the underlying diatonic progression of the example above.

A modulation to a new key requires an eventual cadence to confirm that new key. This cadence will often (though not always) have the following cadential formula:

In his book Form in Tonal Music, Douglass Green defines a \(\left.\text{V}\right.\)–\(\left.\text{I}\right.\) authentic cadence with a pre-dominant prefix as a “full cadence.”

The cadential formula above is found in the following example.

Notice that this cadential formula establishes a key more strongly than the simple \(\left.\text{V}\right.\)–\(\left.\text{I}\right.\) of an authentic cadence. This means there will be ambiguity between a tonicization and a short modulation ending in an authentic cadence, especially in music with fast harmonic rhythm, like Bach chorales (usually in quarter-note harmonic rhythm).

To determine pivot chords and the new key, listen to the music to hear the cadence in the new key, then work backward from the cadence to see if the dominant in the new key was approached by pre-dominant chords (\(\left.\text{ii}\right.\) or \(\left.\text{IV}\right.\)) in the new key. Then, analyze from the beginning of the phrase until you reach the new key. Finally, look for a logical pivot point. Sometimes two successive chords could logically be pivot chords. If so, include two chords on either side of your pivot bracket.

Before we start analyzing and writing modulations, we will examine key relationships and pivot chords.