Modulation (sometimes called a "key change") involves a longer-term change of tonic.

There are two basic ways a composer can introduce a new key:

A direct, abrupt modulation (Example 1)

A pivot chord modulation, which is more subtle (Example 2)

Sometimes, a composer will blur the lines between a tonicization and a modulation. We refer to such cases as "extended tonicizations."

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We've seen that tonicization involves making a non-tonic chord sound like a temporary tonic. In this chapter, we discuss modulation, which, in contrast to the temporary nature of tonicization, involves a longer-term change of tonic. Sometimes people refer to modulation as a “change of key.”

Analyzing Modulations

There are two basic ways a composer can introduce a new key: they can make the key change abrupt (Example 1), or they can be more subtle about it (Example 2). Two pieces of advice are helpful for identifying modulations:

Remember that cadences establish keys, so if you can identify cadences before you start your analysis, you'll know where new keys occur.

The presence of the same accidentals over and over again in a passage is an indication of potential modulation. If you start seeing a consistent accidental, see if you can identify a cadence that establishes the new key corresponding to the change in accidentals.

Direct modulations (these are abrupt)

Abrupt modulations are often called “direct modulations” because the composer goes directly to the new key. These are also sometimes called “phrase modulations” because they tend to occur at phrase boundaries. To recognize a direct modulation in analysis, simply label the new key, then continue with your harmonic analysis as in Example 1.



Example 1. Direct modulation in Joseph Bologne, String Quartet no. 4, I, mm. 15–29 (0:27-0:56).

Pivot chord modulations (these are subtle)

A composer can use a variety of techniques to make a modulation more subtle, but one of the more common ways to do it is through the use of a pivot chord. A pivot chord is a single chord that is diatonic in (i.e., that belongs to) both the home key and the new key. Example 2 shows that we analyze a pivot chord using a special symbol where the upper Roman numeral labels the chord in the old key and the lower Roman numeral labels the chord in the new key. In measure 6 of Example 2, we would say “iv7 becomes ii7.” There's no single method that always works to find a pivot, but one strategy that's helpful is to analyze in the old key until it stops making sense, then back up a chord and try analyzing that as your pivot. If that chord doesn't work as a pivot either, try backing up one more chord.



Example 2. Pivot chord modulation in Josephine Lang, "Der Winter," mm. 1–12.

Sometimes multiple chords could serve as pivots. In such cases, the best chords are ones where the upper and lower Roman numerals are both predominant chords. That's because V will usually appear shortly after the pivot, and having a predominant in both positions for your pivot chord label suggests that we’re on the way to V in both the old and new keys. Your second best option would be a tonic chord in the old key becoming a predominant in the new key (I becomes IV). Since a tonic chord can go directly to V, the analysis here still makes functional sense. Poor pivot chord analyses are usually ones that involve the dominant. An analysis such as "V becomes I," for example, suggests that the same chord is simultaneously unstable (V) and very stable (I), which isn’t how we’re likely to hear it.

Closely related keys

While a composer may modulate anywhere, some modulations are more common than others because of the number of chords the two keys share. Key signatures within one accidental of one another (e.g., C major and G major) are considered closely related keys, sharing many common chords. To find all of the closely related keys for a given home key, do the following. You may find it useful to reference the circle of fifths (Example 3).

[](https://viva.pressbooks.pub/app/uploads/sites/12/2020/05/Circle_of_fifths_deluxe_de.jpg) Example 3. The circle of fifths. Click to enlarge.

Create a grid with three columns and two rows.

Place the home key in the center of the upper row.

Add a sharp (or subtract a flat—the equivalent of adding a sharp) to the home key’s signature and list that key to the right.

Add a flat to (or subtract a sharp from) the home key’s signature and list that key to the left.

In the lower row, list the relative major or minor keys for each key in the upper row.

If you were to do this with F major as a starting point, you should end up with something like Example 4. Notice that the keys will always correspond to every major or minor triad in the home key’s universe of Roman numerals (so, in major: I, ii, iii, IV, V, and vi; in minor: i, III, iv, v, VI, and VII). This is a good way to check your work.

One step flatwise

Starting key signature

One step sharpwise

starting key

B♭

F

C

relative key

Gmi

Dmi

Ami

Example 4. Identifying closely related keys of F major.

While it's possible to modulate to any key, certain keys are much more common than others:

In major: I→V and I→vi (e.g., C→G and C→Am)

In minor: i→III and i→v (e.g., Cm→E♭ and Cm→Gm)

Writing modulations with pivot chords

If you're writing a modulating phrase that uses pivot chords, you'll need to choose a pivot chord, then determine an appropriate progression.

Identifying potential pivots

To identify potential pivot chords between two keys (Example 5):

Create a table with two columns.

List all triads in the old key on the left.

List all triads in the new key on the right.

Match triads that appear in both columns.

Remember that the best pivots are ones that are predominants in both keys.

[](https://viva.pressbooks.pub/app/uploads/sites/12/2020/08/pivots.png)

Example 5. Identifying piv