III. Modulation and Chromatic Harmony

# 28.1 Introduction

Until now, we have focused on relatively small-scale musical events. Our discussion has focused on topics such as voice-leading and the relationships between individual chords. In this chapter, we will broaden out scope to look at larger contexts in order to address the topic of modulation.

Almost inevitably, a piece of tonal music explores one or more key areas besides the global tonic. Composers incorporate non-tonic key areas to provide contrast and to create anticipation for a return to the global tonic. (It is quite rare, in tonal Western art music, for a piece to end in a key other than the one in which it began.) In some pieces these non-tonic keys are more structurally significant than others. Furthermore, certain key relationships are more prevalent than others—the relationship between the tonic and the key of the dominant, for instance, being by far the most common.

In the chapter off applied chords (Chapter 27) we discussed the difference between tonicization and modulation. This chapter will begin with a similar discussion highlighting several characteristics that define the latter. From there we will move to a generic exploration of the topic, outlining a number of common modulations in both major and minor keys along the way. Finally, the chapter will conclude with a brief discussion of chromatic modulations, setting the stage for similar discussions of advanced techniques in the chapters that follow.

# 28.2 Tonicization vs. modulation

Applied chords, as we saw in Chapter 27, emphasize diatonic chords by momentarily giving them tonic color. However, the diatonic function of the tonicized chord does not change. A ii chord, for example, retains its pre-dominant function even when tonicized by a V7/ii. The progression V7/ii–ii reminds us of the ubiquitous V7–I, but the ii chord remains a pseudo-tonic—it never actually attains true tonic function. In a modulation, by contrast, the listener does hear a new tonic.

One must keep in mind, however, that even a modulation is a temporary change of key because the vast majority of tonal music eventually returns to the global tonic. The important distinction between tonicization and modulation has to do with structural significance. First, non-tonic keys last longer. Unlike a tonicized chord, which retains its diatonic function, non-tonic keys remain in effect long enough to allow listeners to adjust to hearing them as new tonics. Further, they have greater weight because they tend to include one or more decisive cadential progressions.

There are a number of clues that will help you identify modulations. Since a modulation will explore a new key area, accidentals will appear and remain present for a prolonged period of time. Sometimes, for lengthier non-tonic key areas, the composer (or, perhaps, publisher) may even temporarily change the key signature. As mentioned above, strong cadential progressions are particularly effective in confirming a modulation. The presence of a cadence (or several) with a pre-dominant–dominant–tonic progression in a key other than the global tonic is a strong indication that the music has modulated. Tonicizations, on the other hand, are often limited to a single applied chord and its resolution.

# 28.3 Techniques of modulation

One of the most interesting aspects of the topic of modulation has to do with how composers manage to move from one key area to another. Several techniques are common. The simplest one is known as direct modulation. In a direct modulation the composer ends a section in one key (typically with a cadence) and simply begins the next section in another. This technique is a useful way to modulate to the dominant: a composer can end a phrase with a half cadence (on the dominant chord) and then simply begin the next phrase in the dominant key. The following example illustrates this method:

This excerpt begins in the key of G major, which is confirmed by the imperfect authentic cadence in m. 4. In m. 8 we arrive at a half cadence: a D-major chord with a 6/4 suspension in the right hand. After this brief moment of repose, the music continues in D major, with C#s instead of C§s, eventually leading to a perfect authentic cadence in m. 23. The cadence in m. 8 terminates G major, and D major begins directly in m. 9. The change of key is noticeable, but not particularly startling since the same harmony is found at the end of one phrase and the beginning of the next.

Example 28–2 shows another direct modulation:

The first phrase in Example 28–2 ends very clearly in the key of F major with an imperfect authentic cadence. On the fourth beat of m. 2, however, a C# is introduced in the bass. As the rest of the second phrase confirms, the music has modulated to the key of D minor (the relative minor) and C# is the new leading tone. The modulation is immediate: the second phrase begins in the new key directly after the fermata .

Although direct modulations are common in tonal music, they are not always appropriate because of the jarring effect of the abrupt change from one key to another. Composers often strive for harmonic smoothness, which a direct modulation disrupts.

The most common technique for changing keys is with a pivot chord modulation. A chord that occurs diatonically in both keys can serve as a point of overlap—or, pivot—between them. Consider the following chord in the key of Ab major:

This same chord may also appear as a diatonic triad in the dominant key of Eb major:

The most common pivot chords are those that function as a pre-dominant chord in the goal key. The F-minor triad in Example 28–3 and Example 28–4 is an effective pivot because it functions as a pre-dominant chord in the key of Eb, and can lead directly to the dominant which, in turn, resolves to the new tonic and confirms the modulation. In the context of a modulation from Ab major to Eb major, the F-minor chord would initially be heard as the vi chord in Ab major. As the music continues in the new key, the F-minor chord will be retroactively reinterpreted as the ii chord in Eb major. This change in function is typically confirmed by a strong cadence in the new key.

Note: Pivot chords are indicated with two lines of Roman numerals: the original key is usually on top with the new key just below it. An asymmetrical bracket is drawn between the two lines to show where the one key ends and the other begins:

Consider the following example of a pivot-chord modulation:

The beginning of this movement establishes the global tonic of C major and arrives at a (tonicized) half cadence in m. 4. The second phrase, beginning in m. 5, is recognizable as a repetition of the first and continues in C major. The high C, played by the violin in m. 6, is now harmonized, with an A-minor triad. Initially, we hear the chord as vi in C major. The music that follows, however, shows a modulation to G major (the dominant). The first unmistakable indication of the change of key is the dominant seventh of G major—the major-minor seventh chord built on D—in m. 7 which resolves in a perfect authentic cadence in m. 8. In retrospect, the A-minor chord in m. 6 is reinterpreted as a pre-dominant ii chord in G major.

The following example shows a very similar scenario:

Here, after a key-defining phrase in A major (mm. 21–24), we find another phrase continuing in the same key. The D# in m. 26, however, suggests a change of key. The authentic cadence in mm. 27–28 confirms the modulation and invites the listener to reinterpret the F-minor triad on the downbeat of m. 26: what was heard as vi in the original key may now be heard as ii in the new key.

As mentioned above, pivot chords are most effective when they function as pre-dominant chords in the goal key. In both Example 28–6 and Example 28–7 above, the vi chord becomes a pre-dominant ii chord in the new key.

Note: Some of the excerpts in this chapter, including the excerpt shown in Example 28–7, are notably short and the modulations that take place therein do not last very long. One might argue that some of these modulations are in fact tonicizations due to their brevity. Nonetheless, common modulatory procedures are present even at this small scale, and the examples discussed here are useful for demonstration.

# 28.4 Common modulations

Modulation is technically possible between any two keys. As the tonal practice evolved in the nineteenth century, composers explored more and more distantly related keys for their expressive effects. For now, we will limit our discussion to modulations between closely-related keys.

A closely-related key is one whose tonic triad is diatonic in the global tonic key. Example 28–6 contained a modulation to a closely-related key: C major modulated to its dominant, G major. The key of G major is considered closely-related to C major because its tonic triad is a diatonic chord in C major (the V chord). In other words, if the tonic of the new key is a diatonic member of the old key, the two keys are closely-related.

For any given key there are five closely-related keys. For a major key, closely-related keys include those whose tonics are the ii, iii, IV, V, and vi chords. (viio is not included because no key has a diminished triad as its tonic and I has been left out because to modulate to the tonic key would not be a modulation at all!) Closely-related keys to a minor key include those that have III, iv, v, VI, or VII as their tonic. These keys are considered closely-related because they share so many pitches with the primary key. For example, C major differs from the closely-related key of G major by only one pitch: F# instead of F. All of the other pitches are common to both keys. As you may have noticed, the tonics of all the closely-related keys are the same chords that can be tonicized with applied chords.

Activity 28-1

Activity 28–1

### Question

In tonal music, most modulations move to closely-related keys (keys whose tonic triad is a diatonic chord in the original key). Name the five keys that are closely-related to G major.

Hint

For a key to be closely-related to G major, its tonic triad must be a diatonic chord in G major.

A minor, B minor, C major, D major, and E minor.

In the remaining sections, we will look at specific modulatory goals and discuss the potential pivot chords for reaching them. The examples discussed below, however, are by no means the only possible modulations. As mentioned above, over the course of the nineteenth century composers became more adventurous in their modulations for expressive purposes. It became acceptable for pieces to modulate to increasingly distant keys. Accompanying this were several modulatory techniques other than by diatonic pivot. For now, though, our discussion will stick to closely-related keys.

# 28.5 Modulations from major keys

By far, the most common modulatory goal for a major key is the key of the dominant. Because of the close relationship between these two keys, modulation to the dominant provides contrast while maintaining unity in a composition. As mentioned above, one method of modulating to the dominant key consists of ending a phrase with a half cadence and simply continuing with the dominant harmony treated as the new tonic. That method (direct modulation) can also be understood as a pivot-chord modulation. As the dominant chord arrives, it functions as the dominant of the primary key. As the music continues, the chord becomes tonic of the new key.

There are four possible pivot chords between a major key and its dominant. The following table uses C major and G major as examples:

Table 28–1
 C major (the primary key): G major (the dominant key): Chord spelling: I = IV (C, E, G) iii = vi (E, G, B) V = I (G, B, D) vi = ii (A, C, E)

Each row of Table 28–1 shows a possible pivot chord. For example, the second row shows that the iii chord in C major (an E-minor triad) can be reinterpreted as a vi chord in G major (also an E-minor triad). Other chords in the key of C major (ii, IV, and viio) cannot be used as pivot chords because the quality of the analogous chord in G major is different. The chord built on D in C major is minor while the chord built on D in G major is major, and so forth.

Activity 28-2

Activity 28–2

### Question

The dominant key of F major is C major. Name four pivot chords that might be used in a modulation from F major to C major (remember to use uppercase Roman numerals for major chords and lowercase Roman numerals for minor chords):

F major: = = = =

I = IV (F, A, C), iii = vi (A, C, E), V = I (C, E, G), and vi = ii (D, F, A)

Of the four possible pivot chords outlined in Table 28–1, vi = ii is the most common (see Example 28–6 and Example 28–7). The I = IV pivot, though certainly possible, is less common because it is difficult to hear the tonic triad as anything other than I once the key has been established. The same is true for V = I—it is difficult to hear the dominant of a key as anything else without a chord coming before it (in which case, V = I is no longer the pivot chord). The iii = vi pivot is less commonly used because the mediant harmony is relatively infrequent in tonal music.

Nonetheless, examples of these less common pivots do appear with some regularity. The following example shows a modulation to the dominant key via a I = IV pivot chord:

The excerpt in Example 28–8 begins very clearly in the key of Eb major: the entire first line of the song (mm. 916) is presented in the home key and ends with an authentic cadence. The second phrase (mm. 1724), however, ends with an authentic cadence in the key of the dominant, Bb major. This particular modulation is achieved via a pivot chord at the end of m. 22. The Eb-major chord in m. 22, despite being heard previously as the tonic, is retrospectively reinterpreted as IV in Bb major.

As mentioned above, the I = IV pivot chord is not used very frequently because it is difficult to reinterpret the tonic harmony as anything but. In Example 28–8, weak metric placement coupled with the strength of the cadential 6/4 chord helps weaken its authority as tonic. The following example progresses in a similar fashion, though here the pivot appears on the downbeat, at the beginning of the second phrase:

Because the pivot chord appears here in such a prominent position, it is also possible to hear this as a direct modulation with the second phrase beginning without preparation in the new key. Nonetheless, the use of a chord that is native to both keys helps smooth out the transition between them.

Note: As you encounter more and more modulations, you will find that it is occasionally difficult to distinguish between, say, direct modulations and pivot-chord modulations (as was the case in Example 28–9). Don’t get too hung up try to fit things into categories. Music is often a little ambiguous. After all, if every modulation unfolded in the exact same way, the music might become monotonous!

While modulation to the dominant key is the most common, the submediant is another frequent goal. The key of the submediant is the relative minor. As such, it shares all of its pitches with the primary major key and allows for smooth modulations. Because the pitch content of the two keys is exactly the same, any chord can be used as a pivot chord:

Table 28–2.
 C major (the primary key) A minor (the submediant key) Chord spelling I = III (C, E, G) ii = iv (D, F, A) iii = v (E, G, B) IV = VI (F, A, C) V = VII (G, B, D) vi = i (A, C, E) viio = iio (B, D, F)

As mentioned above, pivot-chord modulations are most effective when one or both interpretations of the pivot chord have pre-dominant function. For this reason, ii = iv and IV = VI are common pivot chords between a major key and its relative minor.

Activity 28-3

Activity 28–3

F# minor is the relative minor of A major. For each of the following chords, give the Roman numeral in A major and in F# minor (remember to use uppercase Roman numerals for major chords and lowercase Roman numerals for minor chords).

### Question

Triad This chord in the key of A major B minor (B, D, F#): =

B minor is ii in A major and iv in F# minor.

### Question

Triad This chord in the key of A major D major (D, F#, A): =

D major is IV in A major and VI in F# minor.

### Question

Triad This chord in the key of A major E major (E, G#, B): =

E major is V in A major and VII in F# minor.

Modulation to the supertonic (ii) is also possible:

Table 28–3.
 C major (the primary key) D minor (the submediant key) Chord spelling I = VII (C, E, G) ii = i (D, F, A) IV = III (F, A, C) vi = v (A, C, E)

The following example shows a modulation to the supertonic very close to the beginning of a piece:

After the opening phrase concludes with a half cadence in m. 4, we hear the second phrase beginning with a B-minor chord in first inversion. In the established context of A major, this chord will be heard as ii6. In the measures that follow, however, we find A#s and a G§, indicating a move to B minor. An authentic cadence, complete with a pre-dominant and cadential 6/4 chord, confirms the change of key. The chord on the downbeat of m. 5, then, may be reinterpreted as a tonic in the key of B minor.

Despite examples like the excerpt shown in Example 28–10, in a modulation to the key of the supertonic, all of the possible pivot chords are problematic because they are the tonic, mediant, or dominant chord in the goal key. For this reason, modulation to the key of the supertonic usually occurs via a different method. In such cases, the modulation begins as a tonicization and simply continues in the tonicized key.

Taking our example from the introduction to this chapter, a V7/ii–ii progression, though by itself a momentary tonicization, may initiate a modulation if a pre-dominant–dominant–tonic progression in the key of the supertonic were to follow. Hearing the modulation initially as a tonicization helps smooth over the abruptness of the key change. In other words, the new key is introduced with an applied dominant or leading-tone chord and simply continues the tonicization. The following excerpt shows an example of this type of modulation:

Here, following a perfect authentic cadence in the global tonic, the phrase beginning with the pickup to m. 5 appears to continue along in the same key. Following the E major harmony on the downbeat of m. 5, however, we come across a diminished triad built on A# (the D in the bass is an accented passing tone). This sonority is an applied leading-tone chord tonicizing ii, which appears in root position immediately after. Following this tonicization, we consistently find G§s and A#s leading to a perfect authentic cadence in B minor in m. 6. The modulation to B minor (the supertonic of A major) was achieved with the applied chord in m. 5.

Activity 28-4

Activity 28–4

### Question

The supertonic key of Bb major is C minor. Although pivot-chord modulations are not as common when modulating to the supertonic, there are several common chords between two so-related keys. Name four pivot chords that might be used in a modulation from Bb major to C minor (remember to use uppercase Roman numerals for major chords and lowercase Roman numerals for minor chords):

Bb major = = = =

I = VII (Bb, D, F), ii = i (C, Eb, G), IV = III (Eb, G, Bb), and vi = v (G, Bb, D)

Occasionally, a piece will modulate to the key of its subdominant (IV). This modulation is less common and for good reason. In modulating to the subdominant, the tonic of the primary key must be heard as the new dominant. This change in function can be disruptive to the listener because of the special relationship between tonic and dominant in tonal music. Modulating to IV too early in a piece can cause the listener to lose track of the home key. (This is not an issue in minor keys, because the minor i chord cannot sound like V/IV because it is minor.) Nonetheless, modulations to the subdominant do occur. The possible pivot chords are as follows:

Table 28–4.
 C major (the primary key) F major (the subdominant key) Chord spelling I = V (C, E, G) ii = vi (D, F, A) IV = I (F, A, C) vi = iii (A, C, E)

The excerpt below shows an example of modulation to the subdominant:

The first phrase of this chorale begins in G major but has modulated to C major by the end of the first phrase. In this case, the modulation occurs via a pivot chord on beat three of the first full measure. This G-major chord is retroactively reinterpreted as V in C major.

Example 28–12 also demonstrates the problematic nature of modulations to the subdominant. The G-major chord on beat three of m. 1 (I in G major) is preceded by a D-major chord (V in G major). The V–I progressions that open the piece are intended to firmly establish the tonic key of G major. In other words, retroactive reinterpretation will require considerably more effort to hear a G major chord as V in C major.

Note: Because it is more difficult for a listener to reinterpret a tonic triad as V in a modulation to the subdominant, composers tend to use V7/IV more frequently than just V/IV. The added seventh is a chromatic pitch in the original key and helps loosen the grip of the reigning tonality.

Activity 28-5

Activity 28–5

### Question

The subdominant key of F major is Bb major. Name four pivot chords that might be used in a modulation from F major to Bb major (remember to use uppercase Roman numerals for major chords and lowercase Roman numerals for minor chords):

F major = = = =

I = V (F, A, C), ii = vi (G, Bb, D), IV = I (Bb, D, F), and vi = iii (D, F, A)

# 28.6 Modulations from minor keys

Because of a strong tendency to gravitate toward the relative major, minor keys frequently modulate to the mediant. (You may wish to review Chapter 7 for more information regarding the structural characteristics of the minor scale and the privileged status of the relative major.) As with major keys modulating to their relative minors, every chord is a potential pivot:

Table 28–5.
 A minor (the primary key) C major (the submediant key) Chord spelling i = vi (A, C, E) iio = viio (B, D, F) III = I (C, E, G) iv = ii (D, F, A) v = iii (E, G, B) VI = IV (F, A, C) VII = V (G, B, D)

Of these possibilities, the most frequently used are i = vi, III = I, iv = ii, and VI = IV.

Activity 28-6

Activity 28–6

F major is the relative major of D minor. For each of the following chords, give the Roman numeral in D minor and in F major (remember to use uppercase Roman numerals for major chords and lowercase Roman numerals for minor chords).

### Question

Triad This chord in the key of D minor G minor (G, Bb, D): =

G minor is iv in D minor and ii in F major.

### Question

Triad This chord in the key of D minor D minor (D, F, A): =

D minor is the tonic in D minor and vi in F major.

### Question

Triad This chord in the key of D minor Bb major (Bb, D, F): =

Bb major is VI in D minor and IV in F major.

The following examples show two modulations to the relative major, the first via a VI = IV pivot chord and the second with a iv = ii:

In Example 28–13, the pivot chord is followed by a dominant-seventh in the new key. As mentioned elsewhere (see Chapter 19 on the dominant seventh chord and Chapter 27 on applied chords), the dominant seventh sonority is unique among diatonic seventh chords, and as such immediately implies a specific key. Example 28–14 follows suit, though here another strong dominant-function chord—the cadential 6/4delays the arrival of the new V7. In both examples, the pivot chord functions as a pre-dominant harmony. When it is followed by a dominant chord, there is already a strong implication of the new key. In both cases, the modulation is then confirmed with an authentic cadence.

Minor keys also modulate to the minor dominant (v). It is important to remember that the major dominant of a minor key (V) is not a closely-related key. In A minor, for example, the major dominant would be the key of E major. Compare the key signatures of A minor and E major. They differ by four accidentals (the diatonic pitches of the A minor scale are all natural while E major contains four sharps).

When a minor key modulates to the dominant key, it tends to modulate to the diatonic chord built on scale degree $\hat5$. In the key of A minor, this would be E minor. The possible pivot chords for modulating to the minor dominant are as follows:

Table 28–6.
 A minor (the primary key) E minor (the minor dominant key) Chord spelling i = iv (A, C, E) III = VI (C, E, G) v = i (E, G, B) VII = III (G, B, D)

The next example shows a modulation from G minor to D minor, the minor dominant:

In Example 28–15, the first clear indications of the move to the minor dominant are the C# and E§ in m. 6. The chord right before this moment—a G-minor triad—is native to both keys: it is the tonic in the original key but may be reinterpreted as the subdominant in the new key.

It is also common for a piece in a minor key to modulate to the relative major temporarily on the way to the minor dominant. Consider the following example:

In Example 28–16, the first three phrases prolong the tonic key of E minor. The phrase beginning in m. 7 sounds at first like E minor as well. Despite the lack of accidentals in m. 7, it makes more sense to interpret beats two through four as an expansion of G major with an auxiliary dominant seventh chord than to hear m. 7 as though still in E minor. The cadence in the following measure supports this hearing.

In the next phrase, the tonic harmony of G major is reinterpreted as the VI chord of B minor (the minor dominant). This modulation is also confirmed with a perfect authentic cadence. (Do not be fooled by the D# on the downbeat of m. 11. The momentarily raised third scale degree in a minor key is a stylistic convention known as a Picardy third, and does not indicate a modulation to the parallel major key.) The brief modulation to the key of the relative major in mm. 7–8 acts as a stepping stone to the broader modulatory goal of the minor dominant. (Note that the modulatory goals outline a large-scale arpeggiation of the tonic triad: E–G–B!)

Activity 28-7

Activity 28–7

In this activity, you will track several modulations in a row. The example below shows the final five phrases of a chorale.

### Question

In what key does this piece begin?

E minor

### Question

Dose the first phrase modulate or remain in the same key?

The first phrase does not modulate. It remains in the key of E minor.

### Question

The second phrase ends with a perfect authentic cadence in m. 10. In what key is this cadence?

The second phrase modulates to G major.

### Follow-up question

What key is this in relation to the global key of E minor?

mediant or relative major

### Question

The third phrase ends with a perfect authentic cadence in m. 12. In what key is this cadence?

The third phrase modulates to A minor.

### Follow-up question

What key is this in relation to the global key of E minor?

subdominant

### Question

The piece ends with a perfect authentic cadence in m. 17. In what key is this cadence?

The final two phrases modulate back to E minor.

# 28.7 Modulations to distant keys

So far in this chapter we have limited our discussion to modulations that move between closely-related keys since these are the most common. But, as mentioned above, it is possible to modulate from one key to any of the other twenty-three keys. To introduce the idea of modulating to distant keys, we will revisit the subject of Chapter 20: the fully-diminished seventh chord.

Fully-diminished seventh-chords can be used as pivot chords in modulations. They are particularly useful in this regard when modulating to distant keys. Consider the structure of a fully-diminished seventh chord. In Chapter 20, we described the sonority as a diminished triad with a diminished seventh added above the root. You can also think of it as a stack of minor thirds:

Stacking another minor third on top of this would result in the enharmonic equivalent of the root—in this case Cb, the enharmonic equivalent of B§. The implication of this unique property is that any of the four pitches can be interpreted and heard as the root of an applied fully-diminished chord. The following example shows how the same chord can be enharmonically interpreted as viio7 in four entirely different keys:

Each of the chords in Example 28–18 sounds exactly the same. Because of its special construction, a fully-diminished seventh chord can be heard in four different ways.

The sound of a fully-diminished seventh chord is unique and immediately identifiable—part of the reason why it works so effectively as an applied chord. Composers will occasionally exploit this recognizability and its potential for enharmonic reinterpretation in chromatic modulations. Consider the following example:

In Example 28–19, we first encounter a fully-diminished seventh chord in m. 134: viio4/3 resolves to i6 in G minor. In the next measure, however, Eb (the seventh of viio7) is respelled as D#. The altered notation signals a change in function. Instead of leading to the tonic, the fully-diminished chord now functions as an applied leading-tone chord to E minor (#vi in G minor). By reinterpreting the seventh of the original chord as the root, the passage modulates smoothly from G minor to the distant key of E minor.

# 28.8 Summary

Tonal pieces routinely explore tonal areas other than the home key. The process of changing keys is known as modulation. Modulation differs from tonicization both in length and in structural significance. A tonicization temporarily lends tonic color to some chord other than the tonic, while a modulation creates the sense of a new tonal center.

There are several methods of modulation and a number of common modulatory goals. The methods include direct modulation, pivot-chord modulation, and extended tonicization, with pivot-chord techniques being the most common. In major keys, the most common modulatory destination is the key of the dominant; other possible destinations are the submediant, supertonic and subdominant. Minor keys typically modulate to their relative majors or minor dominants.

Although this chapter is primarily concerned with modulations to closely-related keys, modulations to distant keys are also possible. Composers occasionally use specialized techniques for such chromatic modulations including enharmonic reinterpretation of fully-diminished seventh chords. Other techniques will be discussed in the following chapters.