III. Modulation and Chromatic Harmony

# 31.1 Introduction

In the chapter on advanced mixture (Chapter 30) we introduced the Neapolitan: a type of chromatic chord that is notated as a major triad built on the lowered second scale degree (b $\hat2$). Another example of this sonority can be found in m. 45 of the following excerpt (the Neapolitan chord is labeled N6):

With its major quality and lowered second scale degree, the effect of the Neapolitan is striking. As you can hear, the chord brings dramatic weight to the ensuing cadence and intensifies the passage in a way that a diatonic pre-dominant chord cannot.

In this chapter, we will examine the origins and structure of the Neapolitan chord. Depending on the context, the Neapolitan can be derived in several ways—hence the label N6 instead of a Roman numeral. With an understanding of how these derivations work, we will investigate how the Neapolitan functions in various conditions. We will also discuss how the Neapolitan behaves over larger spans when it is tonicized or used in a modulation.

# 31.2 Origin and structure

The Neapolitan chord may be thought of as a voice-leading sonority derived from an embellished subdominant triad:

Example 31–2a shows a iv chord in C minor. Example 31–2b shows the same iv with its fifth decorated by a chromatic upper neighbor tone (Db). In Example 31–2c, the root and third of the iv chord are sustained under the upper neighbor. With the chromatic neighbor assimilated into the chord, a new consonant triad is formed (Db-major). It is labeled N6. Note that the superscript 6 here does not indicate an inversion, since scale degree $\hat4$ is still the foundation. Rather, it is a bass figure and indicates that a sixth appears above the lowest note.

This understanding of the Neapolitan accounts for its tendency to appear as what looks like a first-inversion triad, with the chordal third doubled. If the Neapolitan is considered a derivation of iv, it is in fact the root (the bass) that is being doubled—the norm for root-position triads! Consider the following example:

Here, a Neapolitan chord appears in m. 142. The F# in the bass allows for a smooth, stepwise ascent to scale degree $\hat5$ (m. 143). As you can see in the melody, the D§ is a chromatic upper neighbor to C#. The following example replaces the D§ with a diatonic C# in m. 142:

With C# sustained through m. 142, the resultant sonority would be a iv chord in root position. Like a root-position iv chord, the Neapolitan usually appears with scale degree $\hat4$ in the bass (see also Example 31–1).

The following excerpt consists of two phrases, the second of which has a Neapolitan chord:

The two phrases in Example 31–5 (mm. 1320 and mm. 2128) are nearly identical. The primary difference may be found by comparing m. 17 to m. 25. In m. 17 we find a iv6 chord acting as functional pre-dominant leading to the cadence that ends the phrase. The notes in m. 25 are exactly the same except the fifth of the iv chord (A) has been replaced with its chromatic upper neighbor (Bb). (The bass note has been changed too—from F to D—allowing for smooth passing motion between the i6 in m. 24 and the cadential 6/4 in m. 26.) The parallelism between these two measures shows the strong connection between iv6 and N6.

Activity 31-1

Activity 31–1

The Neapolitan can also be thought of as an embellishment of a minor subdominant triad. Each of the following examples shows an unaltered iv chord. Make the necessary adjustments to create Neapolitan chords.

### Question

Adjust the necessary pitch in the following iv chord to create a Neapolitan in B minor:

Hint

In order to make a Neapolitan out of a iv chord, you need to replace the fifth with a chromatic note.

B must be replaced with C§.

### Question

Adjust the necessary pitch in the following iv chord to create a Neapolitan in E minor:

Hint

In order to make a Neapolitan out of a iv chord, you need to replace the fifth with a chromatic note.

E must be replaced with F§.

### Question

Adjust the necessary pitch in the following iv chord to create a Neapolitan in G minor:

Hint

In order to make a Neapolitan out of a iv chord, you need to replace the fifth with a chromatic note.

G must be replaced with Ab.

### Question

Adjust the necessary pitch in the following iv chord to create a Neapolitan in D minor:

Hint

In order to make a Neapolitan out of a iv chord, you need to replace the fifth with a chromatic note.

D must be replaced with Eb.

The Neapolitan chord can also be thought of as a chromatic alteration of the diatonic ii chord. Example 31–6 shows how Neapolitan chords can be derived this way in both major (a) and minor (b) keys:

In both cases, the resultant chord consists of the same three tones. Note that in major keys, however, the Neapolitan requires two accidentals: b $\hat2$ (Db in this case) and b $\hat6$ (Ab). Though not rare in major keys, Neapolitan chords are more commonly encountered in minor. The major quality of the Neapolitan differs dramatically from the diminished diatonic iio chord and provides an effective means of stabilizing it by eliminating the tritone between its root and fifth (minor scale degrees $\hat2$ and $\hat6$).

Note: The name of the Neapolitan chord links it to the so-called “Neapolitan school”—a group of composers active in and around Naples, Italy in the 18th century. However, there is little historical justification for this as the chord was certainly used earlier and by composers as far away as England.

You might also see the chord labeled “Phrygian II,” referring to Phrygian scale which differs from major and minor scales by beginning with a minor second between its first and second degrees. (This name should not be taken to imply that the music has shifted to Phrygian, but rather that the chord has some similarity in sound with the scale.) Other texts use the abbreviation bII6, since the chord can also be thought of as a major triad built on b $\hat2$. For our purposes, we label the chord N6 and refer to it as the Neapolitan.

The following example shows a Neapolitan derived from an altered ii chord (Example 31–7b provides a reduction of Example 31–7a):

The ii6/5 chord in m. 366 leads to a Neapolitan in m. 368. Following the voice leading in the upper parts, we can see that the Bb of the Neapolitan comes directly from the root of the ii6/5 chord (B§). Though it has the same construction as a Neapolitan derived by embellishing iv, this Neapolitan is clearly an altered ii chord. Nonetheless, the chord is once again supported by scale degree $\hat4$ in the bass.

Activity 31-2

Activity 31–2

The Neapolitan chord can be derived by altering a ii chord (iio in minor) to make a major triad built on the lowered second scale degree. Each of the following examples shows an unaltered supertonic chord. Make the necessary adjustments to create Neapolitan chords.

### Question

Adjust the necessary pitch or pitches in the following ii6 chord to create a Neapolitan in G major:

Hint

Remember, in a major key, the root and fifth of the ii6 chord need to be lowered.

A must be replaced with Ab and E with Eb

### Question

Adjust the necessary pitch or pitches in the following iio6 chord to create a Neapolitan in C minor:

Hint

Remember, in a minor key, the root and iio6 chord needs to be lowered.

D must be replaced with Db.

### Question

Adjust the necessary pitch or pitches in the following iio6 chord to create a Neapolitan in F# minor:

Hint

Remember, in a minor key, the root and iio6 chord needs to be lowered.

G# must be replaced with G§.

### Question

Adjust the necessary pitch or pitches in the following ii6 chord to create a Neapolitan in F major:

Hint

Remember, in a major key, the root and fifth of the ii6 chord need to be lowered.

G must be replaced with Gb and D with Db.

To summarize, the Neapolitan can be thought of in two ways. In the first, the fifth of a subdominant triad is replaced by its chromatic upper neighbor. The resultant sonority is a major triad: N6. (Remember that in this case the superscript 6 is a bass figure indicating that a sixth appears above the lowest note. It does not indicate that the chord is in an inverted position.) In the second conception, the Neapolitan is derived by chromatically lowering the root of a diatonic iio chord. (In major keys, scale degree $\hat6$ must also be lowered.) These dual derivations are why we label the Neapolitan generically, using N6 instead of a Roman numeral.

Of the two, the latter is more common today since the usual notation of the Neapolitan more readily resembles a bII6 chord than a iv chord with an altered fifth. Nonetheless, it is important for analysis that you be able to conceive of the Neapolitan in both ways. Consider the following example:

In this excerpt from a Chopin Nocturne, we find a Neapolitan following a root position III chord. In this case, the Neapolitan must be considered an embellished iv. To view this Neapolitan as bII6 would be counterintuitive and would contradict the norms of harmonic root movement. The Neapolitan is a passing chord from III to V. In other words, the progression III–ivb6–V6/4 makes much more sense than III–bII6–V6/4.

Now consider the following example (Example 31–9b provides a reduction):

This passage consists of two parallel phrases. The first of these (mm. 7–13) includes a Neapolitan chord as an extension of iv through an auxiliary passing 6/4 chord: i–iv6–(i6/4)–N6–V–i. A parallel phrase follows in mm. 15–19. This time, however, the Neapolitan has been replaced by iio 6. By presenting these two chords—N6 with its b $\hat2$ and then iio 6 with its diatonic $\hat2$within parallel phrases in close proximity, the composer highlights the contrast between different versions of the ii chord. As you can see, it is important that you be able to conceptualize the Neapolitan in both ways.

Activity 31-3

Activity 31–3

Write Neapolitan chords as indicated.

### Question

Write a Neapolitan chord with scale degree $\hat4$ in the bass in C minor:

Hint

Remember, a Neapolitan resembles a major triad built on b $\hat2$ with $\hat4$ in the bass.

(Answers may vary as long as F is the lowest pitch and the upper voices consist of Db, F and Ab.)

### Question

Write a Neapolitan chord with scale degree $\hat4$ in the bass in F minor:

Hint

Remember, a Neapolitan resembles a major triad built on b $\hat2$ with $\hat4$ in the bass.

(Answers may vary as long as Bb is the lowest pitch and the upper voices consist of Gb, Bb and Db.)

### Question

Write a Neapolitan chord with scale degree $\hat4$ in the bass in A major:

Hint

Remember, a Neapolitan resembles a major triad built on b $\hat2$ with $\hat4$ in the bass.

(Answers may vary as long as D is the lowest pitch and the upper voices consist of Bb, D and F§.)

### Question

Write a Neapolitan chord with scale degree $\hat4$ in the bass in C# minor:

Hint

Remember, a Neapolitan resembles a major triad built on b $\hat2$ with $\hat4$ in the bass.

(Answers may vary as long as F# is the lowest pitch and the upper voices consist of D§, F# and A.)

# 31.3 Other positions of the Neapolitan

Although the Neapolitan usually appears with scale degree $\hat4$ in the bass, other positions are possible. The following example shows one such instance:

On the second beat of m. 12, we find a Neapolitan chord with the chromatic pitch (b $\hat2$) in the bass. (Note that instead of N6, the chord is labeled N5/3 indicating the third and fifth that appear above the bass.) This voicing brings out the chord’s startling, dramatic effect by dramatizing the tritone in the low register when the bass, reinforced by octaves, leaps from Db to G. Cases of b $\hat2$ in the bass supporting a Neapolitan are far less frequent than those with $\hat4$ in the bass. This voicing of the Neapolitan is rare because composers usually tend to avoid accentuating tritones in this manner.

# 31.4 Function, voice-leading, and context

Regardless of how you think of the Neapolitan chord— as a neighbor-note embellishment of iv (IV in major) or as a chromatic root-alteration of iio (ii in major)—it retains the pre-dominant function of its origin. In other words, the Neapolitan chord routinely signals and leads to some form of dominant. It frequently moves directly to the dominant (V or V7), as in the following excerpt:

Here the Neapolitan chord appears in m. 8 after two full measures of tonic harmony. It then moves directly to a V chord in the following measure which in turn resolves to i at the end of the phrase.

Note that in Example 31–11, b $\hat2$ (Ab) is emphasized as the highest note in the piano part and leaps down a diminished third to the leading tone (F#). While this diminished melodic interval would typically be avoided, composers tend to highlight it in the case of the Neapolitan by putting it in the soprano. Like the leading tone, b $\hat2$ is only a semitone away from the tonic and as such has a strong tendency to resolve to $\hat1$. However, because the Neapolitan is a pre-dominant chord, the dominant chord further delays the resolution to $\hat1$. The heightened harmonic tension brought on by this delay makes the Neapolitan chord a potent dramatic tool.

Activity 31-4

Activity 31–4

When analyzing Neapolitan chords, it is essential that you be able to recognize the altered pitch or pitches and trace the voice-leading from one chord to the next.

### Question

Identify the Neapolitan chord in the following excerpt:

The Neapolitan is in the second half of m. 3.

### Follow-up question

Does the b $\hat2$ of the Neapolitan move to the leading tone or diatonic $\hat2$?

b $\hat2$ leaps down a diminished third to the leading tone.

When N6 moves to V, the upper voices usually move in contrary motion to the bass. The bass note (scale degree $\hat4$) almost invariably steps up to $\hat5$ while the upper voices move down to the nearest chord members:

In SATB settings such as the one in Example 31–12, the bass note ( $\hat4$) is usually doubled. This is due in part to the remaining chord members having a strong tendency to move down: (b) $\hat6$ steps down to $\hat5$ and, as described above, b $\hat2$ leaps down a third to the leading tone.

When N6 moves to V7, the doubled note ( $\hat4$) may be suspended in one of the upper voice:

Problems arise when the notes of the Neapolitan do not move in contrary motion to the bass:

In Example 31–14, the motion from b $\hat2$ to § $\hat2$ in the soprano line creates an awkward chromatic contour. The lowered second scale degree will sometimes lead to the diatonic second scale degree, but this tends to be restricted to inner voices since the upward motion contradicts the tendency for b $\hat2$ to resolve down to $\hat1$.

Activity 31-5

Activity 31–5

Complete the following progressions from N6 to V.

### Question

Complete the progression by adding a note in each voice part.

Hint

All of the upper voices should move in contrary motion to the bass (most importantly b $\hat2$, which will leap to the leading tone).

### Question

Complete the progression by adding a note in each voice part.

Hint

All of the upper voices should move in contrary motion to the bass (most importantly b $\hat2$, which will leap to the leading tone).

### Question

Complete the progression by adding a note in each voice part.

Hint

All of the upper voices should move in contrary motion to the bass (most importantly b $\hat2$, which will leap to the leading tone).

### Question

Complete the progression by adding a note in each voice part.

Hint

All of the upper voices should move in contrary motion to the bass (most importantly b $\hat2$, which will leap to the leading tone).

In other cases, the Neapolitan does not move directly to V. Instead, an intervening chord may delay the dominant. Consider the following examples:

The Neapolitan chord in Example 31–15—itself embellished with an auxiliary sonority in m. 144—leads to an applied viio 7/V in m. 147 before moving to the cadential V chord. The same technique appears in Example 31–16. Here, an unprepared Neapolitan is used to begin a phrase following a half cadence. A viio 7/V delays the dominant, which arrives one beat later.

Note: Despite the key signature with just one flat, Example 31–16 is in G minor. In Johann Sebastian Bach’s time, it was common for minor key signatures to be written with one less accidental, owing to remnants of earlier notational conventions.

Example 31–17 shows a similar situation in which the Neapolitan leads to a cadential  6/4 chord:

Note that in this example, the VI chord preceding the Neapolitan can also be interpreted as an applied dominant (continuing the falling fifth pattern from the previous measures). If the first half of m. 5 is regarded as V/N, then the Neapolitan in this case has loosened its ties to the original iv chord with 5–6 motion over the bass ( $\hat4$). The Neapolitan has taken on a harmonic identify of its own, by virtue of the preceding applied dominant. We will return to this topic momentarily in the section on tonicizing the Neapolitan.

Whether the Neapolitan proceeds to an applied diminished seventh chord (as in Examples 31–15 and 31–16) or to a cadential  6/4 (Example 31–17), b $\hat2$ may at first appear to resolve melodically directly to $\hat1$. But that $\hat1$ is a false resolution and is not heard as a true arrival since it is not supported by consonance with the bass. It acts instead as a passing tone—a dissonant diminished fifth or perfect fourth above the bass—on the way to the leading tone. The melodic resolution of b $\hat2$ occurs with the arrival of the leading tone over V, and the harmonic resolution occurs when that V resolves to I.

Activity 31-6

Activity 31–6

As a pre-dominant chord, the Neapolitan leads to dominant harmony. Sometimes, however, another pre-dominant chord intervenes. Recognizing this delay in the arrival of the dominant is an important part of analysis.

### Question

Identify the first appearance of the Neapolitan chord in the following excerpt. (Note that despite the key signature, this passage is in the key of A major.):

Hint

A good way to identify Neapolitan chords is to look for the expected chromatic alterations. In a major key, these are the lowered scale degrees $\hat2$ and $\hat6$.

The Neapolitan chord first appears on the downbeat of m. 30.

### Follow-up question

In this case, the Neapolitan does not move directly to the dominant. In what measure does the root-position dominant seventh arrive?

Hint

Look for a chord that measure whose pitches are that of a dominant seventh chord.

The true dominant harmony arrives in m. 34.

### Follow-up question

What two other pre-dominant chords intervene between the Neapolitan and the true dominant harmony?

The Neapolitan leads to a viio7/V in m. 32 and then a cadential 6/4 in m. 33 before getting to the dominant in m. 34.

The same chords that are typically used to approach ii(o)6 are also used to approach the Neapolitan. Example 31–10 and Example 31–17 show Neapolitan chords following VI. Example 31–15 has a Neapolitan following iv—the Abs beginning in m. 143 act initially as chromatic upper neighbors to the fifth of the iv chord. Example 31–7 has a Neapolitan following ii6/5 and Example 31–1 and Example 31–3 approach the Neapolitan with tonic triads.

# 31.5 Tonicizing the Neapolitan

Composers frequently tonicize the Neapolitan. The structure of the minor scale makes this particularly convenient since the diatonic VI chord is equivalent to the dominant of the Neapolitan. In other words, the progression VI–N6 can sound like V/N–N6(a tonicization of the Neapolitan) since the root motion is the same as V–I.

Consider the following example:

In Example 31-18, after a pair of authentic cadences in (m. 4 and m. 9), we hear a deceptive cadence in m. 12. This F-major chord is heard initially as VI in A minor. On the other hand, the root of this chord (F) lies a perfect fifth above—or a perfect fourth below—the root of the Neapolitan that follows. The F-major chord may, in other words, also be heard as V/N setting up the chromatic Bb in m. 13.

Composers will occasionally expand this sort of tonicization by modulating to the key of the Neapolitan for extended passages. Tonicizations of—and modulations to—the Neapolitan in a minor key are possible because, as pointed out earlier, chromatically altering $\hat2$ to become b $\hat2$ stabilizes the unstable, diminished iio triad into a major triad, bII.

A similar scenario appears in the following example:

The Neapolitan is tonicized here with an applied dominant seventh chord in m. 13. This applied chord is derived by adding a minor seventh above the root of the preceding VI chord (Eb).

The following excerpt provides another example of a tonicized Neapolitan

This passage includes a Neapolitan chord in the opening phrase. On the second beat of m. 2, we see an E in the bass with G and C§ in the upper voice—a typical example of a Neapolitan chord. Preceding this, we find a VI chord consisting of G in the bass with B and D in the upper voice. This chord can also be interpreted as an applied dominant to the Neapolitan. (It is labeled V/N in Example 31–20.) As an applied dominant, this tonicization of the Neapolitan continues a falling fifth progression begun in the previous measure. By moving to the Neapolitan, Bach avoids the tritone root motion that would have resulted from VI to a diatonic iio chord. (For more information on applied chords, see Chapter 27.)

No matter what the length—single chords, tonicizations, modulations—appearances of the Neapolitan soon lead to the dominant. Emphasizing the Neapolitan by making it sound temporarily like a tonic dramatizes the arrival of the dominant.

Activity 31-7

Activity 31–7

For each of the following exercises, identify the pitches of an applied dominant seventh chord on the Neapolitan of the specified key.

### Question

In the key of D minor, what would be the root of V7/N?

Hint

The root of V7/N is the fifth of the Neapolitan chord.

Bb

### Follow-up question

What are the three remaining pitches of the dominant seventh chord that has this pitch as its root?

D, F, and Ab

### Question

In the key of A minor, what would be the root of V7/N?

Hint

The root of V7/N is the fifth of the Neapolitan chord.

F

### Follow-up question

What are the three remaining pitches of the dominant seventh chord that has this pitch as its root?

A, C, and Eb

### Question

In the key of D major, what would be the root of V7/N?

Hint

The root of V7/N is the fifth of the Neapolitan chord.

Bb

### Follow-up question

What are the three remaining pitches of the dominant seventh chord that has this pitch as its root?

D, F, and Ab.

### Question

In the key of F# minor, what would be the root of V7/N?

Hint

The root of V7/N is the fifth of the Neapolitan chord.

D§

### Follow-up question

What are the three remaining pitches of the dominant seventh chord that has this pitch as its root?

F#, A, and C§

# 31.6 Summary

The Neapolitan chord (sometimes referred to as Phrygian II) is notated as a major triad built on b $\hat2$, but can be conceptualized in different ways. It can be thought of as a melodically embellished subdominant chord whose fifth has been replaced by its chromatic upper neighbor—an explanation that accounts for the tendency of the Neapolitan to appear with $\hat4$ in the bass, and for the bass, as root, to be doubled. It can also be thought of as a chromatically altered ii(o) chord, in which the root has been lowered by a semitone.

The respective Neapolitan chords of parallel keys contain the same tones, though two accidentals are required in major as opposed to the single accidental required in minor. Neapolitan chords appear more frequently in minor keys, in part because they avoid the tritone between $\hat2$ and $\hat6$ in the iio chord.

As a pre-dominant chord, the Neapolitan’s typical function is to lead to the dominant. It often does this directly—moving to V or V7 without delay—though frequently an applied chord or cadential 6/4 intervenes. Any chord used to approach ii(o)6 can also precede a Neapolitan: i, i6, VI, or iv among others. Composers also tonicize it or modulate to that key. In any case, the Neapolitan eventually leads to some form of dominant harmony.

All in all, the Neapolitan is generally used as an expressive device. The chromatic alteration is striking in any context and is often used to heighten the dramatic tension of important passages.