II. Diatonic Polyphony and Functional Harmony

# 24.1 Introduction

In discussing the way a cadence brings a sense of closure to a phrase, Chapter 22 introduced the idea of harmonic function and described two roles that a chord might perform: tonic function and dominant function. A tonic-function chord at the beginning of a piece or passage is harmonically stable. It establishes the key and orients the listener. A dominant-function chord, on the other hand, is built using tendency tones—pitches that sound comparatively more restless than those of the tonic. When a dominant-function chord follows a tonic-function chord, it provides contrast and builds harmonic tension. The tension is released when the dominant resolves back to the tonic, as in an authentic cadence.

Composers can get quite a bit of mileage out of just these two functions! Consider the following example:

This excerpt consists of only I chords and V7 chords. In practice, however, progressions consisting exclusively of tonic and dominant are rare. Compare Example 24–1 to the excerpt below which includes two other chords:

This example—the very next piece in the same collection—also consists primarily of I and V7 chords. In this case however, there are also a couple of ii6/5 chords, one in m. 2 and another in m. 6. These two chords make a big difference! Whereas Example 24–1 seems to swing back and forth, back and forth between tonic and dominant, the opening phrases of this example seem more goal oriented. The ii6/5 chords expand the harmonic motion from the tonic to the dominant, giving the listener a sense of directed motion and setting up the cadences in m. 4 and m. 8. Chords such as these are said to perform a pre-dominant function.

In this chapter, we will begin with a brief review of the tonic and dominant functions and the way they work in the context of a musical phrase. We will explore how a functional area in a phrase may be expanded by way of one or more prolongational auxiliary sonorities. We will then discuss the pre-dominant function and how chords that perform this function may be used to heighten the harmonic drama of a phrase. (Along the way, we will also discuss one last type of cadence which uses the same sonorities but in a functionally different way.)

After discussing the pre-dominant, we will have covered all three of the primary roles a chord may perform. We will then introduce the idea of the tonal phrase model—a harmonic paradigm that appears in a wide variety of tonal music. We will conclude by considering how this simple model is adapted from piece to piece and how it connects music from dramatically different styles.

# 24.2 Phrases using only tonic and dominant

As we have discussed, it is entirely possible for a phrase to consist exclusively of motion from a tonic chord to a dominant chord and then back to the tonic. In the following example, a second line of analytical markings has been added below the Roman numerals to highlight the harmonic function of each chord. A capital T indicates a tonic-function chord and a capital D indicates a dominant-function chord. (The parallel lines between the Ts at the end of m. 4 simply clarify the boundary between two phrases.)

Each of the two phrases in this excerpt begins with a tonic chord that lasts for two bars before moving to a dominant seventh. Each V7 then resolves in an authentic cadence back to I, bringing its respective phrase to an end with an authentic cadence. Each of these phrases, then, follows the same basic structure: TDT.

Now consider the following example:

Once again, this phrase begins with a tonic triad and ends with an authentic cadence. Unlike the phrases in Example 24–3, however, this phrase appears to have two dominant chords: a G-major triad appears in m. 2 and again on the third beat of m. 3. But while these two sonorities are comprised of the same pitch classes, they perform very different functions. The G-major chord at the end of m. 3 is a part of the phrase-ending cadence. It is a functional dominant and has been labeled D.” The G-major chord in m. 2, however, does not participate in a cadence. Although it does move to a I chord in m. 3, this motion is not heard as the end of the phrase. This chord is therefore not a functional dominant and so it has not been labeled D.” It is instead an auxiliary sonority (see Chapter 23). Its role in this phrase is to extend or prolong the initial tonic function. This is indicated by the dotted line beginning at the initial T.” Heard this way, the phrase in Example 24–4 exhibits the same TDT structure as the phrases in Example 24–3.

Activity 24-1

Activity 24–1

### Question

Each of the boxes in the example below contains the pitches of a V7 chord in F major. Listen to the passage and determine whether or not each sonority is a functional dominant.

Hint

For a V or V7 to be considered a functional dominant, it should be part of a half or authentic cadence.

Box “a” is not a functional dominant. It is an auxiliary sonority prolonging the initial tonic.

Box “b” is a functional dominant. It is the final chord in a phrase ending with a half cadence.

Box “c” is not a functional dominant. It is an auxiliary sonority prolonging the initial tonic.

Box “d” is a functional dominant. It is the dominant in a phrase-ending authentic cadence.

# 24.3 The pre-dominant (PD) function

The example below shows the voice leading in a typical TDT phrase:

We might think of the succession of sonorities in Example 24–5 as the most basic tonal chord progression: it begins with the tonic, a point of initial repose; moves to the dominant, a moment of poised contrast; and then resolves back to the tonic, confirming its function as goal. Indeed, this very progression is at the root of all tonal harmony. In practice, however, this progression by itself is not considered very exciting. More often than not, composers will expand it and thereby dramatize the harmonic narrative.

One of the fundamental ways in which composers expand the basic TDT progression is by delaying the arrival of the dominant, thereby heightening the contrasting tension. One way to do that would be to prolong the initial tonic with an auxiliary sonority, as seen in the examples above. Another way would be to complete an arpeggiation of the tonic triad in the bass with I6 or iii:

Both of the progressions shown in Example 24–6 delay the arrival of the dominant, but I6 and iii tend to be heard simply as expansions of the initial tonic harmony. Chords built on scale degrees $\hat2$ and $\hat4$, on the other hand, contain scale degrees with strong tendencies to lead to pitches of a dominant chord. These chords—ii, IV, and their respective seventh-chord versions—are therefore much more effective at mediating between the tonic and dominant. Chords that introduce dominant harmony in this manner are collectively known as pre-dominant chords.

Note: You may occasionally encounter other terminology as well. Some teachers and texts refer to such chords as intermediate harmonies or dominant preparation chords. Others, noting that occasionally several different pre-dominant chords may appear alongside one another, refer to a subdominant area. All of these terms are valid and you should recognize their interchangeability.

The most common pre-dominant chords are those composed of diatonic pitches: iio(7) and IV(7) in major, iio(7) and iv(7) in minor. Note that pre-dominant iio(7) chords usually appear in first inversion, especially in minor where doing so helps conceal the tritone between $\hat2$ and $\hat6$. These chords are particularly useful as pre-dominants since each of their scale degrees leads smoothly to the pitches of a dominant chord:

Note the resemblance of these two progressions. The IV chord has C (in the soprano) while the ii chord has D, but otherwise the two examples are identical. This similarity in makeup explains the interchangeability of ii and IV in mediating between the tonic and dominant.

Activity 24-2

Activity 24–2

In this exercise you will expand the motion from tonic to dominant in a given harmonic progression by adding a pre-dominant chord.

### Question

Expand the motion from tonic to dominant by adding the specified pre-dominant chord.

Hint

Determine which scale degrees belong to the chord in question. Place them in the four voices by considering the voice-leading conventions described in Chapter 12 and Chapter 14.

### Question

Expand the motion from tonic to dominant by adding the specified pre-dominant chord.

Hint

Determine which scale degrees belong to the chord in question. Place them in the four voices by considering the voice-leading conventions described in Chapter 12 and Chapter 14.

### Question

Expand the motion from tonic to dominant by adding the specified pre-dominant chord.

Hint

Determine which scale degrees belong to the chord in question. Place them in the four voices by considering the voice-leading conventions described in Chapter 12 and Chapter 14.

### Question

Expand the motion from tonic to dominant by adding the specified pre-dominant chord.

Hint

Determine which scale degrees belong to the chord in question. Place them in the four voices by considering the voice-leading conventions described in Chapter 12 and Chapter 14.

Now, consider the following example:

Like the excerpts shown above, this phrase begins with a tonic-function chord (I) and ends with a dominant-tonic authentic cadence (V7–I). In this case, however, the initial tonic does not move directly to the dominant. Instead, the bass leaps up to $\hat4$, which is harmonized with a G-major triad. Unlike the auxiliary sonority in Example 24–4, this chord does not prolong a single harmonic function. Rather, it expands the motion from the initial tonic to the dominant. It performs a pre-dominant function—the last of the three basic harmonic functions—and has been labeled PD.” The overall structure of the phrase, then, is: TPDDT.

The example below follows a very similar pattern:

The progression of harmonic functions in this excerpt is identical to Example 24–9: TPDDT. The main difference is that here the expansion of the motion from the initial tonic to the dominant—the pre-dominant function—is performed by a ii6 chord instead of a IV chord. Notice, too, that with the ii chord inverted, the bass line remains the same: $\hat1$ $\hat4$ $\hat5$ $\hat1$.

In the following example, a pair of chords work together to perform the pre-dominant function:

Whereas Example 24–9 and Example 24–10 used IV and ii6, respectively, as functional pre-dominants, this excerpt has both working together. This does not change the function of the chords. In fact, we may hear this combination of IV and ii6 as strengthening the pre-dominant function via prolongation.

Note: The joining of IV and ii6 into a single pre-dominant is sometimes referred to as the pre-dominant complex. When this occurs in music it is much more common for the ii6 to come after the IV than the other way around. Note, too, that it is also possible to hear such the combination of IV and ii6 as an expanded ii6/5 since it includes the full set of four pitch classes found in the two triads:

Keep in mind, however, that not all ii and IV chords function as pre-dominants. They frequently appear in various other capacities—as auxiliary sonorities, for example:

At first glance, it may appear that the excerpt shown in Example 24–13 has three pre-dominant chords: two IV chords in m. 1 and a ii6/5 in m. 2. Of these, only the third has a pre-dominant function. The chords on beats one and three of the first full measure are auxiliary sonorities expanding the initial tonic. It is essential that you be able to distinguish such functional differences between similar chords.

Activity 24-3

Activity 24–3

It is essential that you be able to distinguish true pre-dominant chords from other sonorities that appear very similar. In each of the following excerpts, identify whether or not the boxed chord is a pre-dominant.

### Question

Identify whether or not each of the following boxed chords contains a functional pre-dominant chord.

Hint

Always look to the following chord or chords to see where the harmony is headed.

Box “b” contains a functional pre-dominant chord; box “a” does not.

### Question

Identify whether or not each of the following boxed chords contains a functional pre-dominant chord.

Hint

Always look to the following chord or chords to see where the harmony is headed.

Box “e” is the only one that contains a functional pre-dominant. All of the other boxes contain auxiliary sonorities.

# 24.4 The tonal phrase model

The TPDDT structure of harmonic functions seen in Example 24–9 and Example 24–10 is often referred to as the tonal phrase model. Combined with the prolongational techniques discussed in Chapter 23, we find that this model may be used to describe phrases from compositions across the tonal canon. It links pieces from different composers working in different parts of the world over a span of several centuries. But despite being so widely used, most listeners of tonal Western art music do not find it to be tedious, dull, or over-used. Composers working in the tonal paradigm have developed a great many techniques for embellishing the tonal phrase model and shaping its various parts to fit their needs.

At the most fundamental level, there are four basic variations of the tonal phrase model. A phrase may incorporate all four of the harmonic functions in order (TPDDT) or it may omit the pre-dominant (TDT). As we saw in Chapter 22 a cadence does not need to end with a tonic-function chord to be heard as the conclusion to a phrase. The tonal phrase model, then, also accounts for phrases the move from tonic to dominant and end without returning to tonic (TPDD and TD). The following table summarizes:

Table 24–1. Four basic variations of the tonal phrase model.
TPDDT authentic or deceptive cadence with pre-dominant
TDT authentic or deceptive cadence without pre-dominant

The following examples, show a variety of phrases that each follow the tonal phrase model in some way. As you listen and read through the analytical descriptions, take note of the many stylistic difference you hear in light of the similarities in their underlying structures.

The following example shows two phrases that do not incorporate pre-dominant chords:

As with Example 24–4, the two phrases in this excerpt each begin with a tonic chord prolonged by an auxiliary sonority before moving to a functional dominant. The first phrase ends with a half cadence. There is no concluding tonic, so its structure is simply TD. The second phrase resolves the V7 in a PAC. Its structure is TDT.

The following phrase does incorporate the pre-dominant function:

Like the phrases in Example 24–14, this phrase begins with a prolongation of the initial tonic with an auxiliary V7 chord. In m. 3, the tonic function moves on to the pre-dominant function, here performed by a ii6 chord. The dominant function is expanded with a cadential 6/4 chord before the functional V7 resolves back to the tonic in an authentic cadence. With all four harmonic functions in place, this phrase follows a TPDDT structure.

The following phrase follows the same TPDDT structure, but prolongs the initial tonic in a different way:

Once again, this phrase begins with a tonic triad. The G-minor triad in m. 2 is a vi chord in Bb-major. In Chapter 22, we saw how in a deceptive cadence a vi chord can perform a weak tonic function. Here we may understand the vi chord acting as a tonic substitute once again, expanding the tonic function at the beginning of the phrase. Other than this initial prolongation, the phrase exhibits the same TPDDT structure as Example 24–15.

The following example combines several of the techniques seen above:

In this phrase, the initial tonic is twice prolonged with an auxiliary V7 chord. The vi chord continues the tonic prolongation in m. 5 and draws the bass line down toward $\hat4$. A quick PDDT closes the phrase with a PAC. Any of the four functions in the tonal phrase model may be prolonged, but it is quite common for the initial tonic function to last much longer than any of the others as it does here.

Activity 24-4

Activity 24–4

Add a Roman numeral analysis to each of the TPDDT phrases below. Make sure to identify harmonic functions and prolongations in the manner shown above.

### Question

(Begin in m. 2. The first chord has been analyzed for you.)

Hint

Find the initial tonic first, then work backwards from the end.

### Question

Hint

Find the initial tonic first, then work backwards from the end.

The following example presents a type of cadence that we have not yet discussed:

In the concluding measures of this well-known piece, we hear one final cadential gesture consisting of a G-major chord moving to a D-major chord in the key of D major. As discussed above, IV chords are usually seen performing a pre-dominant function. This IV chord, however, does not move to the dominant. Instead, it resolves directly to the tonic and should therefore not be considered a pre-dominant. This is known as a plagal cadence and it has been labeled “PC.”

Plagal cadences frequently come after a strong authentic cadence, as in the following example:

In a way, the PAC in mm. 118–119 feels like the true end of the piece. It resolves all of the tendency tones of V7 to a stable, root-position tonic. In that regard, the plagal cadence that follows feels more like an afterthought—an extra prolongation of the tonic, tacked onto the end of the piece.

Plagal cadences are sometimes referred to as amen cadences since they appear most frequently at the ends of sacred choral compositions. They do appear from time to time, though, in secular works as well. Consider the following examples:

Example 24–20 consists of two phrases. The first phrase ends in m. 4 with a plagal cadence. The second phrase ends with a more conclusive sounding IAC in m. 8. Example 24–21 features a series of plagal progressions—iv–i–iv–i, etc.—culminating in a plagal cadence at the very end.

Note: The B§s in mm. 53–55 of Example 24–21 make major triads out of what should be a minor tonic. This modal alteration is known as a Picardy third and will be discussed in greater detail in Chapter 29.

Activity 24-5

Activity 24–5

### Question

Identify the two cadences at the end of this excerpt. Identify the cadence type as well as Roman numerals for any chords that form a part of these cadences.

Hint

Listen for moments of resolution, then analyze the harmonic content at those moments.

This excerpt includes an imperfect authentic cadence at m. 42, followed immediately by a plagal cadence at the end.

# 24.6 Common harmonic progressions

As we have now seen, certain harmonic progressions are more common than others. The following diagram summarizes some of these generalities:

Arrows in the diagram show common motions from one diatonic harmony to another. The series of arrows along the top, for example, indicate that a tonic triad may lead to any other diatonic harmony. Moving from left to right across the diagram, we find first the common tonic-function chords (I, iii, and vi), then the common pre-dominant chords (IV and ii, either of which may have added sevenths), followed by the common dominant-function chords (V and vii and their seventh-chord versions). These dominants may, as they often do, resolve back to the tonic, as shown by the arrow pointing to the right-most box, or they may resolve deceptively to vi, as indicated by the thicker arrow looping back to the left. Plagal progressions are indicated by the thicker arrow from the pre-dominant box, skipping over the dominant box and moving right to the tonic. The large, left-pointing arrow along the bottom of the diagram indicates that phrase-ending tonics frequently become the tonic of a new phrase, and that the cycle may repeat indefinitely.

Keep in mind that this diagram shows only the most commonly-encountered harmonic motions. There are numerous other possibilities and you will most certainly encounter progressions that are not shown on this chart.

Note: Although its appearance may be overwhelming at first, the diagram shown in Example 24–22 is a useful tool when faced with the task of harmonizing a melody. Take, for example, the melody shown below. To harmonize this melody one might first consider all of the diatonic chords that include each of the scale degrees in the melody. The initial $\hat3$, for example, could be harmonized as the root of a iii chord, the third of a I chord, the fifth of a vi chord, or the seventh of a IV7 chord. The $\hat1$ on the following downbeat could be harmonized with I, vi, IV, or ii7, and so on:

Now, using the diagram and our familiarity with common harmonic idioms, we can chart an informed path through these possibilities. A typical phrase starts and ends with the tonic-function, so it would make sense to start and end with I chords. Working backward from the end, it would make sense if the I at the end of the phrase was the resolution of an authentic cadence. The penultimate note ( $\hat4$), then, would have to be harmonized as the chordal seventh of a V7. Taking one step further back—to the downbeat of the second full bar—we find another $\hat4$. Harmonizing this $\hat4$ with a pre-dominant would set up the authentic cadence so we’ll harmonize it with IV. (Harmonizing the $\hat4$ with a ii6 would work equally well.)

With I at the beginning of the phrase and IV–V7–I at the end, we have the basic structure of a TPDDT phrase. The first bar, then, could be devoted to expanding the initial tonic. The notes on the first, third, and fourth beats ( $\hat1$, $\hat3$, and $\hat5$) could be harmonized with I chords. We could invert the first and third of these to avoid a repetitive bass line A passing auxiliary on the second beat—V6/4, for example—could be used to harmonize $\hat2$. With our chords selected we can write out the bass line Notice that all of these chord-to-chord progressions may be found in the diagram from Example 24–22. (The numbers between the two staves confirm that all of the interval progressions between these two voices are valid.)

Completing the harmonization is simply a matter of filling in the inner voices in the manner described in Chapter 12 and Chapter 14.

Activity 24-6

Activity 24–6

### Question

Harmonize the following melody. First identify the scale degree of each note in the melody then select a chord for each note using your knowledge of common tonal harmonic progressions and the diagram shown in Example 24–22. Add a bass line that corresponds with your selections and analyze the harmonic functions of the chords as well as the counterpoint formed between the two voices.

Hint

The example below lists all of the potential harmonizing chords for each note in the melody.

# 24.7 Summary

Phrases may consist entirely of tonic and dominant harmonies. These functions may be prolonged with auxiliary sonorities to make a harmonic progression more interesting, but in most cases composers tend to incorporate chords that mediate between the initial tonic and the dominant, thereby building dramatic tension. These chords are said to perform a pre-dominant function. Chords built on $\hat2$ or $\hat4$—iio(7) and IV(7) in major, iio(7) and iv(7) in minor—are particularly useful in this regard since they contain tendency tones that lead smoothly to the pitches of the dominant. Chords built on $\hat2$ are usually inverted to conceal the tritone between $\hat2$ and $\hat6$.

The three harmonic functions used in the order TPDDT comprise the tonal phrase model. Combined with prolongations via auxiliary sonorities and functional harmonic substitutes, this paradigm accounts for a wide variety of phrases in the tonal repertoire. A diagram of the most common chord progressions found in such phrases may be used as a helpful tool when harmonizing a melody.

While IV chords usually perform a pre-dominant function, they may be found occasionally resolving directly to I at the end of a phrase. This type of phrase ending is known as a plagal cadence or amen cadence and occurs mostly in sacred choral music. Since it frequently appears after a more conclusive authentic cadence, we may think of the IV chord in a plagal cadence as performing a prolongational role, expanding the concluding tonic harmony at the end of a piece.