II. Diatonic Polyphony and Functional Harmony

# 14.1 Introduction

In this follow-up to Chapter 12, you will be given an opportunity to expand basic interval progressions by adding more voices. Whereas Chapter 12 was concerned with two-part textures and therefore dealt only with progressions of intervals, the addition of a third (and fourth) voice opens up the possibility of writing complete triads.

In this chapter we will continue the now familiar convention of labeling interval progressions generically with Arabic numerals (1, 2, 3, etc.), but more importantly we will also place each of these progressions in the context of a key. In doing so, our discussion becomes less abstract and more closely-related to the sounds one encounters in actual tonal compositions. We will use Roman numerals (I, ii, iii, etc.) to indicate the harmonies suggested by the sounding notes—even when the written chord is incomplete. If you are not familiar with the construction of triads and the concept of labeling them with Roman numerals, it is suggested that you review the material in Chapter 13 before proceeding.

This chapter will begin with a brief aside, discussing how different scale degrees sound and function in relationship to one another. We will then move on to techniques and considerations for adding a third voice to a two-part texture. Working with three voices will raise your sensitivity to the behavior of interval progressions in tonal music, providing a helpful intermediate step on the way to handling more complex textures. Once the three-part texture is secure, we will add a fourth voice. We will see how these principles apply to what many teachers and musicians see as the standard format for tonal part-writing and the harmonic foundation for many other compositional styles: chorale-style textures with separate parts for soprano, alto, tenor, and bass voices (SATB). Along the way, we will analyze compositions from a variety of composers to show how interval progressions work in traditional repertoire.

# 14.2 Tendency tones

In this chapter we will be looking at how different melodies work and relate to one another in the context of a key. In order to do so, we must consider how different scale degrees work and relate to one another in the context of a scale.

Play or listen to the following example of an ascending major scale, pausing at scale degree $\hat7$:

It is likely that you experienced the pause at B as feeling particularly unsettled. You probably wanted to hear the scale continue just one more step up to the tonic. In fact, this desire to hear the leading tone resolve may have been so strong that in your mind you imagined the resolution before it actually happened. Listeners of tonal music are extremely well-accustomed to the sound of degree $\hat7$ moving up a half step to $\hat1$. Because we encounter this resolution so frequently we find ourselves expecting it—or at least left wanting when it doesn’t happen. Consciously or not, we come to understand the leading tone as having a tendency to resolve to the tonic.

Certain tones of the diatonic scale are more stable than others. Scale degrees $\hat1$, $\hat3$, and $\hat5$—the pitches of the tonic triad—are the most stable. Other scale members ( $\hat2$, $\hat4$, $\hat6$, and $\hat7$) form dissonances with these stable tones and are therefore heard as relatively unstable. Because of this dissonance, those scale members tend to pull strongly toward the stable tones. Unstable pitches that gravitate towards points of greater stability are referred to as tendency tones.

In the following example, the curved arrows show the typical melodic resolutions as tendency tones (filled-in noteheads) move by step toward more stable tones (open noteheads). Scale degrees $\hat2$, $\hat4$, and $\hat6$ are usually found resolving down by step while scale degree $\hat7$ tends to resolve up by step:

Several tendency tones lie a half step away from a tone of greater stability. Scale degree 7, for example, forms a dissonant minor second with the tonic while scale degree 4 forms a minor second with scale degree 3. In the diatonic minor scale (see Chapter 7), scale degree 6 is a tendency tone that resolves to 5 for the very same reason. In such cases, where the stable tone is so close, the urgency to resolve seems stronger.

(Note that while Example 14–2 shows a major scale, the same tendencies are present in the natural minor scale. Scale degree 7 in minor is exceptional. See Chapter 17 for a detailed discussion of how composers address this discrepancy.)

None of this is meant to imply that scale degrees $\hat2$, $\hat4$, $\hat6$, and $\hat7$ must resolve in the manner demonstrated by Example 14–2. There are, of course, innumerable melodies where these scale degrees do exactly the opposite. Rather, you should understand that a tendency tone resolving in the expected manner will have one effect—usually, a sense of repose or resolution—while defying expectations will have another—in many cases, a sense of increased tension.

# 14.3 Basic interval progressions in three voices

Working initially with three voices will clarify how basic interval progressions behave in complex textures. The examples below will begin with a two-voice, soprano/bass framework. We will then add a third voice, creating standard interval progressions with each of these framing voices. Working with three simultaneous interval progressions requires careful planning and close attention to the conventions described in Chapter 12. As we will see later on, a four-voiced texture has a total of six interval progressions between voices! Limiting ourselves, for the time being, to just three voices will help us ease into more complex textures.

This part of the chapter is broken into three sections examining three common types of progressions. These three types are based on root motion between two chords: by fifth (as in V–I), by third (as in I–vi or I–iii) and by step (as in IV–V).

# 14.4 Root motion by fifth

We begin with the following example of a V–I progression:

Above, you see a common interval progression in two voices. Roman numerals indicate which chords are used. V–I is a progression which illustrates root movement by fifth since the chord roots—in this case G and C—are a fifth apart. We will now add a third, inner voice to this progression. The movement of the third voice will be decided by the standard interval progressions.

There are three important constraints to follow when adding a third voice:

• The added pitches must be members of the given chords. (In this case, for example, the added voice above the V must be a member of the V chord: G, B, or D. The added voice above the I chord must likewise be a C, E, or G.)

• The added pitches must form valid interval progressions with at least one of the given voices.

• The added pitches must not form parallel fifths, octaves, or unisons with any of the given voices.

For the time being, since we are only working with three voices, do not worry about creating complete triads. Tripled roots and open-fifth sonorities are acceptable for now. Complete triads will become more of a concern further on, when we create four-voice textures. For now, though, try to include the third of the triad whenever possible while creating valid interval progressions. The result will be a richer, fuller harmony.

Keeping the three constraints above in mind, let us try adding a third voice to the Example 14–3. Since the V chord already has a root (G) and fifth (D) let us start by adding a B:

The next step, after picking a first pitch, is to survey the list of standard interval progressions. By adding a B to the V chord, we’ve created an interval of a third with the soprano voice. On the next beat, the soprano ascends away from the middle voice. Ask yourself which of the standard interval progressions begins with a third. 3–1 begins with a third, but since the soprano in our example ascends, the two parts cannot converge onto a unison. What about a 3–5 progression?

At first glance, this might seem like a good answer. But remember, one of the three constraints requires that added voices must be members of the given chords. The pitch A is not a member of the I chord in this key, so B–A is not a valid inner voice.

What if our middle voice ascended by step, forming parallel thirds with the soprano?

In this case, both of the added pitches are chord members: B is the third of V and C is the root of I. The 3–3 progression is also valid. Furthermore, B is the leading tone in this key and has a tendency to resolve to the tonic C.

What if we chose a different starting pitch for our added voice? Let us try to find a valid middle voice that begins with G, the root of the V chord:

This G forms a fifth with the upper voice. What are some potential interval progressions that begin with a fifth and have the upper voice ascending by step? We know that the added voice cannot also ascend by step, because this would lead to parallel fifths. One possibility is the oblique 5–6 progression:

In this case, the added voice maintains the pitch G, which is a member of both the V and I chords. This is a valid added voice.

Activity 14-1

Activity 14–1

As you will see with multi-voice progressions, there is often more than one possible outcome for a given setup.

### Question

Taking the setup from Example 14–7, can you think of another pitch (other than sustaining G) that the middle voice could move to?

The middle voice could move from G up a fourth to C, creating a 5–3 progression with the soprano. (Note: Moving down to E will create a 5–8 progression with the soprano. While the 5–8 progression is valid, it is typically found between the bass and one of the upper voices.)

Now we will add a middle voice to a slightly longer passage. Here we have a short progression of four chords, each with falling-fifth root motion:

Let us begin by adding a C as a middle voice, creating a sixth with the soprano:

We can see that on the next beat, the soprano sustains its A. With this sustained pitch, we know that the interval progression must have oblique motion. What is the only standard interval progression that exhibits oblique motion?

Activity 14-2

Activity 14–2

### Question

What is the only standard interval progression that exhibits oblique motion?

5–6 or 6–5

The sixth must contract to a fifth:

In the next step, from the ii chord to the V chord, the soprano ascends by step from A to B. Before selecting the next note for the alto line, remember that V has the leading tone of the key as its chordal third. In this case, the leading tone (B) is already present in the soprano part. It resolves as expected by moving up a half step to the tonic (C). As you continue writing the alto line, you may be tempted to move down a third to create a 5–8 interval progression with the soprano. Although this interval progression is perfectly valid on its own, it would create a problem when the V continues on to I. Because scale degree $\hat7$ is has such a strong tendency to resolve to scale degree 1, both Bs above the V chord would exert a strong pull to C. This would in turn create parallel octaves between the soprano and the middle voice:

Play or listen to Example 14–12 and notice how the soprano and alto become locked in with one another. They lose their independence. It is for this reason that parallel octaves are not permitted in this style.

With a leap to B off the table, you might be tempted to have the alto leap up to G in m. 2. Moving up a fourth to G will create a valid interval progression with the soprano (5–3), but beware of the parallel fifths created with the bass:

At this point, there aren’t very many options left! What pitch(es) could the middle voice move to on the downbeat of m. 2?

Activity 14-3

Activity 14–3

### Question

Using basic interval progressions, what pitch could the middle voice move to and be a member of the V chord?

The best answer would be for the middle voice to hold on D. By sustaining D, the middle voice creates another oblique interval progression with the soprano.

The best option is for the middle voice to remain on D, creating another oblique progression with the soprano:

Finally, as the progression moves from V to I, the soprano ascends from the leading tone to the tonic pitch. There are two valid pitches that the middle voice could move to. What are they?

Activity 14-4

Activity 14–4

### Question

There are two valid pitches that the middle voice could move to, what are they?

The middle voice could step up to E creating parallel sixths with the soprano. It could also step down to C creating a 6–8 with the soprano and a 5–8 with the bass.

Of the two options, E or C, C is the better choice because of the stronger sense of resolution created by the valid interval progressions with both the soprano and the bass:

Note: You may have noticed in the examples above that the lowest voice—the bass—is far more disjunct than the voices above it. As the alto and soprano parts progress from one chord to the next they either move by step or remain singing the same pitch. The bass part, on the other hands, leaps up and down by fourths and fifths. This is quite common. In most multi-voiced settings, the upper voices (soprano, alto, and tenor) tend to have smooth, often repetitive melodic lines while the bass jumps up and down as required by the harmonic progression. Of course, these types of melodic motion are not mutually exclusive—upper voices may leap and basses may move by step.

# 14.5 Root motion by third

So far, all of the progressions to which we’ve added a third voice have had root motions of a fifth. Let us now try adding a voice to a progression in which the roots move by a third:

As mentioned earlier, it is a good idea to include the third of the chord whenever possible. Doing so creates a fuller sounding harmony. Here, we’ve added the third of the I chord (E) as the middle voice:

To what pitch could the middle voice move that both belongs to the chord and forms valid interval progressions?

Activity 14-5

Activity 14–5

### Question

What pitch could the middle voice move to that both belongs to the chord and forms valid interval progressions?

Moving down a third to C is the best choice since it is a member of the vi chord and creates valid interval progressions with both the bass (3–3) and the soprano (3–6). (Note: there are other possibilities to move to members of the vi chord, but they do not create valid interval progressions with the outer voices.)

C is the best choice, forming a 3–3 progression with the bass and a 3–6 with the soprano:

The same process could be applied to a progression in which the root motion ascends by a third. The following example shows a completed, three-voice progression:

Here, the root-progression moves up by a third from I to iii. The outer voices form the familiar 8–5 progression. To these, an inner voice has been added, consisting of the third of the I chord (E) moving to the third of the iii chord (G). This inner voice forms valid interval progressions with both the soprano (6–3) and the bass (3–3).

# 14.6 Root motion by step (step progression)

Finally, there is one other type of progression to consider: root motion by step. This type of progression is slightly more difficult because of a greater risk of parallel fifths and octaves. Let us start with a typical step progression:

Here we have a IV–V progression with the outer voice framework forming a 5–3 progression. Let’s try adding a middle voice beginning on F:

Noting that this F lies a fifth below the soprano C, it might be tempting to have the middle voice step up to form a 5–3 progression between these two voices. While the two upper voices form a valid interval progression, this motion in the middle voice creates parallel octaves with the bass:

As noted above, parallel fifths and octaves are a common threat in step progressions. The best way to avoid those problematic interval progressions is to strive for contrary motion between the bass and the upper voices. In this case, the middle voice may descend to D:

Having the middle voice descend from F to D creates valid interval progressions with both the bass and soprano.

Activity 14-6

Activity 14–6

### Question

The progression given in Example 14–20 could also have a middle voice beginning on A (the third of the IV chord). What member of the V chord could this A move to while forming valid interval progressions?

Stepping down to G will create valid interval progressions with the soprano (3–3) and the bass (3–1). (Note: While stepping up to B might seem to be a valid answer as it creates valid interval progressions with both the bass and the soprano, it leads to a doubled leading tone in the V chord. Since B has such a strong pull to C in C major, this will lead to a parallel unison.)

# 14.7 Analysis of a three-part composition using basic interval patterns

Three-part compositions are not very common. Historically, when composers wrote for more than two voices they opted for the fuller, richer sound of a four-part texture, as described in the closing sections this chapter. Nonetheless, examples do exist. Consider the following excerpt from a three-part madrigal by Giovanni Pierluigi da Palestrina:

Example 14–25 shows the basic interval progressions present between each pair of voices from Example 14–24:

In Example 14–25a, we see that the interval progression heard between the outer voices consists mainly of perfect fifths and octaves. A dissonant seventh in m. 14 fills in the motion from an octave to a fifth as IV moves to V. (See Chapter 15 for a detailed discussion of such dissonant and nonharmonic tones.) Example 14–25b shows that the top and middle voices move almost exclusively in parallel thirds. A dissonant fourth in m. 14 breaks up the monotony before the two voices converge on a unison at the end. Finally, in Example 14–25c, we see a great deal of intervallic variety between the middle and bottom voices. Overall, each voice is distinct, projecting its own musical identity while blending harmoniously with the other two.

# 14.8 Basic interval progressions and four-part textures

The principles outlined above form the foundation of voice leading in tonal music. To demonstrate, we will now examine several chorale-style SATB passages to see how standard interval progressions work in a four-voice texture. Consider, for example, the following four-voice progression:

This short passage can be broken down to show that each inner voice forms a standard interval progression with at least one other voice. Let us begin with just the outer voices:

This is a very common outer-voice framework for a I–V–I progression. We can add an inner voice by having the soprano act as the upper part of a standard interval progression. In the following example, the alto voice is added, forming first a 6–5 progression with the soprano and then a 5–6:

The tenor voice can be added in a similar way. In this case, the tenor follows the soprano in parallel tenths:

And so we have created a four-voice texture for this I–V–I progression. It is worth noting that the intervals between the tenor and alto also follow a standard interval progressions (5–6–5). This will not always be the case. Consider the following example:

Just as before, the added voices form standard interval progressions. In this case, the alto part creates parallel sixths with the soprano…

…and the tenor part forms a 6–5–6 with the alto part:

However, this example differs from the previous one in one important respect. Look at the intervals between the soprano and the tenor parts. These two parts form a 4–3–4 progression. Neither 4–3 nor 3–4 is a standard interval progression. In fact, perfect fourths do not appear at all among the basic interval progressions. As explained earlier, fourths are considered dissonant in two-voice textures and are therefore best avoided. However, that rule must now be amended for textures with three or more voices.

When perfect fourths come about as the byproduct of adding additional voices, they are valid and common between any voice pairs not involving the bass. (Perfect fourths involving the bass require a further qualification of the rule regarding their use. This is discussed in Chapter 23.) In other words, they are allowed between a pair of upper voices.

In such situations, the fourths are referred to as resultant intervals—byproducts (results) of standard interval progressions between other voices. This is because when perfect fourths occur between upper voices, they are actually inversions of (consonant) perfect fifths. A fourth formed with the bass, on the other hand, is in almost all cases a dissonant fourth, the result of a melodic event. (We will return to this subject in Chapter 15 on nonharmonic tones.) It is important that you be able to distinguish resultant intervals from those that are part of standard interval progressions.

Activity 14-7

Activity 14–7

### Question

In this activity, you will complete the two inner voices of a I–V progression in G major. The first pitches have been provided:

Hint

Remember, both voices must be members of the V chord and form valid interval progressions.

B in alto moves down by step to A and G in tenor moves down by step to F#.

Note: Various forms of the completed progression shown in Example 14–30 and Example 14–32 are quite common in Western art music. Consider the very similar voice-leading found in the following passage:

The first three chords in this excerpt are shown in reduced form in Example 14–33b. Other than the decorative F# (indicated by a small, parenthesized notehead) and the leap up in the lowest voice as V moves to I, the voice-leading is the same as in Example 14–30 and Example 14–32, though here the upper voices have been rearranged.

Again, every pair of voices in this passage follows standard interval progressions. The soprano creates an 8–3–8 pattern with the bass while moving in parallel sixths with the tenor. The alto voice sustains an A, creating an oblique 5–8–5 progression with the bass while forming resultant dissonances with the soprano (4–3–4) and the tenor (3–4–3). Finally, the tenor and bass move first in contrary motion from a third to a fifth and then in similar motion back to a third.

(Notice that the same progressions may be found several more times later in the same excerpt!)

In Example 14–26 through Example 14–32, we considered standard interval progressions at work in a progression with root motion of a fifth. The same situation exists with progressions of chords whose roots are a third or a step apart. In the following example, let us determine how the inner voices move in a step progression:

The bass and soprano, in this case, form a 10–8 progression:

It is particularly important to be wary of parallel fifths and octaves when moving between chords whose roots are a step apart. If our tenor voice were to start on C and move up by step, it would create parallel fifths with the bass:

The tenor line from Example 14–34 is much better. It forms a 5–3 progression with the bass and a 6–6 progression with the soprano:

It might be tempting at this point to write in an alto line that moves by step from F up to G. This, however, would create parallel octaves with the bass:

A much better solution would be to have the alto line move from F down a third to D, forming an 8–5 progression with the bass:

The 3–4 progression between the soprano and alto and the 4–3 progression between the alto and tenor are, as in Example 14–32, resultant intervals.

You may have noticed that in the example above the upper voices all move in contrary motion to the bass, two of them by step, the other by a leap of a third. Following this model is generally a good idea when moving between two triads whose roots are a step apart. Doing so will help avoid the parallel fifths and octaves seen in Example 14–36 and Example 14–38.

Note: As with the I–V–I progression discussed above, IV–V is ubiquitous in Western art music. Consider the following measures taken from The Chorale Book for England:

Just before the end of this excerpt, we find a IV–V progression used to harmonize the text “keep Thy.” As in our example, the composer has matched the ascending step in the bass (Bb to C) with each of the upper voices moving in contrary motion down to the nearest chord tone: the soprano and alto voices step down from F to E and D to C, respectively, while the tenor leaps down a third from Bb to G. A resultant dissonance is found in the 3–4 progression between the tenor and alto.

(Another progression featuring stepwise root motion may be found in the previous measure. There, a V chord moves to vi under the text “truth and.” Again, the bass steps up while the upper voices move down. Notice, too, that a Bb is used to fill in the third as the tenor moves from C down to A.)

Activity 14-8

Activity 14–8

### Question

In this activity, you will analyze the voice leading in a progression from V to vi. Fill in the blanks that follow the progression:

Voice pair: Interval progression:
Bass and soprano:
Bass and alto:
Bass and tenor:
Tenor and soprano:
Tenor and alto:
Alto and soprano:
Voice pair: Interval progression:
Bass and soprano: 3–1
Bass and alto: 5–3
Bass and tenor: 8–5
Tenor and soprano: 3–4
Tenor and alto: 5–6
Alto and soprano: 6–6

### Follow-up question

Do any of these progressions contain resultant intervals?

Yes: the tenor and soprano.

# 14.9 Analysis of a four-part composition using basic interval patterns

Now that we are able to build four-part textures using basic interval patterns, we can analyze larger pieces of music. Consider the following chorale by Johann Sebastian Bach:

Analyzing the entire chorale may seem daunting at first, so let us begin with the first phrase:

If we consider only the outer voices we can see the standard interval progressions that form the basis of this chord progression:

As you can see, all of the intervals between the soprano and bass form valid interval progressions. Even the decorative passing eighth note in the bass takes advantage of the oblique 5–6 progression.

Adding the alto voice, we see that most of the intervals formed with the bass or soprano are valid:

For the most part, the alto voice harmonizes the soprano with parallel thirds. At the end of the first measure, however, the intervals between the alto and soprano diverge to form fourths. These dissonant intervals are justified by the interval progressions formed by the alto and the bass. These are all valid progressions and we can see that the alto is harmonizing the bass at the end of m. 1 (8–10–10–10). The dissonant fourths, therefore, are resultant intervals.

When we add the remaining voice, the tenor, we can see that it forms valid interval progressions with the soprano (except for the dissonant seventh on beat two of the second measure) and the bass:

Except for the third on the downbeat of m.1 and the 5–3–5 at the end of the same measure, the intervals formed between the alto and bass are mostly resultant intervals.

Activity 14-9

Activity 14–9

In this activity, you will analyze the interval progressions of the second phrase of the same chorale.

### Question

Identify the interval progressions between the tenor and the soprano voices:

8, 6, 6, 4, 5, and 6

### Follow-up question

Do any of these progressions contain resultant intervals?

Yes: the fourth on beat three of the first complete measure.

# 14.10 Summary

The standard interval progressions discussed in Chapter 12 form the basis of multi-voiced tonal music. A great deal of multi-part music is found in chorale-style SATB setting. Keeping track of four voices at once can be a formidable task, so familiarity with the workings of two- and three-voice progressions will aid in the writing and analysis of more complex textures.

In three-voice textures it is possible to maintain valid interval progressions between all voice pairs. This is not always the case with four-voice textures. Because of the increased number of inter-voice relationships, dissonant, resultant intervals are often formed. These dissonances arise as the result of valid interval progressions between other voice pairs and are effectively covered up by the consonances.

These basic interval progressions are the foundation of multi-voiced textures and govern many complex compositions. By breaking an SATB setting down first into its outer voices and then adding the inner voices, you will be able to trace these fundamental progressions and explain the resultant dissonances that inevitably occur.