II. Diatonic Polyphony and Functional Harmony

# 16.1 Introduction

Chapter 7 introduced the diatonic minor scale. There we saw that parallel scales—the pair of major and minor scales that begin on the same pitch class—share four of their seven scale degrees ( $\hat1$, $\hat2$, $\hat4$, and $\hat5$). The remaining three ( $\hat3$, $\hat6$ and $\hat7$) are each a semitone lower in minor than in the parallel major. Therefore, the defining pattern of whole steps and half steps is different: W-W-H-W-W-W-H in the major scale and W-H-W-W-W-H-W in the diatonic minor.

We refer to the scale shown above as the natural or diatonic minor since it consists of only those pitches specified by the key signature. In practice, however, composers tend to make small melodic and harmonic adjustments to make the minor scale sound and function more like its major counterpart. There are, in other words, several commonly used variants of the minor scale.

In this chapter, we will describe two adjusted forms of this scale. In each case, we will discuss the various musical contexts in which it appears as well as the factors motivating a composer to use it. As we will see, these variants incorporate tonality-defining characteristics of the major scale.

# 16.2 The seventh scale degree in minor

In Chapter 7 we discussed how the diatonic minor scale differs from the major scale. The differences become apparent when the natural minor scale is used in melodies and harmonic progressions. Consider, for example, the following example:

The melody in this passage arrives at E# on the downbeat of m. 3. This E#an altered form of scale degree $\hat7$pulls strongly toward the F# tonic that follows, bringing the first musical idea to satisfying conclusion. (The quick G# at the end of m. 3 is simply a decoration of the F#.) In m. 5, the melody returns to scale degree $\hat7$, but this time closer to the beginning of a musical gesture. Here, where there is less of a need for a strong resolution to scale degree $\hat1$, the E is left natural, in its diatonic form.

Now listen to the passage again, but with diatonic E§s replacing all of the E#s:

Compared to Example 16–2, Example 16–3 lacks the strong pull of E# to F#. The melody seems off. The listener’s sense of closure in m. 4 is not nearly as strong. The reason for the lack in pull toward the tonic—both in Example 16–3 and in the diatonic minor scale in general—is the absence of a leading tone.

Look again at Example 16–1 and note that the seventh scale degree is a whole step away from the tonic. The half-step relationship between the leading tone and the tonic in the diatonic major scale has a clearly perceptible directional force, while the analogous scale degree in the diatonic minor lacks that force. Because of its tendency to resolve to the tonic, the leading tone is one of the most important pitches of the major scale. Since the diatonic minor scale lacks a leading tone, the tension and pull toward the tonic are absent.

Note: In the sections below we will use the term “composite” to define and describe a pair of adjustments often made to the minor scale. This term is not commonly used outside of this book. Nonetheless, we feel it conveys an accurate sense of both the historical origins of these idioms as well as the listener’s experience.

# 16.3 The harmonic minor composite

Consider the following chord progression which uses only the diatonic pitches of C minor:

This progression does not exhibit a strong pull toward the concluding tonic harmony. Similar to what we saw with Example 16–2 and Example 16–3, this is due to the absence of the leading tone. The harmonic minor composite (often referred to as the “harmonic minor scale”) adjusts scale degree $\hat7$ of the diatonic minor scale in imitation of the major scale in order to create the otherwise missing leading tone. The Bb of the diatonic C minor scale is adjusted upward to B§, creating the needed leading tone, as shown here:

The following example reproduces Example 16–4, this time with the leading-tone adjustment:

As you can hear, the presence of the leading tone in Example 16–6 creates a stronger, more satisfying sense of resolution at the arrival of the tonic.

As Example 16–7 shows, the raised seventh scale degree applies only to the chords built on scale degrees $\hat5$ and $\hat7$. If these chords were built using the pitches of the diatonic minor, V would be minor (v) and viio would be major (VII). Neither v nor VII pull toward the tonic as strongly as their leading-tone adjusted forms, although both appear in other functional roles in a minor key. Listen again to Example 16–4 and compare it to Example 16–6. Which version of the V chord has a stronger pull back to tonic? The addition of a leading tone gives Example 16–6 a stronger sense of resolution. The same would be true of a progression using viio instead of VII. In adjusting the diatonic minor scale by incorporating the leading tone from the major scale, we have the same V and viio triads in minor as we do in the parallel major.

Note: You may be wondering why the harmonic minor applies to the chords built on scale degrees $\hat5$ and $\hat7$ but not $\hat3$. This is due in part to the functions that these chords typically perform in tonal music. We will explore the concept of harmonic function more fully in Chapter 22. For the time being, however, consider the quality of the chord built on scale degree $\hat3$. If the seventh scale degree were to be raised in a III chord, the result would be an augmented triad. The triad built on scale degree $\hat3$ is the tonic of the relative major. Having an augmented triad here would subvert this important relationship and is therefore not permitted. In this light, one should think of the harmonic minor scale not as a key in its own right, but rather a variant of the diatonic minor used at times to create a stronger sense of tonality.

Activity 16-1

Activity 16–1

The harmonic minor composite incorporates a leading tone to give a stronger sense of tonality. In this activity, you will be presented with a series of chords in minor keys. Some of these chords require a raised leading tone while others do not. Adjust the notes to incorporate a raised leading tone where appropriate.

### Question

Does this chord require any adjusted notes? If so, adjust the notes where necessary to reflect the harmonic minor composite.

Hint

Remember, in the harmonic minor composite, the leading tone is raised for chords built on scale degrees $\hat5$ and $\hat7$.

G should be G#.

### Question

Does this chord require any adjusted notes? If so, adjust the notes where necessary to reflect the harmonic minor composite.

Hint

Remember, in the harmonic minor composite, the leading tone is raised for chords built on scale degrees $\hat5$ and $\hat7$.

No change needed.

### Question

Does this chord require any adjusted notes? If so, adjust the notes where necessary to reflect the harmonic minor composite.

Hint

Remember, in the harmonic minor composite, the leading tone is raised for chords built on scale degrees $\hat5$ and $\hat7$.

C should be C#.

### Question

Does this chord require any adjusted notes? If so, adjust the notes where necessary to reflect the harmonic minor composite.

Hint

Remember, in the harmonic minor composite, the leading tone is raised for chords built on scale degrees $\hat5$ and $\hat7$.

A should be A#.

### Question

Does this chord require any adjusted notes? If so, adjust the notes where necessary to reflect the harmonic minor composite.

Hint

Remember, in the harmonic minor composite, the leading tone is raised for chords built on scale degrees $\hat5$ and $\hat7$.

No change needed.

### Question

Does this chord require any adjusted notes? If so, adjust the notes where necessary to reflect the harmonic minor composite.

Hint

Remember, in the harmonic minor composite, the leading tone is raised for chords built on scale degrees $\hat5$ and $\hat7$.

F should be F#.

# 16.4 The melodic minor composite

The melodic minor composite (often referred to as the “melodic minor scale”) provides a further modification of the diatonic minor to accommodate certain melodic circumstances. As with the harmonic minor composite, the melodic minor has a leading-tone adjustment. The raised seventh scale degree serves the same purpose as in the harmonic minor composite: it creates a pull toward the tonic. Just as the V chord in Example 16–6 resolves to tonic harmony, the leading tone of the melodic minor scale resolves to scale degree $\hat8$. This type of goal-directed melodic motion is at the heart of tonal Western art music.

Raising scale degree $\hat7$ to create a leading tone, however, creates a melodic problem: an augmented second appears between the sixth and seventh scale degrees:

Augmented intervals are difficult to sing, sound awkward in the tonal style, and are therefore generally avoided. In the harmonic minor composite, the augmented second disrupts the otherwise smooth flow of half- and whole-step motion in the melodic ascent. Furthermore, scale degree $\hat6$ in minor is a half-step away from scale degree $\hat5$ and thus tends strongly toward scale degree $\hat5$. By raising scale degree $\hat6$, one may avoid both of these issues. The interval between $\hat6$ and $\hat7$ contracts to become a major second, thereby smoothing out the melodic line, and the whole-step distance between $\hat5$ and $\hat6$ eliminates the downward pull of $\hat6$ toward $\hat5$. When a melody descends through a minor scale, there is no longer a need for the raised scale degrees and the adjusted pitches typically revert back to their diatonic forms.

Example 16–9 summarizes the melodic minor composite, with the adjusted forms of scale degrees $\hat6$ and $\hat7$ in the scalar ascent, and the diatonic forms of those degrees in the descent.

Scale degrees $\hat6$ and $\hat7$ in minor appear in diatonic or adjusted form depending on several factors, primarily the melodic context. In practice, however, the form used is best explained on a case-by-case basis. Consider the following example:

Notice the D# in m. 1 and especially the C#–D# in m. 2. In both cases, the melody is directed toward scale degree $\hat1$. The raised sixth and seventh scale degrees strengthen this upward motion to the tonic. Notice, too, that these scale degrees return to their natural, diatonic form at the end of m. 2 where the melody descends, moving away from the tonic.

Compare the sound of Example 16–10 with that of Example 16–11, which uses only diatonic pitches:

Here, the music in mm. 1-2 feels heavy and meandering. It seems to lack direction when compared to the unaltered version above where the melody incorporates the melodic minor.

Activity 16-2

Activity 16–2

Like the harmonic minor composite, the melodic minor composite sometimes incorporates a leading tone to create a pull towards the tonic. To avoid the augmented interval between the submediant and the leading tone, the melodic minor composite will raise scale degree $\hat6$. In this activity, you will be presented with a series of diatonic minor scales. For each example, change scale degrees $\hat6$ and $\hat7$ to conform to the adjustments made in the melodic minor composite.

### Question

Change scale degrees $\hat6$ and $\hat7$ to conform to the adjusted melodic minor composite.

### Question

Change scale degrees $\hat6$ and $\hat7$ to conform to the adjusted melodic minor composite.

### Question

Change scale degrees $\hat6$ and $\hat7$ to conform to the adjusted melodic minor composite.

### Question

Change scale degrees $\hat6$ and $\hat7$ to conform to the adjusted melodic minor composite.

The minor mode is less straightforward than the major mode. It consists of a primary form, the diatonic minor (also known as the natural minor), and two composite forms that incorporate elements of the diatonic major scale. Because the diatonic minor scale lacks a leading tone, it does not allow for a strong resolution to the tonic. In order to allow for that vital progression in a minor key, scale degree $\hat7$ of the diatonic minor is adjusted (raised by a semitone) to create a leading tone, in imitation of the major scale, resulting in a composite scale commonly known as the harmonic minor. Another composite minor scale, commonly known as the melodic minor, adjusts scale degree $\hat6$ upward in addition to raising scale degree $\hat7$ in order to eliminate the awkward augmented second between $\hat6$ and $\hat7$ and to smooth out the melodic motion between scale degree $\hat5$ and $\hat8$. Scale degrees $\hat6$ and $\hat7$ are commonly restored to their diatonic forms in scalar descents.
It is important to remember that the diatonic minor scale is the basis of the two composite forms. The diatonic minor scale constitutes a key, the counterpart of the major key. The harmonic and melodic minor composites do not constitute independent keys. Rather, they are mixed-mode scales featuring adjustments to diatonic degrees $\hat6$ and $\hat7$ to suit certain harmonic and melodic contexts.