II. Diatonic Polyphony and Functional Harmony
When performing, analyzing, or listening to Western art music, you will occasionally encounter passages where a harmonic pattern coupled with a melodic pattern repeats at successively higher or lower pitch levels. An example of this appears in the following excerpt:
Following an authentic cadence in m. 5, we find a series of chords whose roots descend by fifths. Comparing m. 6 with mm. 7–8, we find a repeated pattern in each measure, the only differences being the pitch level of each repetition. In the highest voice, the pattern begins on F in m. 6, and then repeats on E in m. 7 and D in m. 8 before landing on C in m. 9. In the bass, the repeated pattern begins on D in m. 6 and steps down through C (m. 7) and B (m. 8) before arriving on the tonic (A) in m. 9. Harmonically, the pattern ends right where it began: with a I chord. With that in mind, we can consider the entire passage from the second half of m. 5 to the downbeat of m. 9 to be an expansion of tonic harmony.
When successive repetitions occur at different but predictable pitch levels, as in Example 25–1, the patterning is called a sequence. Sequences appear with greatest frequency in Baroque music, but were used in every era of the common practice period. As we will discuss in this chapter, sequences function in a number of ways, but always derive from a handful of basic interval progressions. (See Chapter 12 to review basic interval progressions.)
We will begin with a brief discussion of the general nature of sequences and will then proceed with an examination of some common variations on the basic principles. This chapter focuses on the most common types of sequence and is accompanied by a follow-up chapter (Chapter 26) that considers several less common varieties.
25.2 The nature of sequences
Composers generally employ sequences either to expand a single harmony—as we saw in Example 25–1—or as a transitional device from one framing harmony to another, sometimes from one key to another. In all cases, identifying the function of a sequence depends on a listener’s ability to recognize the repeated pattern in context. Generally, we first hear the repetition in the contour of the leading melodic voice. But these repeated lines or motives are always linked to strong harmonic patterns, which in turn derive from basic interval progressions.
Sequences are based on the same harmonic progressions that appear everywhere in tonal music. Progressions in which the chord roots descend by fifth are by far the strongest and most frequent, but ascending-fifth and descending- and ascending-third progressions are also quite common (see Chapter 26). In this sense, sequences are an extension of basic tonal practices expressed in a unique way.
Let’s take another look at the excerpt from Example 25–1.
Identify each of the harmonies indicated by the blank lines in the following sequence in A minor. Use Roman numerals and identify the chord roots by their letter names. The beginning and ending chords have been done for you:
Remember to use uppercase letters for major chords and lowercase for minor.
The following example shows the harmonic progression of the excerpt from above:
The root of each successive triad, starting with the tonic chord on the third beat of m. 5, is a diatonic fifth lower than the previous one: A–D–G–C–F–B–E–A. (Some of these descending fifths are expressed as ascending fourths. This is done to stay within a reasonably narrow pitch range.) Here, the sequence traverses an entire cycle of descending fifths, from tonic back to tonic. This is common—particularly with descending-fifth sequences—but most sequences consist of only three to five repetitions since completing an entire cycle can become tedious.
Note: This sequence and the others considered in this chapter are diatonic: all of the chords are native to a single key. Because the repetitions are not literal, you will find some variation in quality. In Example 25–2, the chords in m. 6 are minor and major, while those in m. 7 are both major. Regardless of the changes in quality, the similarity of the melodic contour and the consistency of the root motion between successive chords are explicit enough for the listener to recognize the repeated pattern.
In addition to considering the repeated material—melodic and harmonic—it is essential that you be able to recognize the underlying interval patterns that form the basic structure of sequences. In multi-voiced settings, look to the outer voices for these governing progressions. The following example provides a reduction of the sequence in Example 25–1, showing the successive intervals formed by the highest and lowest voices:
In mm. 5–6, the upper voice moves from E up to F and initiates the sequence. That F remains in effect throughout the measure, even while the bass leaps up to G forming a dissonant seventh. This dissonance between the outer voices impels the progression to continue and the pattern repeats—10–7–10–7–10–7—until the pattern is broken in m. 9. Such patterns are sometimes referred to as linear intervallic patterns, or, LIPs for short. Each of the sequences discussed in this chapter can be similarly analyzed as LIPs.
The reduction given in Example 25–3 also shows a second level of Roman numerals. In this case, we can see that the sequence functions as a prolongation of the pre-dominant area of a basic phrase: tonic–pre-dominant–dominant–tonic.
25.3 Descending-fifth sequences
Sequences in which the chord roots descend by fifth are common enough that they should be instantly recognizable by ear. Compare the following excerpt with the example from above:
Despite some superficial differences, these two passages have a very similar sound. In this case, however, the sequence does not complete the cycle of descending fifths, but rather goes only as far as the dominant (m. 65). Following a C-minor chord in m. 60, the chord root moves down a fifth (or, in this case, up a fourth) to the iv7 chord in m. 61. The root progression continues to descend by fifth (or ascend by fourth) through a VII7 chord in m. 62 and a III7 chord in m. 63. Starting in m. 64, the sequence speeds up. Composers will sometimes speed up the harmonic rhythm like this to add variety to a sequence. Here, each successive harmony lasts only two quarter notes instead of three: VI7–iio7–V7 in mm. 64–65. Finally, the VI chord in m. 66 breaks the pattern and ends the sequence with a deceptive progression.
Now consider the interval progression formed by the outer voices. Example 25–5 provides a reduction:
On the downbeat of m. 61, the highest voice (Ab) forms a tenth above the bass (F). That Ab is suspended into the next measure where it forms a seventh above the new bass note (Bb). This pattern repeats twice more in mm. 63–65. The sequence, therefore, follows the same LIP that we saw in Example 25–3. The 10–7 pattern is the most common voice-leading structure for descending-fifth sequences. The final dissonant seventh (the G and F of the V7 chord in m. 65) resolves inward to a perfect fifth with the deceptive cadence that ends the sequence. Like the one in Example 25–2, this sequence prolongs the subdominant section of the basic phrase (iv to iio).
Note: Another consequence of using only diatonic chords is the inevitable inclusion of diminished and augmented intervals. Composers negotiate these dissonant sonorities in several ways, as you’ll see from the various examples in this chapter. In this excerpt, for example, the tritone that arises between the roots of the VI and iio (Ab and D) chords is obscured by the weak (and unexpected) metric placement of the diminished chord.
The following excerpt from a Schubert impromptu includes a complete cycle of descending fifths, this time in a minor key:
Following a cadence in m. 24, Eb major becomes Eb minor with the addition of Gb (and, subsequently, Db and Cb). The descending-fifth sequence that follows, beginning with iv in m. 26, completes the cycle from the initial i chord to the tonic in m. 32. Harmonically, the iv chord in m. 33 continues the descending-fifth series, but by then, the melodic pattern in the upper voice is broken.
Sequences in minor keys, in addition to the extra tritone between scale degrees 2 and 6, bear the added complication of the harmonic and melodic composites of the scale. (See Chapter 16 for more information on the harmonic and melodic minor composites.) Typically, in a minor-key sequence, scale degrees 6 and 7 are left in their diatonic form, appearing in their raised form only at sequence-ending cadences. Notice that in mm. 25–30, every instance of scale degrees 6 and 7 is diatonic (Cb and Db, respectively). Using diatonic 7 avoids the diminished triad built on the leading tone. It is only with the V chord towards the end of the sequence (m. 31) that we find the raised leading tone, effectively signaling the end of the progression.
Now, let’s look at the outer-voice interval progression:
As Example 25–7 shows, this excerpt is based on the same interval progression already familiar from Examples 25–1 and 25–4: tenths becoming suspended sevenths. After the initial Gb is heard in m. 25 as the third of the now minor tonic, the upper voice leaps up to Cb in m. 26. That Cb is heard again in m. 27, though there it appears as a seventh above the new bass (Db). (This suspension is indicated with a tie in the reduction.) The pattern is then repeated in mm. 28–29, and again 30–31, leading back to Gb and the minor tonic in m. 32.
Other outer-voice interval progressions are possible as well. The progression that defines a sequence depends on whether or not the harmonies appear in inversion and, in large part, on which chord members appears in the upper voice. Below are the 10–7 LIP already discussed and the resultant 10–5 pattern that would arise by alternating between root position and first inversion chords.
a. 10–7 LIP
b. 10–5 LIP
As you can see from Example 25–8, alternating between root position and first inversion chords creates a smoother bass line and alters the LIP. Such altered sequences are quite common., as the following excerpt demonstrates (Example 25–10 provides a reduction):
Following a borrowed major tonic in m. 69 (see Chapter 29 for more on borrowing), a descending-fifth sequence begins, starting on the diatonic subdominant chord. The root-motion descends by fifth for three full measures before the ending with the tonic chord on the downbeat of m. 73. The sequence is very similar to Example 25–7 discussed above, the only difference being the inversion of every other chord and the resultant 10–5 LIP.
As you may have deduced, 10–7 and 10–5 are far from being the only possible LIPs in a descending-fifth sequence. Other LIPS are also possible. Consider the following example:
This excerpt includes another descending fifth sequence in mm. 84–86: ii–V6–I–IV6–viio. Unlike the examples above, however, the interval progression here alternates between thirds and sixths before the pattern breaks in m. 87 for the ending of the phrase.
The following example shows the harmonic framework of a descending-fifth sequence in four voices. Consider the interval progressions formed by each of the upper voices with the bass:
Identify the LIPs between the outer voices of the following sequence. (For example, you would write 10–7 for a LIP that alternates between tenths and sevenths, beginning with a tenth.)
What is the LIP between the outer voices?
6–10 or 6–3. As written, the outer-voice LIP of this sequence alternates between sixths and tenths. But any of the upper voices could have been written on top. It is important that you be aware of LIPs between inner voices as well for this very reason.
What is the LIP between the alto and bass?
10–8, 3–8, or 3–1. The alto and bass alternate between tenths (compound thirds) and octaves via a series of suspensions.
What is the LIP between the tenor and bass?
6–5. The tenor and bass alternate between sixths and fifths via a series of suspensions.
In Example 25–13, successive harmonies alternate between first inversion and root position. The soprano voice yields a 6–10 pattern with the bass, while the alto and tenor yield 10–8 and 6–5 patterns with the bass, respectively. Again, the LIP will vary depending on which chord member the composer places in the soprano. The sequence could, of course, also begin with a root-position chord: I–IV6–viio–iii6–etc., which would likewise affect the outer-voice intervals of the LIP.
Other outer-voice progressions are made possible by adding sevenths to each chord or by arranging them all in root position. In all cases, however, the underlying harmonic foundation remains intact.
Descending-fifth sequences are particularly prevalent in music of the Baroque era. The following excerpt, for example, makes great use of this device:
Beginning with the vi chord on the anacrusis to m. 14, a series of arpeggios in the left hand outline a descending fifth sequence through the remainder of that measure. In m. 15, the descending-fifth harmonic pattern set into motion by the sequence continues through V, I, and IV, despite the altered melodic pattern in the bass. At this point, the sequence is broken off, leading to an authentic cadence. Sequences such as this—which complete an entire lap around the circle of fifths and then some—are commonplace in Baroque music but were generally considered monotonous by later composers.
The outer-voice interval progression is particularly clear in this sequence. Beginning with the vi chord in m. 13 and going through the IV6 in m. 15, what is the LIP between the outer voices?
Look at the lowest note in each arpeggiation in the left hand.
3–5, 5–3, 10–5, or 5–10.
The outer-voice interval progression is particularly clear in this example. A series of suspensions in the upper voice creates a pattern of alternating thirds and fifths with the bass:
As the second level of Roman numeral analysis shows, this sequence prolongs the tonic for nearly one and a half measures before continuing on to the predominant chords and the ensuing cadence.
The following excerpt has a descending-fifth sequence in mm. 39–40. Identify each of the harmonies in the key of A major indicated by the blank lines:
The chords on beats one and three of each measure are missing their fifths. Also, the second of each group of three eighth notes is a nonharmonic tone.
m. 39 = ii–V–I–IV; m. 40 = viio–iii–vi–ii
Now that you’ve identified the progression as a descending-fifth sequence with root position harmonies, identify the LIP between the outer voices.
In this case, the upper voice consists of dotted quarter notes suspended into the next beat.
Sequences consist of melodic and harmonic patterns repeated at different pitch levels, which, after a few repetitions, become predictable. Diatonic sequences rely on the listener’s ability to recognize the basic design of the patterns, since the qualities may change from step to step in conforming to the key. Composers use sequences in a number of ways, primarily to prolong a specific harmony or to move from one harmony to another. Composers may therefore employ sequences to expand one or more parts of the tonic–pre-dominant–dominant–tonic phrase model. This chapter focused on non-modulatory sequences, but sequences can also be designed for modulating.
Each step of a sequence—that is, each cycle of the pattern—is successively transposed up or down at a specific interval until the harmonic goal (or key) is reached. The root movement in a majority of sequences is by descending fifths (or ascending fourths), which reflects the general prominence of descending-fifth root motion in tonal music.
Significantly, the voice-leading of sequences follows the same basic interval progressions that govern all tonal music. Being able to recognize these patterns in a sequence is an important part of understanding how they work. (It is not important to memorize all of the possible interval patterns that form the skeleton of the various sequence types.) These outer-voice linear intervallic patterns (LIPs) are determined partly by which chord member appears on top, and partly by whether all chords appear in root position or alternate between root-position and first-inversion.