A Handbook for Composition and Analysis
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When we repeat a musical pattern transposed up or down to another scale degree, we create a sequence. Sequences built upon unaltered scale degrees are diatonic sequences. Most often, diatonic sequences serve to delay V or prolong I.
Sequences serve two functions: They help create tension by delaying the arrival of an important harmony. They allow musical tension to unwind by expanding and prolonging a harmonic goal. A sequence has two parts:
The musical figure that we repeat is the sequential unit. As a rule, sequential units move by step or by third. They can ascend or descend.
Each sequential unit contains a pair of chords called the sequential progression. We distinguish among four basic diatonic sequences (see example 16-1).
Ex. 16-1 Basic Diatonic Sequences
Notice that the sequential units of examples 16-1a, 16-1b, and 16-1c move up or down by step. (In the examples, the sequential units are separated by bar lines.) That is, each measure of these three examples is transposed down (or up) by step in each of the following measures. The sequential progressions, however, move by fifths (examples 16-1a and 16-1b) or by a combination of thirds and fifths (example 16-1c). That is, the root progression of the succeeding chords is by fifth or thirds and fifths.
In contrast, the sequential unit of example 16-1d moves down by thirds. The sequential progression, however, moves by a combination of fifths and seconds.
As a rule, descending sequences are more goal-oriented than ascending sequences. Hence, most sequences descend. As a rule, sequential motion by descending step creates the strongest voice leading. Hence, most sequences descend by step.
Sequences that progress between scale degree triads are diatonic sequences. A diatonic sequence gets its name from its sequential progression. Example 16-1a is a descending-fifth sequence since the root progression between chords is by descending fifth. Remember, though, the sequential unit of this descending-fifth sequence moves by descending seconds.
The most common diatonic sequence is by descending fifths. The voice leading of each descending fifth mimics the voice leading of a dominant-tonic progression.
Remember: Only the roots of the sequential progression move by descending fifths.
Ordinarily, the bass does not move literally by descending fifths. It might move a fifth down and then a fourth up, still maintaining all chords in root position. Often, one or both of the chords in the sequential progression may appear in inversion.
Ex. 16-2 Mozart, Piano Sonata, K. 545, first movement
The sequence in example 16-3 prolongs the tonic by moving from I to I with a cycle of descending fifths. Note that the first chord of each measure is in first inversion, providing a stepwise motion into the root of the second chord of each unit. This adds special emphasis to the root position chord on the third beat of each measure. As a result, the final I of the sequence arrives in root position - even though we began the sequence on I6.
A succession of descending s can function sequentially. They form the simplest sort of diatonic sequence. In a descending sequence, both the sequential unit and the sequential progression move by step.
Ex. 16-3 Mozart, Piano Sonata, K. 284, first movement
Here a succession of s prolongs the motion from a contrapuntal dominant (V6) to I6. Each measure constitutes a sequential unit. Each constitutes the sequential "progression." The succession of 7-6 appoggiaturas descends by step - as does the rest of the sequential unit. Note that all the voices move in parallel.
Ascending Fifths. Sequences by ascending fifths are rare by comparison with sequences by descending fifths. They are usually incomplete, following the pattern of example 16-1b. As often as not, they prolong the motion from I to the lower-third divider, vi.
Ex. 16-4 Beethoven, Seven Bagatelles, Op. 33, No. 2
In example 16-4, Beethoven prolongs a I-vi-IV- motion with an ascending-fifth sequence. He uses the sequence to prolong the motion from I to vi. He does this by inserting the two (ascending) fifths that stand between I and vi, making the progression I-(V-ii-VI#).
Why the major triad on VI? The first unit moves from I to its upper fifth divider, V (measures 1-4). The second unit does the same (measures 5-8). If ii is the "tonic" of this unit, then vi must become a major triad in order to act as "dominant" of ii. In effect, then, VI# tonicizes the ii that precedes it. The ii-VI#-IV progression, then, sounds like a i-V#-VI deceptive progression in ii, D minor. This is still a diatonic sequence - despite the altered note. Why? Because the root progression is by scale degrees. That is, the progression is diatonic.
Notice that example 16-4 has two sequential units, each occupying four measures. The second unit transposes the first up by a step. Each unit contains two harmonies (I-V, ii-VI#), with the roots of each ascending by fifth to the next.
Ascending 5-6. Ascending 5-6 sequences arise even less often than ascending fifth sequences. When they do arise, they will, as a rule, following the pattern outlined in example 16-1c.
Ex. 16-5 Mozart, Piano Concerto, K. 488, first movement (piano solo)
In example 16-5, Mozart expands a prominent IV with an ascending 5-6 sequence. He arrives on IV in the first measure shown. That IV then ascends by sequential 5-6s back to I. Once on I, it returns to the root position IV on which it began and continues where it left off. The sequential unit is a half note long. Each unit ascends by step.
Sequences by descending thirds move from I through the lower-third divider (vi or IV6) to the lower-fifth divider (IV or ii6). Ordinarily, this motion precedes a move to the dominant.
We often see descending s paired to create a sequence of descending thirds.
Ex. 16-6 Mozart, Piano Sonata, K. 283, first movement
Example 16-6 begins with a succession of s embellished by 7-6 suspensions (measures 1-2). An embellished version of the same progression follows immediately (measures 4-5). The sequential unit of this second sequence (X) descends by thirds to the lower-fifth divider and then to the dominant: I-vi-IV-V.
The sequential progression of the descending 5-6 ascends by fifth then descends by step. The sequential unit descends by thirds. We find a classic example of this sequence in Mozart's final opera Die Zauberflüte ("The Magic Flute").
Ex. 16-7 Mozart, Die Zauberflüte, Act I, No. 5, "Drei Knäbchen"
As the bass moves by step from to an octave lower, s alternate with s to support it. The final I moves into a half cadence on V.
Because of the altered pitch classes in the minor, sequences become more complex. Minor sequences can function as they would in the major, making allowances for altered notes.
Ex. 16-8 Mozart, Piano Sonata, K. 310, third movement
This motion from i to i through a cycle of descending fifths is almost identical to example 16-3, above. Notice that Mozart alters scale degrees only when necessary. That is, he avoids alterations except at the beginning and the end as V approaches i. As a result, III is momentarily tonicized.
Composers often focus a minor sequence on the relative major, III. For example, descending- and ascending-fifth sequences often outline the upper-third divider (III) in a move to V. When they do, they frequently follow the pattern shown in example 16-9. Ex. 16-9 Sequences by Fifth in the minor
Notice that in ascending-fifth sequences in the minor, the sequence begins on the third divider (see example 16-9a). The descending-fifth sequence in the minor, however, ends the sequence on the third divider (see example 16-9b). In both cases, III is momentarily tonicized.
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