Descending-Fifths Sequence

Consider the following example (Example 1), often referred to as the “descending-fifths sequence.”

Example 1. A diatonic descending-fifths sequence.

The sequence model, a root progression by descending fifth, is transposed down by second in each subsequent copy of the model. Because the sequence uses chords entirely from the key of G major, the root motion doesn’t match exactly throughout the sequence. For example, the root motion between the IV and viio chords is an augmented fourth, whereas the root motion between every other pair of chords is either a perfect fifth or perfect fourth. We “cheat” in the sequence in this way in order to keep the music within a single key. If the interval between successive chord roots was consistently a perfect fifth/fourth, the root progression would be as follows: G–C–F–B♭–E♭–A♭–D♭… and so on. The sequence would rather quickly bring the music outside of the key of G major, and into new chromatic territory. It would become a chromatic sequence.
Chromatic sequences differ from their diatonic counterparts in a few important ways:

• The chords that initiate the sequence model and each successive copy contain altered scale degrees.
• The chords within the pattern are of the same quality and type as those within each successive copy of that pattern.
• The sequences derive from those that divide the octave equally.

Importantly, chromatic sequences are not merely sequences that contain chromatic pitches. Example 2 shows the same descending-fifths sequence, this time with alternating secondary dominant chords. While the sequence contains chromatic chords (the secondary dominants), it is not a truly chromatic sequence because the overall trajectory of the sequence is still one that traverses the scale steps of a single key. Notice that the progression of chord roots on successive downbeats still matches the purely diatonic sequence shown in Example 1: G–F♯–E–D.

Example 2. A diatonic descending-fifths sequence with alternating secondary dominant-seventh chords.

Conversely, we can create a truly chromatic sequence if we ensure that the progression of chord roots maintains a consistent pattern of intervals throughout the sequence. An easy way to do this is to make the second chord of the sequence model into a dominant-seventh chord that can be applied to the first chord of the subsequent copy of the model. In Example 3, the second chord of the model is now F⁷ instead of a diatonic IV chord. We interpret this as V⁷ of the chord that follows, which is, in turn, another dominant-seventh chord.

Example 3. A chromatic descending-fifths sequence with interlocking secondary dominant-seventh chords.

The voice leading in the above sequence requires some attention. Because every chord is interpreted as a dominant-seventh of the chord that follows, it is not possible to resolve both the leading tone and the chordal seventh as normal. As is the case whenever you connect seventh chords with roots a fifth apart, the voice leading requires an elided resolution. Instead of the chord you expect to hear following a dominant-seventh chord, you get a dominant-seventh chord with the same chord root. For example, we expect to hear either a C or Cm chord following a G⁷ chord. An elided resolution would result in a C⁷ chord in place of the expected chord. An example of an elided resolution is shown in Example 4. The example shows the expected C resolution in parentheses. The elided resolution essentially “elides” the chord we expect with the following chord, C⁷. In a sense, we mentally skip over the expected chord to get to the next dominant-seventh chord. An important result of the elision is that the leading tone of the first dominant-seventh chord, B, resolves down by half step to become the new chordal seventh. Likewise, when the chordal seventh in the first dominant-seventh chord, F, resolves down by half step, it becomes the new leading tone. This leading tone/chordal seventh exchange is essential for proper voice leading in chord progressions that use interlocking seventh chords, such as the sequence above. Furthermore, this kind of voice leading is integral to the study of jazz harmony, as you will find in other parts of this textbook.

Example 4. An elided resolution of a dominant-seventh chord.

Returning to Example 3, notice that the progression of chord roots on each successive strong beat divides the octave equally into major seconds. This results in a sense of tonal ambiguity, making the Roman numeral analysis of these chords tenuous, at best. In particular, the chords identified with asterisks in the example are only labeled as such for consistency. In many cases, when analyzing highly chromatic music, it is often quite difficult to assign Roman numerals to chords; this tonal ambiguity is part of the aesthetic of this kind of music. In cases like this, it is often convenient to also analyze the music using lead-sheet symbols. These have been included in the examples in this chapter.

Ascending 5–6 Sequence

Example 5. A diatonic ascending 5–6 sequence.

Example 6. A chromaticized diatonic ascending 5–6 sequence, featuring secondary dominant chords.

The above examples present the diatonic ascending 5–6 sequence (Example 5) and its chromaticized variant (Example 6). Note that both of these include an inconsistent pattern of intervals between chord roots in the second measure. To that point, the pattern of chord roots was a descending minor third followed by an ascending perfect fourth. From beat 1 to beat 2 in m. 2, the chord roots are D to B♭—a major third. To make this a truly chromatic sequence, this interval must be corrected to match the others. Thus, we would change the B♭⁷ to a B⁷. Likewise, we would then change the chord that follows the B⁷ to a chord with a root of E (rather than E♭), to preserve the root progression by perfect fourth (Example 7).

Example 7. A chromatic ascending step sequence, featuring secondary dominant chords.

A similar problem arises with the chord qualities used at the beginning of each subsequent copy of the sequence model. The first chord of the sequence is major, so for it to be a chromatic sequence, we must change the remaining first chords of each iteration to be major as well. The final result is a sequence in which the chord on every strong beat is a major triad with roots a major second apart. If it were to traverse the entire octave, the sequence would divide the octave into major seconds. In Example 7, though, the sequence stops once it reaches the E major triad, treats that triad as a dominant chord, and modulates into A major. The modulation brings the music down a half step from its starting key. Distant modulations such as these are one of the reasons that chromatic sequences can be powerful tools.

Descending 5–6 Sequence

Example 8. A diatonic descending thirds sequence.

Example 9. A chromatic descending 5–6 sequence that modulates from D major to C major.

Example 10. A chromatic descending 5–6 sequence using inverted chords on every weak beat. The sequence outlines the whole-tone scale on every strong beat.

The familiar “Pachelbel” sequence (Example 8) can derive a chromatic sequence in a couple of ways. The diatonic version of this sequence alternates root motion by perfect fourth with either major or minor seconds. The fully chromatic version of this sequence replaces the root motion by second with root motion by minor third (Example 9). This version of the sequence traverses the octave by major seconds, outlining the whole-tone scale and creating a strong sense of harmonic ambiguity by its end. When you listen to Example 10, for instance, notice that the D major chord that finishes the sequence hardly sounds like the tonic, even though, nominally, it is. This version of the sequence also uses inverted chords on every weak beat, creating a bass line that descends through the chromatic scale. In Example 11 below, Schubert uses this sequence as a means of tonic prolongation.

Example 11. A chromatic descending 5-6 sequence.

Parallel 6/3 Chords

Recall the parallel 6/3 chord sequence, which consists of successive triads in first inversion. If you’re writing in four voices, To avoid parallel octaves in this sequence, you will need to have one of the voices hop around, as this sequence is the only one in which we don’t use a two-chord sequence model (notice the tenor voice in Example 12 below).

Example 12. A diatonic parallel 6/3 sequence.

These kinds of sequences are often paired with chains of 7-6 suspensions, as shown in Example 13.

Example 13. A diatonic parallel 6/3 sequence with chains of 7-6 suspensions.

And similar to the previous sequence types, these sequences can be chromaticized by using the same transposition and chord qualities throughout the sequence. This results in a less tonally stable passage, but one that achieves the same goal of prolonging the tonic harmony through to the predominant harmony in the phrase. Example 14 provides an alteration of the two diatonic versions seen above.

Example 14. A chromatic parallel 6/3 sequence with chains of 7-6 suspensions.

Example 15, from Chopin’s Impromptu in A[latex]\flat[/latex] Major, shows a fully chromaticizied sequence of parallel 6/3 chords. Each chord is a major triad, and those triads are transposed down a semitone until the ii chord is reached, which then brings the passage to a half cadence.

Example 15. A a fully chromaticizied sequence of parallel 6/3 chords.

Advanced Variations on the Chromatic Descending-Fifths Sequence

Recall the chromatic descending-fifths sequence from Example 3. One way to give this sequence a smoother bass line would be to invert every other chord, so that there is an alternation between V4/3 chords and V7 chords in the sequence model. Example 16 shows this subtle variation with a new bass line. The leading tone of each chord has been highlighted in red, as it will be come very important to trace this pitch throughout the next several examples.

Example 16. A chromatic descending-fifths sequence with chords alternating between second inversion and root position.

As we learned a long time ago, dominant-seventh chords and diminished-seventh chords have the same function, and in many cases one can be used in place of the other. In Example 17, we have replaced all of the dominant-seventh chords from the previous example with diminished-seventh chords with the same bass note. These chords serve the same function as their dominant-seventh counterparts–note that the leading tone in each chord is the same as the ones found in the previous example.

Example 17. A chromatic descending-fifths sequence that replaces the dominant-seventh chords with equivalent diminished-seventh chords. 

In Example 18, J.S. Bach shows this technique in action. After establishing the key of F minor, Bach presents a sequence of diminished-seventh chords, alternating between applied viio4/2 and viio6/5 chords. Since diminished-seventh chords are symmetrical, this sequence sounds enharmonically equivalent to a descending series of root-position diminished-seventh chords (or any other inversion, for that matter). As is shown in the brief analysis, any one of these chords could be interpreted as a pivot chord into the new key of g minor, where it ultimately ends up with a half cadence a few measures later.

Example 18. A chromatic sequence of diminished-seventh chords that provides a vehicle for modulation.

Returning to our first example of a chromatic descending-fifths sequence, we can vary it again, this time by using a flattened fifth in each chord. When we invert the first chord in the sequence model, as shown in Example 19, we get a chromatic bass line descending in semitones, much like the variation that uses diminished-seventh chords.

Example 19. A chromatic sequence of diminished-seventh chords that provides a vehicle for modulation.

Alban Berg’s “Schlafend trägt man mich,” shown in Example 20, offers a wonderful example of this technique that not only shows off the sequence itself, but the way in which this kind of chromaticism pushes the boundaries of tonality to its limits. While this song uses a key signature, it is quite difficult to hear a tonic throughout. The chromatic descending-fifths sequences is laid out clearly in the piano, both in the opening and at the end of the piece. The forward motion driven by this sequence harmonizes the singer’s text in which they year for their homeland (“in mein Heimatland”). Note that Berg is using this chord progression non-sequentially; the piano does not follow a strict pattern throughout. Rather, the chord progression follows the pattern of dominant seventh chords with flattened fifths laid out in the previous example. Furthermore, the chords are presented in root position. Because of the lack of tonal clarity in this piece, the chords have been analyzed simply with lead sheet symbols, rather than Roman numerals.

Example 20. A sequence of dominant-seventh chords with flattened fifths.

Another way to scrutinize the sequence above is to consider each pair of chords in the sequence model to be a singular unit consisting of an augmented-sixth chord and a dominant-seventh chord in a given key area. For example, while we first identified the initiating chord in the sequence to be Vo4/3 of F, we could also consider it to be a French augmented-sixth leading to V in the key of B♭, as is shown in Example 21. This works because of the enharmonic equivalence between the French augmented-sixth chord and the dominant-seventh chord with a diminished fifth.

Example 21. A sequence of dominant-seventh chords with flattened fifths enharmonically reinterpreted as a succession of French augmented-sixth chords followed by dominant-seventh chords. 

Taking this sequence one step further, we can substitute German augmented-sixth chords for the French augmented-sixth chords, as shown in Example 22. Note that when we do this, we get what is enharmonically equivalent to a succession of dominant-seventh chords descending by semitone. We also produce parallel fifths between each successive chord, which Chopin did not seem to mind in his application of this sequence which you can listen to in Example 23.

Example 22. A sequence of German augmented-sixth chords followed by dominant-seventh chords. 

Example 23. A sequence of German augmented-sixth chords followed by dominant-seventh chords in Chopin’s Mazurka in C♯ Minor Op. 30 No. 4, mm. 124-39.

There are, of course, myriad ways in which we may vary a chromatic sequence. The examples listed throughout this chapter merely represent some of these options. Importantly, all of these chromatic sequences transport the listener away from the tonal center, for the purposes of either a temporary disruption of stability, or to modulate into a distantly-related key. These techniques were used by composers throughout the nineteenth century, and were part of what contributed to pushing tonality to its fringes as we moved closer to the turn of the twentieth century.

1. Chromatic Sequences Assignment (Part-writing and analysis)