Descending-Fifths Sequence

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

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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 progressions don’t match exactly throughout the sequence. For example, the root progression between the IV and viio chords is an augmented fourth, whereas the root progressions 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.

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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.

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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.

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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

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Example 5. A diatonic ascending 5–6 sequence.

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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).

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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

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Example 8. A diatonic descending thirds sequence.

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

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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.

1. Coming soon!