(musicTheory2) Lecture Notes: Harmonic Sequences

Harmonic Sequence Defined

A Harmonic Sequence is a combination of harmonic root movements by a particular interval, and all voices moving in recurring sequential melodic patterns. Root movement by a single interval not combined with melodic sequences in other voices is called cyclical root movement. Note that we are talking about diatonic harmonic sequences, where interval transpostions conform to the current key. The quantity of the interval remains the same, but the quality will vary to remain in the key.

Harmonic Sequences vs. Typical Harmonic Progressions (and doublings)

The linear movement of harmonic sequences can be strong enough to interrupt (or interfere with) typical harmonic progressions. Consider a descending fifth harmonic movement of vii° to iii, which is ok during a sequence but not as a typical progression otherwise. Likewise, you will sometimes encounter chord tone doublings in a sequence (like a doubled leading tone) that are ok in a sequence but not a typical progression.

Root Movement Cycles

Typical root movement cycles are 5ths(4ths), 2nds(7ths), and 3rds(6ths). Typically, 5ths and 3rds descend, so as not to move in direct opposition to typical harmonic progression. 2nds can ascend or descend. Except with descending fifths, it is unusual to cycle through all seven diatonic tones in a single sequence.

Avoiding Parallel Fifths in Sequences of Seconds and Thirds

Harmonic sequences of thirds and seconds are likely to have parallel fifths. To avoid this, first inversion triads are usually inserted between sequential harmonies. The first inversion triads do not conform to the sequential root movement.

For descending thirds, first inversion triads appear between the sequential harmonies, creating a step-wise descending bass line that usually moves in parallel thirds with the melody. The chordal fifth of the sequential harmonies holds over as a common tone to the first inversion chords, before dropping a third to the next sequential root position harmony. (Example on p. 357 of the Gauldin)

For ascending seconds, first inversion triads appear between sequential harmonies in a 5 – 6 interval pattern over a sustained bass. In this case, the bass clearly moves according to the sequential root cycle. The inverted chords appear through linear movement in other voices. (Example on p. 356 of the Gauldin)

Distinguishing (Recognizing) Harmonic Sequences with First Inversion Triads

It is possible, and common, for sequences of descending fifths to alternate between root position and first inversion triads, with all triads being part of the sequential pattern. (Example on p. 347) Instead of a bass line that moves down by fifth, up by fourth, down by fifth, etc., you have a bass line that moves down by third, up by second, down by third, etc.

So how do you tell when the inverted triad is part of the cyclical root movement, and when it is an embellishment? Remember that harmonic sequences refer to movement of the root of the triads.

• Identify the root of each triad.
• Examine whether the root movement is always by the same interval, or if it alternates between two intervals.
  • If the root movement is by a single interval, then the first inversion triads are part of the cyclical movement. This will usually be the case with descending fifth sequences.
  • If the root movement alternates, then examine the interval between every other chord (usually in root position). If these intervals are the same, then that is the sequence (cycle) interval, and the first inversion chords are embellishments. This usually happens with sequences of seconds and thirds.

Harmonic Sequences and Analytic Reductions

Since harmonic sequences typically defy typical harmonic movement, we should consider sequences to be a series of embellishing harmonies. As such, we indicate Roman numerals only for the framing harmonies (first and last), using figured bass only for the interior of the sequence. For descending fifth sequences that end ii – V – I, the V is the framing end chord. Descending third sequences almost always end on ii, and so this becomes the ending framing harmony.

I – (IV – vii° – iii – vi – ii )- V – I –> should be written I – ( ) – V – I.

I – (6 – – 6 – – ) ii6 – V – I —> would be I – V6 – vi – iii6 – IV – ii6 – V – I if each harmony were to be indicated.

All bass and soprano notes are included in the reduction. Soprano and bass notes of interior inverted harmonies are not stemmed, whether they are part of the cyclical root movement or not. Consider them embellishments of the sequence. Soprano and bass notes of root position harmonies within sequences are stemmed.

(Examples on p. 347, desc 5th with inverted triads; p. 357, desc thirds with embellishing inversions between; p. 356, ascend seconds, with voice movement over bass)