HARMONIC SEQUENCE

This page serves as a supplement to The Complete Musician Ch. 17 Harmonic Sequences

What is the difference between music and noise?

Pattern.

Rhythm as pattern…

Rhythms are presented in symmetrical blocks called “measures” or bars with consistent beats defined in the time signature. Repetitive rhythms are referred to as RHYTHMIC MOTIFS or OSTINATO patterns.

Pitch as Pattern …

Most “pleasant,” “comfortable” melodies have some amount of predictability to them and the melody is built on patterns of recurring scale degrees or intervals. Short melodic ideas that recur in musical phrases or across a larger work are also referred to as MELODIC MOTIFS while recurring patterns of scale degrees (including displaced/transposed versions) are called MELODIC SEQUENCES.

Harmony as Pattern …

By now, you (hopefully) agree that in Western Classical tonal music, chords exist in a hierarchy of strength, color, and tonal areas. If we were to throw random diatonic chords into a piece one after another, there would be a lack of structure and predictability that would sound bewildering. To achieve a more “pleasant” harmonic development, we place these chords in their intended areas in each phrase (Tonic, Predominant, Dominant). We can also go one step further to create more rigid patterns of chords that are not only predictable but mathematically precise in what chord comes next. These progressions are called HARMONIC SEQUENCES.

So what is a Sequence?

In Mathematics, a sequence is a list of numbers (ascending, descending, or ascending and descending based on the pattern) that follows a predictable, precise pattern. Some easy sequences include …

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21 … (odd numbers)

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 … (wow, even numbers)

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … (the Fibonacci sequence)

More complex math sequences would be like …

23, 21, 24, 19, 26, 15, 28, 11, 30, 7, 36 (alternate subtracting then adding consecutive prime numbers starting with 2)

2, 9, 3, 18, 4, 36, 5, 72, 6, 144, 7 (+1 to odd terms, x2 to even terms)

3, 8, 15, 24, 35, 48, 63, 80, 99, 120, 143 (starting with 1x3, each term increases the two factors by 1)

Notice that you need at least three terms to confirm the sequence/pattern and having four or more available make the sequence much more obvious. This is also true for musical sequences both melodic and harmonic.

BASIC HARMONIC SEQUENCE

Take a listen to this familiar harmonic sequence …

Starting on a tonic I chord, this pattern moves predictably down five scale degrees for each new diatonic chord, eventually circling back around to I. In the recording, you can hear some of the chords (the even chords) in inversion to accommodate a more melodic bass movement:

I - IV - viiᵒ - iii - vi - ii - V - I

Because this pattern is moving down five degrees on each new chord, it gives us a feeling of V - I motion (I - IV actually feels like V - I in the key of IV … vi - ii actually feels like v - i in the key of ii and so on) and the sequence finishes with literal V - I motion. Because of this motion, this sequence is called the CIRCLE OF FIFTHS PROGRESSION or CIRCLE PROGRESSION for short.

Now, listen to the next harmonic sequence …

If we move in the opposite direction, with the pattern ascending five scale degrees for each new diatonic chord, we feel plagal motion (IV - I movement) between each chord in the pattern. Again, the even chords are in inversion to facilitate stepwise bass. This “opposite” version of the Circle Progression is much weaker and never really used in music but is here to illustrate how sequences can create strong or weak motion.

I - V - ii - vi - iii - viiᵒ - IV - I

While the two sequences above are examples of sequences with the same movement for each “term” of the pattern, most harmonic sequences are a two-step pattern with a relationship between the first two chords and a different relationship between chord 1 and chord 3. This creates an “inner” and “outer” relationship and strong and weak motion within the context of the sequence.

DEFINING HARMONIC SEQUENCES

To save time, it’s faster to refer to a sequence by its chord-relationship function rather than writing out every chord term of the sequence. Most sequences start with a two chord pattern that is then replicated starting on another chord a certain distance from the opening chord. The original pattern (again, usually two chords) is referred to as the MODEL and the replication of the model pattern starting on a new diatonic chord (on a new scale degree) is called the COPY. To define an entire sequence, we use three reference points:

• The direction and distance between the starting chord of the model and each new copy

  • A for ascending, D for descending, and a number representing the interval moved in that direction

• (In parentheses) the direction and distance between the starting chord of the model and the second chord it moves to

  • + for ascending, - for descending, and a number representing the interval moved in that direction

• (/In parentheses) the direction and distance between the second chord of the model and first chord of the copy

  • + for ascending, - for descending, and a number representing the interval moved in that direction

“Descending Second” Sequence - D2 (-5/+4)

So a typical sequence could look like:

D2 (-5/+4)

The sequence label above would represent a pattern where odd-term chords are descending one diatonic step while the inner (even) chords are sounded a diatonic fifth below the previous (odd) chord. In Roman numerals, that would look like:

I ↓IV ↑viiᵒ ↓iii ↑vi ↓ii ↑V ↓I

In C, that would look like:

C ↓F ↑bᵒ ↓e ↑a ↓d ↑G ↓C

Sequences will eventually conclude on the same chord they began, although most of the time a composer will chose to abandon the sequence before it has come full circle, using an earlier chord to roll into a Predominant or Dominant area of the tonality. Notice that this above-described D2 (-5/+4) sequence is really just the Circle Progression (circle of fifths) described in the basic harmonic sequence example #1 above …

“Descending Thirds” Sequence - D3 (-4/+2)

Apply the logic from the previous label to this new one. What is D3 (-4/+2) telling us to do in a sequence? Well, the first thing we see is D3 which means there is a descending distance of a 3rd between the first chord and the third (1 ↓ 6). The -4 means we’ll descend a 4th from the first to the second chord (1 ↓ 5) and the +2 means we will ascend a 2nd from the second chord to the third chord (5 ↑ 6). In Roman numerals, that looks like:

I ↓V ↑vi ↓iii ↑IV ↓I ↑ii ↓vi ↑viiᵒ ↓IV ↑V ↓ii ↑iii ↓viiᵒ ↑I

In C major, that would translate to these chords:

C ↓G ↑a ↓e ↑F ↓C ↑d ↓a ↑bᵒ ↓F ↑G ↓d ↑e ↓bᵒ ↑C

As with the D2 sequence above, this much longer sequence rarely sees completion, and is, instead, abandoned by the composer at an opportune moment to move to a different tonal area. Notice that the motion in this sequence is more plagal (IV - I motion) and also has imperfect authentic cadence motion at the end (viiᵒ - I) which makes this sequence a bit “weaker” in comparison to the D2 sequence above.

The D3 sequence is often referred to as the PACHELBEL PROGRESSION as the sequence is famously used in Pachelbel’s “Canon in D Major”. Check out some parody videos below to show other references to this sequence in popular music …

“Ascending Second” Sequences - A2 (+5/-4) & A2 (-3/+4)

A2 (+5/-4) “Fifth Up Progression”

In this sequence, the odd-term chords ascend one diatonic step while the inner (even) chords are sounded a diatonic fifth above the previous (odd) chord. In Roman numerals, that would look like:

I ↑V ↓ii ↑vi ↓iii ↑viiᵒ ↓IV ↑I ↓V ↑ii ↓vi ↑iii ↓viiᵒ ↑IV ↓I

In C, that’s:

C ↑G ↓d ↑a ↓e ↑bᵒ ↓F ↑C ↓G ↑d ↓a ↑e ↓bᵒ ↑F ↓C

This sequence is sometimes referred to as the Ascending Circle of Fifths Progression or the Fifth Up Progression because the entire sequence moves up a diatonic 5th from the previous chord. However, this “I - V” motion is much weaker than the stronger “V - I” motion in the reverse direction which is why the D2 (-5/+4) sequence in the first example gets the basic title of Circle of Fifths Progression.

This progression isn’t used very much in contemporary music examples because the I - V motion (or IV - I if you think about the second, weaker-positioned chord being the actual tonic) feels a bit directionless. One hotly debated tune that features this sequence is Jimi Hendrix’s “Hey Joe.” The videos below feature a recording of “Hey Joe” and YouTube Music Theorist Adam Neely’s 17-minute breakdown of the progression in the context of the tune. It’s super fascinating (as are most of Neely’s videos if you have the time to watch!)

A2 (-3/+4) “Ascending 5-6 Sequence”

In this sequence, the odd-term chords ascend one diatonic step while the inner (even) chords are sounded a diatonic third below the previous (odd) chord. In Roman numerals, that would look like:

I ↓vi ↑ii ↓viiᵒ ↑iii ↓I ↑IV ↓ii ↑V ↓iii ↑vi ↓IV ↑viiᵒ ↓V ↑I

In C, that’s:

C ↓a ↑d ↓bᵒ ↑e ↓C ↑F ↓d ↑G ↓e ↑a ↓F ↑bᵒ ↓G ↑C

It is referred to as the ascending 5-6 sequence because it is often presented in a series of alternating root position (5) and first inversion (6) triads to avoid parallels (refer to the treble clef triads in the example below).

With all of the sequences above, the “even” chords (second chord of the model) are usually serving as a VOICE-LEADING CHORD or helping chord which is a chord that does not serve a strong harmonic function by itself, but rather, supports ease of writing with good voice-leading by avoiding parallel fifths, octaves, and other problems that would arise if the “odd” chords (first chord of the model and copy) were consecutive.

We can also write many of the harmonic sequences to include triads in inversion, 7th chords, and/or 7th chords in inversion! When sequences are comprised of all seventh chords, they are called sequences with INTERLOCKING SEVENTHS and when the sequence alternates between triads (usually odd chords) and seventh chords (usually even chords), they are called sequences with ALTERNATING SEVENTHS. In general, any combination of triads and seventh chords (in root position or inversion) are possible in a sequence provided that the chords are voiced in a way that does not break part-writing rules. This is a great opportunity for composers (including yourself!) to get creative.