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A sequence consists of elements. Each element of sequence (except the first element) is obtained from the previous one by applying the same kind of transposition. A sequence can be melodic or harmonic. Elements of a melodic sequence are melodic patterns. Elements of a harmonic sequence are harmonic patterns i.e. chord progressions. Since this is a book about harmony, we are interested primarily in harmonic sequences. However, for completeness, both melodic and harmonic sequences will be explained.
Melodic sequences
Melodic sequences
A melodic sequence is a sequence of melodic patterns in which each melodic pattern (except the first melodic pattern) is obtained from the previous one by applying the same kind of transposition. Since a transposition of a melodic pattern can be either diatonic or chromatic, there are two kinds of melodic sequences: a diatonic sequence and chromatic sequence.
Diatonic sequences
Diatonic sequences
A diatonic sequence is a melodic sequence based on a diatonic transposition. A diatonic transposition moves notes for a certain number of scale degrees (up or down). The next figure shows an example of a diatonic sequence.
Figure: An example of the diatonic sequence (the first melodic pattern is marked in red)
This diatonic sequence consists of three melodic patterns (the first one is marked in red). The diatonic sequence is in the C major key and is based on the diatonic transposition for two scale degrees up. Thus, the second melodic pattern is obtained from the first one by moving each note two scale degrees up, in the C major key. The third melodic pattern is obtained from the second one in the same way.
We can easily understand what is happening if we write down the scale degrees in the C major key:
For the first melodic pattern, we have: first, second, third, first.
For the second melodic pattern we have: third, fourth, fifth, third.
For the third melodic pattern, we have: fifth, sixth, seventh, fifth.
The scale degrees of the second melodic pattern are obtained by adding the number 2 to the scale degrees of the first one. The same holds for the scale degrees of the third and second melodic patterns.
The next figure shows the beginning of Bach’s Two-part Invention No. 8 in F major. In measures 4 to 7, we find diatonic sequences on both the staves. The whole measure 4, on the upper staff, is used as the melodic pattern of a diatonic sequence for two scale degrees down, in the F major key. This creates the measures 5 and 6 on the upper staff. The same happens on the lower staff, only from the measure 5 to 7. The first melodic pattern in both staffs is marked in red.
Figure: An example of the diatonic sequences in Bach's Two-part Invention No. 8 in F major
Chromatic sequences
Chromatic sequences
A chromatic sequence is a melodic sequence based on a chromatic transposition. A chromatic transposition moves the notes for a certain ascending or descending interval. A chromatic transposition moves a melodic pattern to a different key. The next figure shows an example of a chromatic sequence.
Figure: An example of the chromatic sequence (the first melodic pattern is marked in red)
This chromatic sequence consists of three melodic patterns (the first one is marked in red). It is based on the ascending major third chromatic transposition. Thus, the second melodic pattern is obtained from the first one by moving each note for the ascending major third. The third melodic pattern is obtained from the second one in the same way. We may say that the first melodic pattern is written in the C major key, second one in the E major key and the last one in the G# major key.
Harmonic sequences
Harmonic sequences
A harmonic sequence is similar to a melodic sequence but is related to harmony instead of melody. A harmonic sequence is a sequence of harmonic patterns i.e. chord progressions in which each chord progression (except the first chord progression) is obtained from the previous one by applying the same kind of transposition. Since a transposition of a chord progression can be either non-modulating or modulating, there are two kinds of harmonic sequences: non-modulating sequences and modulating sequences.
Non-modulating sequences
Non-modulating sequences
A non-modulating sequence is a harmonic sequence based on a non-modulating transposition. A non-modulating transposition moves chord roots in a chord progression for a certain number of scale degrees (up or down).
The next figure shows the beginning of Bach’s Prelude No. 21 in Bb major, from Well-Tempered Clavier, book I. In the upper staff, there is a diatonic sequence based on the diatonic transposition for two scale degrees down. The same is happening in the lower staff. The melodic patterns are marked with the red note heads. Besides these two melodic sequences, the harmony analysis shows a harmonic sequence. The harmonic pattern is marked with the red chord and harmony annotations. In the figure, we see the annotation for a harmonic sequence that is used in this book: a line labeled with “SEQ” which connects all elements of the harmonic sequence. If elements of the harmonic sequence contain more than one harmony, harmonies of each element are put in the square brackets. Here, the harmonic sequence contains three elements and each element contains four harmonies. If we compare the chord roots in two adjacent elements of this harmonic sequence, we see that the harmonic sequence is based on the diatonic transposition for two scale degrees down. Thus, this is a non-modulating sequence based on moving two scale degrees down.
To be able to perceive the sequential character of a harmonic sequence, a melodic sequence should be present at least in the part that we perceive as the melody. Typically, that is the part containing the notes with the highest pitches. Parts were explained in chapter Parts. The perception of melody was explained in chapter Perception of melody. Interestingly, the duration of a harmonic pattern can be different than the duration of a related melodic pattern. The next figure shows an example of this in Bach’s Two-part Invention No. 13 in A minor. On the upper staff, there is a diatonic sequence based on the diatonic transposition for one scale degree down. The same is happening on the lower staff. The melodic patterns are marked with the red note heads. The harmony analysis shows the non-modulating sequence based on moving four scale degrees down. The harmonic pattern is marked with the red chord and harmony annotations. We see that the harmonic pattern consists of a single harmony. That is, the duration of the harmonic pattern is a half of measure. The duration of the melodic patterns is one measure. The melodic sequences in the figure contain two elements while the harmonic sequence contains four elements.
A non-modulating sequence can also contain secondary chords. The next figure shows an example of a non-modulating sequence that contains secondary dominant chords from Bach's Prelude No. 2 in C minor from Well-Tempered Clavier. The harmony analysis shows the non-modulating sequence based on moving one scale degree down. There is a secondary dominant seventh chord on the third scale degree resolving to the triad chord on the third scale degree. When moved one scale degree down, they become the secondary dominant seventh chord of the second scale degree resolving to the triad chord on the second scale degree etc. The harmonic pattern is marked in red. If we analyze related melodic sequences in the upper and lower staff, we see that the length of the melodic pattern is two measures. Also, we see some irregularities in the third element of both melodic sequences i.e. in the last two measures in the figure. This is subjective but we can say that the irregularities are small enough so that we still perceive these 6 measures as a harmonic sequence.
Modulating sequences
Modulating sequences
A modulating sequence is a harmonic sequence based on a modulating transposition. A modulating transposition moves chords in a chord progression for a certain ascending or descending interval. A modulating transposition moves a chord progression to a different key.
The next figure shows an example of a modulating sequence from Chopin’s Prelude No. 17 in Ab major. We see the same chord progression, a dominant seventh chord on the fifth scale degree resolving to a tonic triad chord, first in the E major key then repeated in the Eb major key and finally in the D major key. Measure 52 can be obtained from measure 51 by transposing it down for the minor second. In the same way, measure 53 can be obtained from measure 52. The octave at the beginning of measure 51, on the lower staff, does not occur in measures 52 and 53. Also, the non-chord tone in measure 53 does not occur in measures 51 and 52. However, these differences are small enough so that we can strongly fell the sequential character of the passage.
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