chromatic sequences based on the circle of fifths

When the imperfect circle of fifths (see the chapter on Diatonic Sequences) is adjusted to falling perfect 5^ths (fa – ti becomes fa – te), every chord becomes the dominant of the next, resulting in the perfect circle of fifths.

1. The imperfect circle of fifths

2. The circle of perfect fifths avoids the A4/d5 between fa and ti

3. In the complete circle of perfect fifths, every chord is the dominant of the next chord. Note that in the literature, sequences typically only employ several of these links.

a. Triad to 7^th chromatic sequence

Note that the 3^rd of the first chord becomes the 7 ^th of the next chord (3-7, 7-3).

b. Triads with passing 7^ths

c. Variant of 7^th to 7^th using inversions

2 to with passing 7^ths on every chord

d. Combination of possible secondary dominant sevenths

Each secondary dominant seventh chord resolves to the next secondary dominant seventh chord a perfect fifth below. Observe the alternating chain of complete to incomplete dominant seventh chords.

Note that the secondary dominant sequential pattern ends with the IV chord, as the V⁷ of vii^o is not available.

e. Chromatic sequences in minor

Chromatic sequences are most commonly used in major keys. In minor, the use of the Neapolitan chord (see Chapter 25) creates the circle of perfect fifths up to the cadence. 

f. Descending chromatic sequence using secondary diminished seventh chords

In this variant, a secondary diminished seventh chord resolves to a root position diatonic triad.

f. Parallel diminished seventh chords

In this highly chromatic variant, a root position diminished seventh chord on G descends to a second inversion diminished seventh chord on C. That progression is then sequenced down a major 2^nd.

The progression can be analyzed as a secondary dominant circle of perfect fifths progression (vii^o7/Am  –  vii^o/Dm | vii^o7/Gm  –  vii^o/C | vii^o7/F ), though it sounds like parallel diminished seventh chords.

chromatic sequences ascending by step

A falling 3^rd root pair that ascends by a step (#1) can be converted into a chromatic sequence of secondary dominants (#2).

a. Ascending chromatic sequence using secondary dominants

In this version, the bass descends by a 3^rd. The second chord then becomes the dominant of the next chord.

b. Ascending chromatic sequence using secondary dominant seventh chords

c. Ascending chromatic sequence using secondary diminished seventh chords 

The Chromatic Sequence as a Modulating Device

The chromatic sequence is used to modulate to closely related and distant keys. Begin with an ascending or descending secondary dominant chromatic sequence, cut off the progression after two or three repetitions, and conclude with a cadence in the new key.

A. Descending sequences leading to a new key

Using the imperfect circle of fifths (descending secondary dominant seventh chord) sequence:

Using the perfect circle of fifths (descending secondary dominant) sequence:

In this example, the sequence has three pairs (F to E to D) and that the E-flat major triad in measure 2 (D: V/V) moves to the new key.

Using secondary diminished seventh chords:

B. Ascending sequences leading to a new key

This ascending secondary dominant sequence has three pairs: F to G to A.

With inversions: