Audio: functional modulation (0:12)
functional modulation plays a chain of key changes sung by a choir. The functional modulation figure shows the score:
- Bars 1-4 diatonic modulation:
- Bar 1 relative key modulation, I-vi, C to Am.
- Bar 2 relative key modulation, i-III, Am to C.
- Bar 3 close key modulation, I-V, C to G.
- Bar 4 distant key modulation, I-v, G to Dm.
- Bars 5-6 chromatic modulation:
- Bar 5 parallel key modulation, i-I, Dm to D.
- Bar 6 distant key modulation, I-bIII, D to F.
Functional modulation is shorthand for modulation in functional harmony.
The purpose of functional modulation is to develop a harmony. It is one of two main ways to vary a harmony (the other is to expand a chord into a chord progression). The aim is not to change key for its own sake, although this is the pleasurable end result, but to use modulation as a way to extend a short piece into a longer one and to vary the music without sacrificing tonality or losing the interest of the listener.
Harmonic modulation is based on the same principles as melodic modulation. Functional modulation usually occurs at a cadence, so that the next section can start off in the new key. The process is gradual, rarely abrupt. Only major and minor keys are involved, the modulation is not modal, and there is no key change from major to mixolydian, for instance. The new tonic triad must be a major or minor triad and not a diminished or augmented triad.
Functional modulation is classed as diatonic or chromatic. The distinction hinges on the nature of what is called a pivot chord, a chord about which the harmony changes key. A pivot chord that is common to both keys is called a common chord, and common chord modulation means the same as diatonic modulation. The ideal pivot chord is a common chord in diatonic modulation that functions as a predominant chord in the new key. Chromatic modulation occurs when the pivot chord is not a common chord but a chromatic chord in one or both keys.
There is a link between functional modulation and the different types of modulation:
- Diatonic modulation takes place between:
- Relative keys.
- Close keys.
- Distant keys sharing 5 notes in common.
- Chromatic modulation takes place between:
- Parallel keys.
- Distant keys sharing 2-4 notes in common.
Diatonic modulation to a relative key is straightforward and popular. There are plenty of pivot chords to choose from. From minor to relative major, i to III, Am to C, for example, the possible progressions are Am-G-C, Bdim-G7-C, Dm-G-C and F-G-C. The pivot chord is a common chord and acts as a predominant chord in the new key of C. One interesting point is that, in the old key of Am, the G chord is VII, which is diatonic in the key of A natural minor, a mode, but not A harmonic minor or A melodic minor. However, minor harmony is happy to pinch any chord from any of the three minor scales, which is why this modulation is often claimed to be the only pure diatonic modulation in which there is no chromatic chord. Modulation from major to relative minor, I to vi, C to Am, is similarly straightforward. C-E-Am is common and represents I-III-vi in the old key of C, in which the E major, III, is a chromatic chord, and III-V-i, which are all diatonic chords in the new key of A minor.
Diatonic modulation to a close key is often major to major. I to V is a popular choice, I to IV less so. Modulation up a fifth, I to V, C to G, for example, is straightforward and there are plenty of pivot chords. C-D-G, Am-D-G and Em-D-G are all good options. Close key modulation down a fifth, I to IV, C to F, is more problematic because the C major chord acts as the tonic I in the old key and the dominant V in the new key, which makes the tonality ambiguous. A common solution is to convert the tonic triad I in the old key to a dominant seventh, I7, in a I-I7-IV progression, C-C7-F. The pivot chord, C, is a common chord, while the I7, C7, is chromatic in the old key and diatonic in the new key.
Diatonic modulation to a distant key is limited to keys that share 5 notes in common. The two keys will only share two common chords, one of which will be major and the other, minor. This means that the modulating chord progression is largely preset. Modulating from C to D, for example, will proceed either G-A-D or Em-A-D.
Here is a worked example of diatonic modulation using close key modulation from C major to G major, I-V. Chord names are used rather than numbers because notating modulation requires one set of chord names but two sets of chord numbers, which is more cumbersome. It also starts at the end and works backwards:
- Start with a three chord progression x-y-z:
- x is the pivot chord.
- Label z the tonic triad in the new key:
- Modulating to the key of G major results in x-y-G.
- Label y the dominant triad in the new key:
- A root progression down by fifth is the strongest way to emphasise a change of key.
- D is a fifth above G and the modulation becomes x-D-G.
- Look for a pivot chord that is also a common chord:
- When there is only one common chord, select it.
- When there are multiple common chords, choose any.
- The three common chords between the keys of C and G are Am, C and Em. The tonic of the old key is always a sound choice so C is duly selected as pivot. The modulation is C-D-G.
- Check the progression does not conflict with some other requirement of the harmony, such as the need to harmonise a given melody.
- Check voice leading is OK.
- Job done.
When there is no common chord the modulation is chromatic.
Parallel key modulation is chromatic. A common solution is to travel along the circle of fifths from the old to the new key. A quicker option is take advantage of the unique feature of parallel keys, they both share the same dominant chord. For example, modulating from the key of D minor to D major can proceed D-A-Dm, a I-V-i progression. It works in reverse too, from minor to parallel major is i-V-I. Unusual but effective.
Chromatic modulation between distant keys sharing only 2-4 notes in common is the most complex of modulations, not least because there so many routes to take. The splendidly titled omnibus progression is one intriguing example of modulation through all twelve notes in the chromatic scale in sequence. Here are some additional techniques:
- Pivot on a single note.
- End a section with a deceptive cadence to the tonic triad of the new key.
- Modulate to a parallel key then pivot on a common chord between the parallel key and the new key.
- Travel along the circle of fifths until you reach the new key.
Writing a chain of modulations, as in functional modulation, is an excellent way to develop your functional harmony writing skills. However, there may come a time when you cannot be bothered with all the hassle. Then you can choose the last tool in the toolbox:
- End the current key with a good old-fashioned perfect cadence.
- Start the next section in the new key.
Call the technique, phrase modulation, (which it is), in case anyone asks what on earth you are doing.