Modulation
Modulation is a the practice of changing keys inside of a composition. This can be done for a variety of reasons, but its basic purpose is to contrast or create tension against the current (and possibly even prior) key(s). Typical modulations are found when themes or sections change. They can also be used to seemingly add energy to a prior theme/section. In terms of complete pieces, they help create structure and balance.
Contents
PreReqs
Common Modulations
Modulations usually take place between highly-related keys (those with the most common notes). See the table below.
| Key 2 Type and number of common notes | ||||
|---|---|---|---|---|
| Key 1 Type | Key 2 Root's relation to Key 1 Root |
Major | Minor | Harmonic Minor |
| Major | ||||
| U | 4 | 5 | ||
| m2 | 2 | 3 | 3 | |
| M2 | 5 | 6 | 5 | |
| m3 | 4 | 2 | 3 | |
| M3 | 3 | 6 | 5 | |
| P4 | 6 | 3 | 3 | |
| tt | 2 | 4 | 4 | |
| P5 | 6 | 5 | 3 | |
| m6 | 3 | 2 | 3 | |
| M6 | 4 | 7 | 6 | |
| m7 | 5 | 2 | 4 | |
| M7 | 2 | 5 | 4 | |
| Minor | ||||
| U | 4 | 6 | ||
| m2 | 5 | 2 | 4 | |
| M2 | 2 | 5 | 4 | |
| m3 | 7 | 4 | 5 | |
| M3 | 2 | 3 | 3 | |
| P4 | 5 | 6 | 5 | |
| tt | 4 | 2 | 3 | |
| P5 | 3 | 6 | 5 | |
| m6 | 6 | 3 | 3 | |
| M6 | 2 | 4 | 4 | |
| m7 | 6 | 5 | 3 | |
| M7 | 3 | 2 | 3 | |
| Harmonic Minor | ||||
| U | 4 | 6 | ||
| m2 | 4 | 3 | 3 | |
| M2 | 4 | 3 | 3 | |
| m3 | 6 | 4 | 4 | |
| M3 | 3 | 3 | 4 | |
| P4 | 3 | 5 | 4 | |
| tt | 4 | 3 | 4 | |
| P5 | 3 | 5 | 4 | |
| m6 | 5 | 3 | 4 | |
| M6 | 3 | 4 | 4 | |
| m7 | 5 | 4 | 3 | |
| M7 | 3 | 3 | 3 | |
This means the most highly-related keys are the relative major/minor keys, which have the exact same set of notes but different roots (C Major and A Minor). For any major key, the most related major keys are those whose root is the 4th or 5th note of the original key. The most related minor keys (other than the relative minor) are those based on the 2nd and 3nd notes in the major key. Similarly, for a minor key, its most related minor keys are based on its 4th and 5th notes, while its most related major keys are based on the 6th and 7th notes (inverse of 2nd and 3rd).
Harmonic minor's raised 7th causes it to be less related to other keys of all variations covered above; however, it basically shares the same relationships to major and minor keys as its natural minor variation. The most related major keys are based on the 6th and ♭7th notes. The most related minor keys are based on the 4th and 5th. Interestingly, almost all modulations to other harmonic minor keys are equally inter-related.
Examples
- I -> IV - (C -> F, F -> Bb, G -> C)
- I -> V - (G -> D, C -> G, A -> E)
- i -> III - (Am -> C, Em -> G, B♭m -> D)
- i -> ♯iv - (Ahm -> D♯hm)
Modulation Methods
Common Chord
Uses a chord common to the source and destination keys to transition between them.
G Em D/A G
C: I iii
G: vi V/ii I
E--0-------0-------2------3--
B--1-------0-------3------3--
G--0-------0-------2------0--
D--2-------2-------0------0--
A--3-------2-------0------2--
E----------0--------------3--
Enharmonic Chord
Even if two keys do not have the same chords in way of naming conventions, they may have chords that are enharmonically equivalent. For example, the keys of C♯ and C♭ have no chords in common by name. C♯ has only ♯ chords and C♭ has only ♭ chords. Yet, E♭m and D♯m are enharmonic, as are G♭ and F♯.
C# D#m Gb Cb
Ebm
C#: I ii
Cb: iii V I
E---1-------2-------2------2--
B---2-------4-------2------4--
G---1-------3-------2------4--
D---3-------1-------4------4--
A---4---------------4------2--
E-------------------2---------
Common Tone
A note common to the source and destination key is sustained during the transition. For example, a C ==> E modulation could sustain the A in the vi chord of C (Am) while moving to the IV chord of E (A), which also contains A.
C Am A B7 E
C: I vi
E: IV V7 I
E--0-----0-----0-----2-----0--
B--1-----1-----2-----0-----0--
G--0-----2-----2-----2-----1--
D--2-----2-----2-----1-----2--
A--3-----0-----0-----2-----2--
E--------------------------0--
In this case, both E and A are common tones that are carried over, although E Major does not contain the Am chord and vice versa for C Major and the A chord.
While this example has somewhat-related keys, this modulation method can link virtually any two keys, as it's basically guaranteed that any two keys will share at least one common note.
Chromatic
Useful for modulating between two keys that are not closely related, chromatic modulation uses a chromatic line to bridge the keys. In other words, for the chords chosen, one voice can move up or down 2 or more half-steps. This necessarily implies the transition will occur over at least 3 chords. For the strongest effect, the chromatic line should lead into the root of the new key.
For example, consider a modulation from C Major to A Harmonic Minor. C Major has a G note, while A Harmonic Minor has G♯ and A. This allows us to create a G - G♯ - A chromatic line through the following progression: G - E - A. That's (G B D) - (E G♯ B) - (A C E). If we follow good voice leading, we can keep the G, G♯, and A notes in the same voice, thus getting the chromatic line. G is the V chord of C Major. E is the V chord of A Harmonic Minor. The progression could be written as:
G E Am C: V Ahm: V i E--3-------0-------0------ B--0-------0-------1------ G--0-------1-------2------ D--0-------2-------2------ A--2-------2-------0------ E--3-------0--------------
Notice the chromatic line on the G string.
Depending on the keys used, it may be more difficult to achieve the chromatic line with only the diatonic chords of the two keys. In these cases, we can resort to using a secondary dominant or some other non-diatonic chord.
Phrase
A phrase modulation avoids any transition whatsoever, occurring abruptly between two virtually independent phrases. The first phrase in the original key will end on a cadence, finding resolution and ending. The next phrase begins in the new key, with no harmonic or melodic bridge to ease the transition. This modulation is commonly between closely-related keys, preventing a completely disjointed feel. However, the transition is typically quite noticeable, which is the point of this modulation method.
A E A E G# A:I V I E:I iii E-------------------------|----------------... B-------------------------|----------------... G-------------------------|----------------... D-----------0--2----------|-2--1-----------... A--0--2--4----------0-----|-------4--2-----... E-------------------------|-------------4--...
Notice how we end the key of A with a strong authentic cadence; but immediately use a phrase with D♯, which is the only note in E Major that isn't diatonic to A Major. This emphasizes the modulation, with separation between phrases, even though the 2 keys share 6 of their 7 notes.
Sequential/Rosalia
A phrase or progression ending in a cadence can be transposed up or down to a different key and repeated, once or several times. Here the harmonic function of the sequence of chords is less important than the effect of the sequential motion. The transpositions may follow the diatonic notes of the original key, or may move completely chromatically. The sequence can repeat enough times to return to the original key, or be used to arrive at a new key.
For example, consider the following progression:
Cm B Bbm A Abm G Ebm Abm Cm: i VII Bbm: i VII Abm: i VII v i
Chain
Chain Modulation uses multiple modulations to bridge two distantly related keys. Unlike a rosalia above, a chain modulation is not confined to repeating a sequence - each modulation in the chain can have independent durations, melodies, harmonic progressions, etc.
For example, consider a modulation from C Major to E Major. These keys only share 3 notes in common, and are separated on the circle of fifths by 4 movements. They share no diatonic chords. Instead of trying to modulate directly between them, we can use a chain modulation. We could follow the circle of fifths, going major to major key until we reach E (C => G => D => A => E). Or we could shorten that by jumping every other 5th (C => D => E). C Major and D Major share the diatonic G Major chord. D Major and E Major share the diatonic A Major chord. This allows two common chord modulations to easily get from C Major to E Major without any disruptive transitions.
Parallel Key
Parallel keys have the same root but different whole-half step patterns. For example, C Major and C Minor are parallel keys. Knowledge of modes offer us more parallel keys. Modulation between parallel keys is typically not as closely related as usual. For example, major/minor parallel keys only share 4 notes. However, because they retain the same tonal center, the change is not disruptive.
Pitch Axis Theory[1] is an extreme example of this. It uses chord progressions that all feature a common note - often this note is the root of every chord in the progression. The underlying chords are not diatonic to any one key. Instead, the scale used for melody/lead will change to conform with each chord.
Why/When to Modulate?
Clarifying Song Structure by Contrasting Sections
Contrasting Themes within the same Section
Building Excitement
Creating Tension or Ambiguous Tonality
Homework
Choose a major key as your starting key. List all possible major keys you can modulate to, and order them in terms of those closely related to those least-closely related. Do the same for all possible natural minor and harmonic minor keys. Choose another major key and repeat the exercise.
Repeat the above for a natural minor key, then a harmonic minor key.
Compose chord progressions for each modulation technique above. Start with closely related, then loosely related, then distantly related destination keys. Notice how some techniques work better for some modulations than others - in fact, some won't work at all.