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
Notation
In terms of traditional musical notation or guitar-specific tablature, modulations aren't specifically notated. The non-diatonic notes for a certain key simply appear. For traditional notation, the key signature may change; however, this is typically reserved for the start of new section. Rather, you'd see more ♯, ♭, and ♮ signs appear next to notes. For guitar tab, there is no key signature - you would simply see notes used that were not used before that point in the song. Knowing that there is a key modulation is not necessary for the performance of particular piece; it is only necessary for understanding it in terms of theory.
In terms of harmonic analysis, modulations alter the roman numerals used to mark chords. For example, while C is the I chord of C Major, it is the III chord of A Minor. The key must be specified for this analysis to make sense, and sometimes there is overlap. For instance you may see:
Chords - C F G C Em Am D G Analysis 1 - C: I IV V I iii vi Analysis 2 - G: vi ii V I
You can see the "C:" and "G:" in the respective analysis lines indicating the key, with the following roman numerals outlining the member chord from that key. In this case there is overlap, where we may interpret the Em and Am chords as belonging to either key. In other cases where the point of modulation is unambiguous, you may see this condensed to a single line:
Chords - C F D G Analysis - C: I IV G: V I
When discussing modulations outside of notation, we can use an arrow, such as "=>" or "->" to indicate the modulation. For example, "C -> Am" (C Major to A Minor) or "C => G" (C Major to G Major).
If we want to make such modulations generic to any key by using roman numerals, this can get a bit more tricky. For example, if we want to discuss a modulation from a major key to a minor key whose tonic note is the 6th note of the major key, we could say "I -> vi". The uppercase "I" and lowercase "vi" indicate that the original key is major, but the new key is minor, and the "vi" also indicates the new key's tonic note is the 6th's note of the original major key. But what if the tonic note of the new key is non-diatonic to the original key? Then we have to use a ♭ or ♯ to indicate that. So moving from C -> A♭m could be generically written as "I -> ♭vi". Cm -> A would be written "i -> ♯VI" - the 6th note of C Minor is A♭, but we sharp it to get A.
We must use "I" or "i" to indicate the original key. "IV -> V" makes no sense - we are moving from the 4th note of what key? We are also bound to the common heptatonic major and natural minor scales. If the source or destination keys use other scales, they must be written out fully - "A modulation from lydian to the harmonic minor key built on its 4th note".
Common Modulations
Modulations usually take place between highly-related keys (those with the most common notes). See the table below.
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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 that is diatonic to both the source and destination keys to transition between them. In the below example, we modulate from C to G using 2 common chords.
C F G C Em Am D/A G
C: I IV V I iii vi
G: vi ii V/ii I
E--0----1----3----0----0----0----2----3--
B--1----1----3----1----0----1----3----3--
G--0----2----0----0----0----2----2----0--
D--2----3----0----2----2----2----0----0--
A--3----3----2----3----2----0----0----2--
E-------1----3---------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 G# Cb D#m
Ebm Fb Gb Cb
C#: I ii V I ii
Cb: iii IV V I
E---4----6----4----4----6----0----2----2--
B---6----7----4----6----7----0----2----4--
G---6----8----5----6----8----1----3----4--
D---6----8----6----6----8----2----4----4--
A---4----6----6----4----6----2----4----2--
E-------------4--------------0----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 E in the I chord of C while moving to the IV chord of E, which also contains E.
C F G C A B7 E C: I IV V I E: IV V7 I E--0----1----3----0----0----0----2----0-- B--1----1----3----1---(x)---2----0----0-- G--0----2----0----0---(x)---2----2----1-- D--2----3----0----2---(x)---2----1----2-- A--3----3----2----3---(x)---0----2----2-- E-------1----3------------------------0--
Unlike the common chord examples, we move directly between chords that are not diatonic to both keys - C Major does not contain the A chord, and E Major lacks the C chord. Yet the common E note between them bridges the gap particularly well, without creating a stark contrast between keys.
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:
C F G E Am C F G E Am
C: I IV V C: I IV V
Ahm: V i Ahm: V i
E--0----1----3----0----0-- E-------------------------
B--1----1----0----0----1-- B-------------------------
G--0----2--**0----1----2** G--0----2--**0----1----2**
D--2----3----0----2----2-- D--2----3----0----2----2--
A--3----3----2----2----0-- A--3----3----2----2----0--
E-------1----3----0------- E-------1----3----0-------
Notice the chromatic line on the G string.
Here's another example, modulating from C to G, using a chromatic run on the high E string. Notice how seamless this sounds, especially with the chromatic line as the highest-pitched voice (soprano).
C F D G
C: I IV
G: V I
E--**0----1----2----3**
B----1----1----3----3--
G----0----2----2----0--
D----2----3----0----0--
A----3--------------2--
E-------------------3--
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 D Em A:I V I D:I ii E-------------------------|------------------- B-------------------------|------------------- G-------------------------|-------2--0-------- D-----------0--2----------|-0-----------4--2-- A--0--2--4----------0-----|------------------- E-------------------------|------------------- A B C# D E A D A G F# E
Notice how we end the key of A with a strong authentic cadence; but immediately use a phrase with G instead of G♯, to differentiate between the keys of A and D Major. We also use an E in the first measure, but Em in the second. 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 Bb Bbm Ab Abm Gb Ebm Abm Cm: i VII Bbm: i VII Abm: i VII v i E---8--11-10-6-----------6--9--8--4-----------4--7--6--2---------2--4-- B-------------------------------------------------------------4-------- G---------------------------------------------------------------------- D---------------------------------------------------------------------- A---------------------------------------------------------------------- E----------------------------------------------------------------------
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 (also see Wikipedia) 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.
A Am Adim A+ A: I Am: i Awh: io Awt: I+ E--0----------0---------------------1-- B--2----------1----------1----------2-- G--2----------2----------2----------2-- D--2----------2----------1----------3-- A--0----------0----------0----------0-- E--------------------------------------
Note, we have not covered exotic scales, such as the whole-half or whote-tone scales yet, which are referenced above as "Awh" and "Awt".
Why/When to Modulate?
Modulation can be used for a variety of purposes. It is generally used as a means to add contrast to different sections or themes in a song. The altered tonality adds to the change in harmonic progressions or melody. It can highlight how much contrast between themes or sections there is depending on how related the chosen keys you modulate to/from.
Just as an ascending melody can be used to build excitement, modulating keys higher and higher can be used the same way. The frequency of modulations can also be used to indicate such - increasingly frequent modulations can make the piece sound a bit chaotic but also make things seem out-of-control with energy. The same can be done descending as a calming method. If the modulations follow an easily-identified pattern, such as in a rosalia, they will not sound chaotic but mellow - it allows repetition while still creating movement.
Modulations can also be used to make a piece sound disjointed, similar to playing in scales with an ambiguous tonality. Or they can allow the piece to use lots of harmonic and melodic repetition without becoming increasingly boring.
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.