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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--
→Common Modulations
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'''Analysis -''' C: I IV G: V I
When discussing modulations ''outside of a piece of musicnotation'', we can use an arrow, such as "=>" or "->" to mark 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 {{b}} or {{s}} to indicate that. So moving from C -> A{{b}}m could be generically written as "I -> {{b}}vi". Cm -> A would be written "i -> {{s}}VI" - the 6th note of C Minor is A{{b}}, 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.
{|
|
{|class="wikitable"
!colspan="2"|
|-
| '''M7''' || 2 || 5 || 4
|}
|
{|class="wikitable"
!colspan="2"|
!colspan="3"| Key 2 Type<br>and number<br>of common<br>notes
|-
! Key 1 Type
! Key 2 Root's<br>relation to<br>Key 1 Root
! Major !! Minor !! Harmonic<br>Minor
|-
!rowspan="13"| Minor
|-
| M7 || 3 || 2 || 3
|}
|
{|class="wikitable"
!colspan="2"|
!colspan="3"| Key 2 Type<br>and number<br>of common<br>notes
|-
! Key 1 Type! Key 2 Root's<br>relation to<br>Key 1 Root! Major !! Minor !! Harmonic<br>Minor|-!rowspan="13"| Harmonic <br>Minor
|-
| '''U''' || 4 || '''6''' ||
|-
| '''M7''' || 3 || 3 || 3
|}
|
|}
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 C A B7 E C: I IV V I I E: IV V7 I
E--0----1----3----0----0----0----2----0--
B--1----1----3----1---(x)---2----0----0--
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{{s}} and A. This allows us to create a G - G{{s}} - A chromatic line through the following progression: G - E - A. That's ('''G''' B D) - (E '''G{{s}}''' B) - ('''A''' C E). If we follow good [[Voice Leading|voice leading]], we can keep the G, G{{s}}, 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
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--
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).
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 [[Borrowing Chords/Notes#Secondary Dominant|secondary dominant]] or some other non-diatonic chord.
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{{s}}, 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.
For example, consider the following progression:
Cm Bbm7b5 Bb Bbm Abm7b5 Ab Abm Gbm7b5 Gb Ebm Abm Cm: i viiø7 VII Bbm: i viiø7 VII Abm: i viiø7 VII v i
E---8--11-10-6-----------6--9--8--4-----------4--7--6--2---------2--4--
B-------------------------------------------------------------4--------
[[Modes#Pitch Axis Theory|Pitch Axis Theory]] (also see [http://en.wikipedia.org/wiki/Pitch_axis_theory 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|exotic scales]], such as the whole-half or whote-tone scales yet, which are referenced above as "Awh" and "Awt".
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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.
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== Related Lessons ==
* [[Voice Leading|Prev: Voice LeadingCircle of Fifths]]* [[Chromatic Chords|Next: Chromatic Non-Diatonic Chords]]* [[Modes]]* [[Exotic Scales]]
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