A sure way to inject excitement, interest and/or contrast in any piece of music is to have a key change. Some key changes can be very dramatic (Whitney Houston's "I Will Always Love You" is a classic, also see just about any Westlife song). Even people with no music training at all can immediately spot one of these (most move up a tone). However, key changes don't always have to be so dramatic; they can be more subtle, and much less noticeable.
Modulations and key changes can be thought of as dissonance on a larger scale. Just as how there are rules regarding the preparation and resolution of dissonant notes, so too there are similar rules regarding the preparation and resolution of dissonant keys. This post will provide basic information on one of the most common ways to change key.
There are two types of modulation. Passing modulation is a temporary thing. The new key is approached and left rapidly; perhaps only one or two chords belong to this new key before the music goes off somewhere else. In such a case, there isn't enough of the new key to say there has been an actual key change. Thus, the key signature remains the same, and suitable accidentals are introduced. (It is important to note though, that just because you have accidentals or chromaticism, does not necessarily mean there is a modulation - they may instead simply be some form of chromatic non-harmony note for example).
Genuine modulation is where you have a definite key change. The new key is firmly established and lasts for some time. Typically the key signature changes (although it does not have to). In these situations, the new key is treated as the local tonic. This means the harmony is written as if this new key was the tonic.
Note also that, as with harmony, modulation can be implied in a melodic line without necessarily using any accidentals.
This post will primarily be concerned with Genuine Modulation, where you have a definite key change.
In classical music, the most frequent modulations are to closely related keys. These are keys which have many notes in common and have either the same key signature, or only one sharp or flat difference (tonic, subdominant, dominant and the relative majors/minors of each). Many classical pieces will return to the original key near the end of the piece (or, if the tonic is minor, they will sometimes end in the tonic major as this is more stable), but this is not necessary with pop music. More remote keys which have few (or no) notes in common are more dissonant to each other; going between these distantly related keys is more obvious, but harder to achieve a smoother transition.
Keys increasing in sharps (or decreasing in flats) generally increase tension, whereas keys increasing in flats (or decreasing in sharps) generally lower tension. This is why in classical music, music generally modulates to the sharp side of the tonic before the middle of the piece, and to the flat side afterwards.
Before you attempt a key change, it is necessary to make sure the original tonic key is firmly established. It has to last long enough for people to hear it as the 'home key'. Keys are established, not only by the presence of the tonic chord (I), but also by the dominant chord (V), and in major keys, by the subdominant chord (IV) also. The progression leading-note to tonic (rising semitone) is a very strong way to define a key. Typically, there will be at least one cadence (usually perfect) in the original key before you start to modulate. (In fact, often modulation starts just after a cadence).
By far the most important chord to know when modulating is the Dominant Seventh, or V7.
This is the 5th chord of a key with an added minor 7th above the root. (The 7th fits in with the key signature, it is NOT chromatic).
For example, in C major, the dominant seventh is G,B,D,F.
In F major, the dominant seventh is C,E,G,Bb.
(It consists of the 5th, 7th, 9th and 11th notes of the tonic scale).
A perfect cadence is V-I. The introduction of the 7th makes the progression much stronger (V7-I). - Try it out for yourself.
The progression V7-I is usually used at some point when modulating (usually in the new key), as the dominant seventh is particularly good at establishing a key. For proper resolution, the leading-note (seventh of the scale) should rise to the tonic, and the added 7th should fall a step.
For example, in C major:
A very common device often involving the dominant seventh, is the cycle of fifths. This is where the music moves in sequence up or down a fifth at each step (passing modulations). The easiest way is moving flatwards where the tonic of the previous key becomes the dominant of the next. This is one good way of modulating to unrelated keys (you go via the keys in-between). (More information on this can be found here).
At some point before the dominant seventh occurs in the new key, we usually introduce a pivot chord.
A pivot chord is a chord which belongs to both the original key and the new key. They make the transition smoother. For example, if modulating from C major to D major, the difference is 2 sharps, so you could use any chord as a pivot which does NOT contain any kind of Fs or Cs. So; E minor (E,G,B) would be a good choice. This is chord iii in C major and also chord ii in D major. You could also use G major (V in C, IV in D). (Note you could not use C,D,F,A or B chords because these do not fit with BOTH keys).
For closely related keys, there are lots of pivot chords to choose from. For more distant keys keys, there can be very few. In such cases, you may have to be more creative and use a chromatic pivot chord (Neapolitan 6ths for example) which, although might not technically belong to the key, it can be related to the key if prepared or resolved properly. Sometimes in such cases enharmonic change of one or more notes of the pivot chord is involved (Eg, Bb becomes A#). (For example, when modulating from C major to Ab major, the Neapolitan 6th in C major becomes IVb of Ab major).
(If you are new to modulation, then don't worry about chromatic chords)
Sometimes, for a more abrupt modulation, the pivot chord does not necessarily have to have all notes common to both keys, but it must have at least one note in common with the dominant-seventh of the new key. In cases where chromatic movement is required (Eg, moving from F to F#), make sure this occurs in the SAME part. (Ie, avoid false relations). However, chromatic movement in different parts is acceptable if the second note is the seventh of V7.
You should try and avoid using the tonic of either original or new key as a pivot chord, although if this is the only chord available, it is a possibility. When using the tonic of the new key as a pivot, it must occur in a different inversion from how it occurs in the subsequent cadence (but never use a pivot chord in second inversion).
At some point before the pivot chord, you must have the tonic chord in the original key. Usually this is best directly before the pivot chord, but it doesn't always have to be.
So, to summarise modulation:
1) The original key must be firmly established. Often there will be a perfect cadence in the original key, or at the very least, the original tonic chord will be heard at least once.
2) Movement to the new key occurs via a pivot chord. This is a chord which belongs to both keys, or at the very least, has at least one note in common to the dominant seventh of the new key. (Sometimes the 'pivot' is chromatic to one or both keys, but is still related to the tonal hierarchy).
3) The pivot chord is followed by chords in the new key. The modulation is complete with a cadence (usually perfect) in the new key using the dominant seventh.
These stages may occur on consecutive chords, or there may be other chords between each stage (these other chords may introduce a grey area, where you're not quite certain which key you're in).
A simple example:
This example modulates from C major to D major, via the pivot chord of E minor.
As a very general guide, the following might be of use:
A sharpened note is often the leading note of the new key (or possibly the supertonic).
A flattened note is often the subdominant of the new key (or possibly the submediant).
If I have used a term of concept you are not familiar with, look in my Introduction to Music Theory post. I know it's a long read, but it really does explain all the basics. Alternatively, use my Glossary of musical terms.
For a more in-depth discussion of modulation, I highly recommend the book Four Part Harmony.
