First off, I plan on making a series of lessons on music theory for this site. Yes, there is already an abundance of theory lessons but most of them are difficult to understand or use crude tabs (no offense, it's just that most of the tabs aren't explained well) to try to get the point across. Secondly, I’m starting this series with something that draws a lot of attention from musicians, especially from the likes of guitarists that want to learn to play better solos: Modulation.
While this is going to be a fairly straightforward lesson, it is going to represent a couple of weeks of study in a music theory course crammed into something that shouldn’t take any more than an hour to understand, although it may take several weeks to truly learn to apply it. That being said, if you don’t know at least the very basics of music theory (at least how to read music and know what key signatures and relative minors are), then this lesson is not for you, at least, not yet. I’m a sophomore music major, and believe me, this stuff can get pretty hairy sometimes.
So straight into it. What is modulation? Modulation is a process which results in a shift of tonal center. The term applies to those occasions in music when one established tonal center gives way to another. In easier to understand words: it means shifting the tonal center to a different note or key. Say you’re in the key of C Major but playing a scale that is centered around E (this happens to be Phrygian, but more on this later), this is a “shift in tonal center”.
Most modulations occur between closely related keys that differ by no more than one accidental in the key signature (this is where knowing key signatures and relative minors comes in). For example, if the original key is C Major, the closely related keys are G Major and F Major, and the relative minors of each of the three keys, A minor, E minor, and D minor. If you swap out and use A minor instead of C Major, the related keys are the same with the addition of C Major: E minor, D minor, C Major, G Major, and F Major. Remember, Major keys and their relative minor keys are in the same key signature as far accidentals go. If you notice, all of the related keys of C Major are diatonic to the key of C Major. In other words, the chords E minor, D minor, A minor, C Major, G Major, and F Major are all in the key of C Major. To be diatonic means in key.
An easy way to understand modulation is to observe the ebb and flow of circle progressions (quick definition of circle progressions- a common chord progression that provides a structural basis for most tonal music, consisting of a series of chords with descending fifth root relationships). Now, on to actually modulating between keys.
Using Common Chords To Modulate
A common chord, meaning a chord that is common to each of two keys, offers a smooth introduction to the new key, since it is diatonic to both the old and the new key. This common chord is often called a pivot chord because it becomes a sort of middle ground between the two keys.
An example of this would be to use an E minor chord to go from the key of C Major to the key of G Major (meaning that you’re going from Ionian to Mixolydian). Here’s a (very) basic example:
|---------------------0------------------------------0---------------|
|---------------------0------------------------------0-1-0-----------|
|-----------0-2-------0------------------2-4-2-------0-----2---------|
|-----0-2-3-----3-0-2-2------------2-4-5-------5-4-5-2-------3-2-0---|
|-3-2-----------------2------2-3-5-------------------2-------------3-|
|---------------------0--3-5-------------------------0---------------|
C Major Em G Major Em C Major
Phrase Modulation
Phrase modulation, also known as direct modulation, occurs between phrases, periods, or larger sections where a phrase cadences (climaxes) in one key, and the next phrase begins immediately in a different key (mode). Example (hold the last note of each progression for a moment before proceeding to the next, this way you can really feel the change in tone):
|-------------------1-3-5-8-------------------------8-10-12----|
|---------------1-3----------------------------8-10------------|
|-----------2-4----------------------------7-9-----------------|
|-----2-3-5-------------------------7-9-10---------------------|
|-3-5------------------------7-9-10----------------------------|
|--------------------------------------------------------------|
C Major-------------------> E minor
You don't have to stop there. You can continue on through G Major, F Major, A minor, D minor, whatever you feel like playing, as long as it's diatonic to C Major.
There is also Chromatic Modulation, which basically (to me anyway) involves using passing tones withing the modes. When modulating through chords it's a bit more complex but I'm sure you're mostly interested in scales and solos.
There's really so much more to this subject than this simple little piece, but this is meant to be an introduction into modulating, a way for you to understand exactly what modulating is. If you already know the fingerings for the different modes then applying this should be a cinch. If you don't, I advise finding a lesson on here that describes each mode (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian) in particular and gives the positions for them. Once you learn the fingerings and which mode is which, it's very easy to apply them to each key. Anyway, I hope this helped somehow.
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) and because Gmaj is also the V of CMaj the duration of the progression 
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