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Modulation


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#1 OFFLINE   Tekker

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Posted 14 August 2006 - 03:03 AM

Contents:
Modulation using the V7 chord
Modulation Using Common Chords
Modulationg To The Parallel Key
Modulation Using Diminished Chord
  * Theoretical Explanation

Modulation is simply the act of changing keys. There are lots of methods to modulation and there will be a few methods covered here. However, these are simply suggestions not rules. In music there are no hard fast rules and "good" is very subjective, so if it sounds good to you, then it is good.

Modulation using the V7 chord

One method of modulation takes advantage of tendency tones which have a strong pull towards another tone. The V7 chord contains tendency tones within the chord and by playing a V7 chord, you will create a very strong pull towards the tonic in that key. For example, just by playing a G7 chord, you will establish C as being the tonic and then when you play the C you have satisfied that resolution. If you play a D7 chord, you establish G as the root. Taking advantage of the V7’s pull towards the tonic is a popular method for changing keys, because at anytime in a given song you can substitute in a V7 chord of whatever key you want to change to and then play the I from that key and you are now in the new key. You don’t even have to play the I after the V7 chord... Although that would provide the best resolution, you don’t necessarily “have” to resolve it to move into the new key (remember there are no hard fast rules.)

Ok, time for an example chord progression to hear it and put it into practice!

C G F A7 D A G G7 C

The first 3 chords are in C major and then the A7 transitions into D major. The next 3 chords are in D major and then the G7 transitions back into C major and it ends on C.

That's all there is to it. You can use the V7 chord to transition into any key you want to play.


'Cause I don't wanna read the book, I'll watch the movie.

Tekker's Lessons on GfB&B: Music Theory, Recording, and General Guitar

#2 OFFLINE   Tekker

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Posted 14 August 2006 - 03:05 AM

Modulation Using Common Chords

Another form of modulation (which is much simpler than the first way) is to use a transition chord that is a part of both keys. For example, let’s say that we want to start out in C major and end in F major. The easiest way to do this, is to write out all of the chords on both keys so you can see which chords are common to both keys.

C Major - C Dm Em F G Am Bdim
F Major - F Gm Am Bb C Dm Edim

C, Dm, F, and Am are all common chords in both progressions, so any one of them (or several of them together) could be used to transition from one key to the other.

Here’s an example I came up with, with the chord numbers underneath for both keys:

Posted Image

Notice how the progression flows seamlessly, yet you start out in C major and end up in F major. Am and Dm work as transition chords because both of them are in C major and F major.


'Cause I don't wanna read the book, I'll watch the movie.

Tekker's Lessons on GfB&B: Music Theory, Recording, and General Guitar

#3 OFFLINE   Tekker

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Posted 14 August 2006 - 03:07 AM

Modulating To The Parallel Key

The next method of modulation changes to the Parallel Major/Minor key. If you are playing in a major key, the parallel minor is the minor key that has the same root note as the major key. For example A Minor is the parallel minor to A Major. The reverse processes is modulating to the parallel major key if you are playing in a minor key. You can either use substitution to borrow chords from the parallel minor key (as mentioned here) or completely change keys to the parallel minor key.

Here is an example of a composition I did for my music theory class that changes to the parallel minor key. This song is originally in G major, then at 15 seconds it changes to G minor, and changes back to G major at 20 seconds. At about 24 seconds it goes to G minor again and back to G major at 25 seconds.
Orchestra Composition


'Cause I don't wanna read the book, I'll watch the movie.

Tekker's Lessons on GfB&B: Music Theory, Recording, and General Guitar

#4 OFFLINE   Tekker

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Posted 14 August 2006 - 03:23 AM

Modulation Using Diminished 7 Chord

Using the dominant 7 chord to change keys is one way to do it, but another way is with the diminished 7 chord. An interesting difference between these two methods is the dominant 7 chord is an obvious key change, because if you are playing in the key of D major, then Adom7 is the only dominant chord in that key.... So if you play a Gdom7 to lead to the key of C major, the Gdom7 is an obvious key change because Gdom7 is not in the key of D major. When compared to using the diminished 7 chord, you can actually start off in the key of C major, play a Bdim chord in the key of C major and change keys right into the key of Eb major, Gb major, or A major. This uses the fact that a diminished 7 chord is actually four different diminished chords in one. This is explained here.

Lets take a look at how this fact can be used for modulation.

------------------------------------------

Theoretical Explanation

B diminished chord contains the following notes:
B D and F

You may already know that the B diminished wants to resolve to C major. This is because of the B and F notes, these two notes form a diminished 5th, which is a very unstable interval. The diminished 5th causes “tension” in the diminished chord that wants to be resolved. The rule of thumb is that altered tones want to resolve in the same direction that they were altered, so a diminished interval wants to resolve “downward” and an augmented interval wants to resolve “upwards”.

Let’s see an example:
A perfect 5th interval starting on B consists of B and F#. In a diminished 5th the F# is lowered (flatted) to F, then to resolve it the note must again be lowered to E.... However this doesn’t complete the resolution, the B note also has to be moved up to C (because the leading tone wants to move up to the tonic). In other words, the diminished 5th interval leads to the tonic and anytime you have this diminished 5th interval in a chord it will pull towards the tonic. If you were to play these two intervals on a keyboard your hand would be moving “inward” to resolve the diminished 5th.
(For those that don’t have a keyboard, use the picture below for better visualization of the movement in these interval changes. Virtual Keyboard)

Now play this on the keyboard (or the virtual keyboard) to see the movement and then for those that don’t have a keyboard, play it on the guitar and hear the resolution of these intervals:

B F# to C E

That is the key to the diminished chord’s “tension”.

So how does this allow you to change keys? Well, that’s the fun part the diminished chord just happens to be a rather odd chord in that it can also be used as the diminished chord in other keys because they all contain basically the same notes!

B° = B D F
D° = D F Ab
F° = F Ab B
Ab° = Ab B D (theoretically this should be G#° since it's in the key of A, but I want to keep the notes the same using Ab instead of G# to show how the notes in the chords relate)

(The ° symbol stands for “diminished”)

But wait, there is no Ab in the B° chord... So why does this chord work in place of these other diminished chords? One way to think of it is D°, F°, and Ab° all have two common notes in common with B° and as mentioned in the previous lesson on chord substitution any chord with two (ore more) common notes can be substituted for each other.

Another way to think about it is to look at all 4 of these diminished chords as a "diminished 7th" chord. If you add the Ab to the B° chord you get a B°7 chord (B full-diminished), so when you use a B° in place of the other chords, it looks like this:

B° = B D F (1, b3, b5)
D°7 = D F B (1, b3, bb7)
F°7 = F B D (1, b5, bb7)
Ab°7 = B D F (3, b5, bb7)

Therefore, the B° will be the same as a D°7 but without the b5, it will be the same as the F°7 but without the b3, and it will be the same as the Ab°7 but without the 1 (which is simply the B° as it contains the notes B D and F). This is why this chord works in place of these other chords... Which of course leads us up to the B°7 chord, which as you have probably guessed will now contain the exact same notes as the D°7, F°7, and Ab°7 chords.

B°7 = B D F Ab
D°7 = D F Ab B
F°7 = F Ab B D
Ab°7 = Ab B D F


After showing that these chords contain the same notes I'll refer to Ab°7 as G#°7 from now on (remember that Ab and G# are the same note).

G#°7 = G# B D F


Now lets look at why the full-diminished 7 chord can be “4 diminished chords in one”. The reason for this is because the distance between each note in the chord is a minor 3rd:

B --> D = minor 3rd
D --> F = minor 3rd
F --> G# = minor 3rd
G# --> B = minor 3rd
B --> D = minor 3rd... (etc...)

As you can see, no matter how many times you go up a "minor 3rd" you will only ever get these four notes, B, D, F, and G#. This means that since the B°7, D°7, F°7, and G#°7 all contain the exact same notes, they are all exactly the same chord (just in a different inversion, which means that a different note from the chord other than the root is the bass note).


This is a very cool way to do modulation because just like the B diminished chord leads to the C chord (tonic), each of the other diminished chords will also lead to their respective tonic chords as well.

B diminished --> C
D diminished --> Eb
F diminished --> Gb
G# diminished --> A

** This btw, is why the G# diminished couldn’t be an Ab diminished chord, because that chord is leading to an A major chord and you have to use all of the letters in any key. But using the Ab instead of G#, there wouldn’t have been any G chords in that key and there would have been two A chords. Even though they are both the same chords (G# and Ab) using the G# is the “correct” way to spell out the chords in the key.

So by looking at this diagram, you can see how each of those chords could resolve to their tonic chord and by playing just that one chord you can instantly pivot to any of those 4 keys.


One more thing to notice before we conclude is that the Gdom7 and the B° look an awful lot alike...
Gdom7 = G B D F
B° = B D F

No wonder they both have the same pull towards the “tonic”, they contain most of the same notes... AND they both contain that diminished 5th interval as well. Remember from earlier that the diminished 5th wants to resolve to the tonic. This is why both the V and the vii° chords have a strong "pull" towards the tonic. Therefore, these chords can both be used in substitution for the other. Wherever you wanted to play a V chord, you can place a vii° and vice versa to create a little different sound but still keep the same tendency to resolve to the tonic.



* End Of This Series Back To Main Forum

Also be sure to check out the other misc music theory lessons that are not part of this series and the music theory Q&A thread.


'Cause I don't wanna read the book, I'll watch the movie.

Tekker's Lessons on GfB&B: Music Theory, Recording, and General Guitar





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