A little Advanced Chord Theory

That's quite a tall order, but here goes.

First, diminished chords.  

Two stacked minor 3rds (1-b3-b5).  They occur naturally on the 7th degree of the major scale (vii°) and the 2nd degree of the minor scale (ii°).   They contain the 7-9-11 degrees of the scale (7-2-4) and are quite dissonant due to the tritone interval between the 4 and the 7.  They contain mostly the same notes as the V7 dominant chord (5-7-9-11) and these can substitute for each other and fulfil the same function of tension before resolution back to the tonic.

Second, augmented chords.

Augmented chords (two stacked major thirds, 1-3-#5) do not occur naturally in major keys and natural minors.  They occur only in the harmonic and melodic minors on the 3rd degree (IIIaug, 3-5-#7).   They are tense and unresolved like diminished chords.

Third extended chords.

7ths do more to change the character of a chord than other extensions.  On the I and IV chord, you could use a maj7 (wistful, jazzy), a dom7 on the V chord (harsh, tense) and m7ths on the ii, iii and vi (a little smoother and less dark than plain minors).  Blues players often add dom7ths on the I and IV chords.

9ths add a little sweetness and colour, but do not change the fundamental character of the chord.  The iii chord can use a b9 which is harsher.

11ths are more colourful than 9ths and harder to use.  They can sound both sharp and smooth.  The #11 is often used on the IV chord in jazz.

13ths (6ths) add a little sweetness.  A maj6 chord is even happier and brighter than a plain major.  b6s are very dissonant though.

Here is a table of some common chord types:

Chord      Notes      
major      1  3  5
6          1  3  5  6
7          1  3  5 b7
maj7       1  3  5  7
9          1  3  5 b7 9
maj9       1  3  5  7 9
11         1  3  5 b7 11
add11      1  3  5  11
13         1  3  5 b7 13
add9       1  3  5  9
sus2       1  2  5
sus4       1  4  5
5          1     5
minor      1 b3  5
min7       1 b3  5 b7
min9       1 b3  5 b7 9
dim        1 b3 b5
dim7       1 b3 b5 bb7 (6)
min7b5     1 b3 b5 b7
aug        1 3  #5
6/9        1 3   5  6  9

The VAST majority of times diminished + augmented chords are used to change key..

if we look at the diminished and augmented scales we can see its this pattern

T T T T T T T T T T T T (augmented etc)
T S T S T S T S T S T (diminished)

This means all chords formed from this scale will have intervals of a minor 3rd or a major third.

and because of this, most chords are just inversions of each other.

and you can take off the root and add another (major/minor) 3rd and you have a new chord.

And its used for changing keys because of the fact that all these chords are very similar.

EXAMPLE:

G Bb Db F (occurs in Abmaj/Fm)

if you take away the G, you have Bb Db F, which is the Bb diminished chord found in Db major / C minor.

and this way is how easy it is to alter a diminished chord WITHOUT it sounding bad.. but still it fits in smoothly with wherever you want to go.

The same is for the Dominant 7th..

Because the dominant 7th chord is just a diminished chord with a root a major 4th below.

so G B D F (G7).. take off the root, B D F, which is the diminished chord in Cmaj/Amin.

Exactly the same works with augmented.

C E G#
D F# A#
E G# B#
F A C#
G B D#
A C# E#

there is a few augmented chords...

if we take A C# E#.. the harmonic equivilant of E# is F, so we have F A C#.. which is also our Faug chord.

same with E G# B#.. B# is the same as C, so if we look again we have E G# C.. invert it and we have C E G#.. which is our Caug chord.

***

The point is the reason they are used for changing keys is because the majority of these chords used are identical to one another, just inversions.

And this helps the movement between these chords smooth, and then move into another key without it sounding bad.

A very good point that I forgot all about.

Hey Helgi, when you said
The #11 is often used on the IV chord in jazz.

Do you mean like (C major)

F A C.. 11th is B.. so the sharpened 11th is B# (C)
wouldnt that just equal a doubled 5th?

Or have i miscalculated badly somewhere?

Or are you talking about with the 7th, 9th, and #11th in the chord too?

Can you just list the notes this chord would have and ill understand then.

Thanx:)

No, the thing is, chord notes are numbered from the chord root, not from the key centre, so  ......

In  the key of C major, the IV is F.

an F#11 would have

1 - F
3 - A
5 - C
7 - E
9 - G (optional)
#11 - B  (the 11(4) of F is Bb)

ahhh, so 11 is taken from F major and sharpened, not from the scale that your taking the subdominant from.

Got it. :D thanks.

"The VAST majority of times diminished + augmented chords are used to change key.. "

Not really, they are mostly used in key.  The diminished chords will be usually be viiº or iiº (as Helgi already stated); a viº is also possible (la do me). The augmented chord is III+, typically used in a dominant function due to the presence of the leading tone and the 5th scale degree (me sol ti).

It is true, however, that the enharmonic characteristics can lead to modulation - but again, not the primary purpose.  These chords are also real good for creating tonal ambiguity (e.g. Bach's Prelude in C).  

Wow thanks, this is greatly appreciated!

That's quite a tall order, but here goes.

First, diminished chords.  

Two stacked minor 3rds (1-b3-b5).  They occur naturally on the 7th degree of the major scale (vii°) and the 2nd degree of the minor scale (ii°).   They contain the 7-9-11 degrees of the scale (7-2-4) and are quite dissonant due to the tritone interval between the 4 and the 7.  They contain mostly the same notes as the V7 dominant chord (5-7-9-11) and these can substitute for each other and fulfil the same function of tension before resolution back to the tonic.

Second, augmented chords.

Augmented chords (two stacked major thirds, 1-3-#5) do not occur naturally in major keys and natural minors.  They occur only in the harmonic and melodic minors on the 3rd degree (IIIaug, 3-5-#7).   They are tense and unresolved like diminished chords.

Third extended chords.

7ths do more to change the character of a chord than other extensions.  On the I and IV chord, you could use a maj7 (wistful, jazzy), a dom7 on the V chord (harsh, tense) and m7ths on the ii, iii and vi (a little smoother and less dark than plain minors).  Blues players often add dom7ths on the I and IV chords.

9ths add a little sweetness and colour, but do not change the fundamental character of the chord.  The iii chord can use a b9 which is harsher.

11ths are more colourful than 9ths and harder to use.  They can sound both sharp and smooth.  The #11 is often used on the IV chord in jazz.

13ths (6ths) add a little sweetness.  A maj6 chord is even happier and brighter than a plain major.  b6s are very dissonant though.

Here is a table of some common chord types:

Chord      Notes      
major      1  3  5
6          1  3  5  6
7          1  3  5 b7
maj7       1  3  5  7
9          1  3  5 b7 9
maj9       1  3  5  7 9
11         1  3  5 b7 11
add11      1  3  5  11
13         1  3  5 b7 13
add9       1  3  5  9
sus2       1  2  5
sus4       1  4  5
5          1     5
minor      1 b3  5
min7       1 b3  5 b7
min9       1 b3  5 b7 9
dim        1 b3 b5
dim7       1 b3 b5 bb7 (6)
min7b5     1 b3 b5 b7
aug        1 3  #5
6/9        1 3   5  6  9

damn dude that was very descriptive and to the point. good job. alot of folks cant do that

Serickso,

I meant when people modulate to another key, the vast amount of times its using the diminished / augmented trick.

Go on, tell me im wrong, i know your dieing to.

There are many other ways to modulate to another key.

I've never used diminished or augmented chords to modulate, mainly because I don't know how.

Well, neither have I, but I do know how.  As with so many other things, I'm better at theory than practice.

Let's have a look at a dim chord, for example the vii of C major, Bdim.

It has the notes B-D-F.  Add a dim7 (bb7 or maj6) and we have B-D-F-Ab .....

Now let's look at Ddim, the vii chord in Eb.  That has the notes D-F-Ab-B.  Hmmm.....

What about Fdim(E#dim), the vii chord in F# (Gb).  That has F-Ab-B-D.  The plot thickens.

Finally Abdim has the notes Ab-B-D-F.  We come full circle.  All 4 dim chords have the same notes and can thus be used to modulate between 4 different keys.

But there are only 12 notes?  Does that mean there are only 3 dim chords?

Yes.  There are 3:

B-D-F-Ab      (G#)
C-Eb-Gb-A    (D#,F#)
Db-E-G-Bb    (C#,A#)

The same applies in a way, to augmented chords because they too are symmetrical.

Caug (C-E-G#) = Eaug (E-G#-C) = G#aug (G#-C-E)   (Ab)

and so on

I know about dim chords, I've just never seen/heard them used to modulate before. Maybe I'm just listening to bad music.