There are four basic kinds of triads (3-note chords) in music:
Major triads: composed of the root, major 3rd, and perfect 5th of a major scale.
Minor triads: composed of the root, minor 3rd, and perfect 5th of a major scale.
Diminished triads: composed of the root, minor 3rd, and diminished 5th of a major scale.
Augmented triads: composed of the root, major 3rd, and augmented 5th of a major scale.
As an example, the C major scale is:
C, D, E, F, G, A, B, C
So a C major triad would be:
C, E, G
A minor triad would be:
C, Eb, G
A diminished triad would be:
C, Eb, Gb
An augmented triad would be:
C, E, G#
About 90% of the songs we know or hear on the radio or TV (or on our IPOD's or other MP3 player) are written in a major key. That means that most of the chords in those songs are major chords -- only 20% or so are minor chords.
The other 10% of songs and musical compositions are written in a minor key, which means that there will be several minor chords within the context of the piece.
So if nearly 100% of all songs contain major and minor chords, what place is there for diminished and augmented triads?
They are the salt and pepper of a musical meal.
In other words, major chords are like the main dish -- the steak, if you will, of a song. Minor chords are like a side dish of corn or broccoli (yuk!) or whatever.
You would never sit down to a meal of just pepper or just salt, would you? Same way here; you use diminished and augmented triads to add spice to your meat and potatoes.
So here are the 12 diminished triads:
C dim: C, Eb, Gb
F dim: F, Ab, Cb
G dim: G, Bb, Db
D dim: D, F, Ab
E dim: E, G, Bb
A dim: A, C, Eb
Db dim: Db, Fb, Abb (same as G)(By the way, Db dim is enharmonic with C# dim)
Eb dim: Eb, Gb, Bbb (same as A) (Eb dim is enharmonic with D# dim)
Ab dim: Ab, Cb, Ebb (same as D) (Ab dim is enharmonic with G# dim)
Gb dim: Gb, Bb, Dbb (same as C) (Gb dim is enharmonic with F# dim)
Bb dim: Bb, Db, Fb (Bb dim is enharmonic with A# dim)
B dim: B, D, F
So diminished chords are used to add spice to your musical meal. You don't linger on them, but use them as transition chords between a major and another major chord, or between a major and a minor chord, or sometimes even between two minor chords.
For example, let's say you are playing "Amazing Grace" in the key of F and your first chord is F major on the words "Amazing grace". As you transition to the Dm chord on the word "sweet", you can insert a C# diminished triad on the word "how". It only lasts one beat, but it adds interest to the song.
As you play various songs, look for opportunities to use diminished triads as transition chords. And just like salt is to a meal, so diminished triads are to a musical meal.