Triad Chords found in the Major Scale
The Major Scale contains seven triads (3 note chords). In order to see what they are, let's look at the C Major Scale...
The first chord in C, is obviously C Major, it's made up of the notes C, E and G. Following this pattern the next chord that we find in the scale of C Major is D, F and A which is the chord of D Minor. Then we have E, G and B which gives us E Minor. Next up is F, A and C which is F Major. Then G, B, D or G Major. Then A, C, E, A Minor (which is the also relative minor of C Major). The last chord is B, D and F which contains both a flat 3rd and a flat 5th, which gives us a Diminished Chord, in this case B Diminished.
Here's how each chord looks on the Fretboard...
|C Major (C, E, G)
||G Major (G, B, D)
|D Minor (D, F, A)
||A Minor (A, C, E)
|E Minor (E, G, B)
||B Diminished (B, D, F)
|F Major (F, A, C)
But what about the other Keys/Scales?
The other scales/keys also contain 7 (maj, min, dim) triads, they always follow the order: Major, Minor, Minor, Major, Major, Minor and Diminished.
For easy reference, here's a chart of all the keys and associated triads...
What this also shows us, is that each Note has 6 associated chords. If we loose the obscure keys (Db, Gb, Cb) and use their 'Enharmonic' partners instead C#, F# and B, we can formulate a pattern which shows every note surrounded by the 6 chords it's contained within, like so...
Take C, for example. It's obviously contained within C and C minor, but you'll also find it in F, Fm, Am and Ab.