To build all the triads in the key of C, start with C, E, and G. This one, three, five pattern is the basis of all triads.
This first chord called the tonic, is C major. D, F, and A, give us the two minor or the submediant, the D minor chord. E, G, and B, make up the three minor, or mediant, an E minor chord.
F, A, and C, the four chord or sub-dominant chord, F major. Then G, B, and D, the five chord, the dominant chord, G major. A, C, E, the six chord A minor. Notes B, D, and F, give us the only diminished chord in C scale, the seven chord, the B dim. There are no naturally occurring augmented chords since the interval of the augmented fifth does not occur in the normal scale.
Check the intervals with the keyboard and study this method of building chords. You will find a lot of chords in songs which are not based only on the notes in the key of that song.
Often chords are "borrowed" from a related key, for instance an A major chord might be found in a song in the key of G where one would expect to find an A minor which is the normal chord constructed on the second degree of the scale.
The reason for the A major is that it is related to the key of "D" and in the song it functions to give a stronger weight to the "D" chord by making it seem like it is the home or tonic chord in the key of "D" where A major would be the fifth or dominant chord.
This A major chord is called a borrowed dominant or V/V chord since it is the five chord of the key of D which is the key of the five chord of G.
There are many other ways that chords are borrowed or interposed and some of these can be discovered by trial and error. It is good to listen for examples of these creative breakings of the rules.
Sometimes interesting chords can be arrived at by harmonizing root movement by steps or other intervals. Sometimes simply changing the expected minor chord to a major chord or vice versa is effective. More about this later.
A chord may contain almost any combination of notes but most can be understood by starting from the triad and adding or taking away notes to create the desired effect.
A chord with no third is called a modal chord since it is neither major nor minor. Intervals which are commonly added to a chord to give it a more specific sound are the sixth, the seventh, the ninth, and thirteenth, again, always counting from the do or the root of the chord.
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