Understanding how triads and other chords are built

How to analyze triads and more advanced chords?

The starting point is the major triad, in the example in C major, but this concept is valid for all keys, as usual.

The C major chord is built with these three notes:

C  E  G

As we said this triad is built with the Root (C) the 3rd (E) and the 5th (G) of the major scale. Also, if we calculate the intervals between the Root and the other two notes we notice that there is an interval of a major 3rd between C and E and of a perfect 5th between C and G.

So if I wanted to write a formula for the major triad I would write

C   E  G

1   3   5 (Root-Major third-Perfect fifth)

If now we want to find the chord C minor all we have to do is lower the 3rd of the chord (E is lowered to Eb)

So now the triad for C minor is

C  Eb  G

1  b3  5 (Notice how the formula changes Root –Minor Thirds – Perfect fifth)

From this I can tell that the difference between a major and minor chord is in the 3rd.

The diminished and augmented triads can be told from the 5th.

If C major is C E G

C augmented is    C  E   G# (I have raised the 5th of a halfstep)

Formula             1   3   #5

C diminished is     C  Eb Gb (a minor triad with the flattened 5th)

Formula             1   b3  b5

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